text:
Pattern recognition has been employed in a myriad of industrial, commercial and academic applications. Many techniques have been devised to tackle such a diversity of applications. Despite the long tradition of pattern recognition research, there is no technique that yields the best classification in all scenarios. Therefore, as many techniques as possible should be considered in high accuracy applications. Typical related works either focus on the performance of a given algorithm or compare various classification methods. In many occasions, however, researchers who are not experts in the field of machine learning have to deal with practical classification tasks without an in-depth knowledge about the underlying parameters. Actually, the adequate choice of classifiers and parameters in such practical circumstances constitutes a long-standing problem and is one of the subjects of the current paper. We carried out a performance study of nine well-known classifiers implemented in the Weka framework and compared the influence of the parameter configurations on the accuracy. The default configuration of parameters in Weka was found to provide near optimal performance for most cases, not including methods such as the support vector machine (SVM). In addition, the k-nearest neighbor method frequently allowed the best accuracy. In certain conditions, it was possible to improve the quality of SVM by more than 20% with respect to their default parameter configuration.
Citation: Amancio DR, Comin CH, Casanova D, Travieso G, Bruno OM, Rodrigues FA, et al. (2014) A Systematic Comparison of Supervised Classifiers. PLoS ONE 9(4): e94137. https://doi.org/10.1371/journal.pone.0094137
Editor: Hong-Bin Shen, Shanghai Jiaotong University, China
Received: October 31, 2013; Accepted: March 11, 2014; Published: April 24, 2014
Copyright: © 2014 Amancio et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The authors acknowledge financial support from CNPq (Brazil) (grant numbers 573583/2008-0, 208449/2010-0, 308118/2010-3 and 305940/2010-4), FAPESP (grant numbers 2010/00927-9, 2010/19440-2, 2011/22639-8, 2011/50761-2, 2013/06717-4, 2013/14984-2 and 2014/04930-5) and NAP eScience - PRP - USP. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
In the last decades, we have witnessed a progressive increase of data production and storage. Indeed, the informatization of most aspects of human activities, ranging from simple tasks such as phone calls to shopping habits, generates an ever increasing collection of data that can be organized and used for modeling and planning. At the same time, most scientific research projects – such as in genetics, astronomy and neuroscience – generate large amounts of data that needs to be analyzed and understood. This trend has given rise to new terms such as big data [1], [2]. Once such data is organized in a dataset, it is necessary to find patterns concealed in the vast mass of values, which is the objective of data mining [3]–[10]. Because the identification of important patterns (e.g. those that recur frequently or are rare) is impossible to be performed manually, it is necessary to resort to automated pattern recognition. Nevertheless, it is important to note that pattern recognition remains also relevant for organizing and understanding smaller sets of data, such as in medical diagnosis, industrial quality control, and expensive data.
The problem of pattern recognition consists in assigning classes or categories to observations or individuals [7], [8], [10]. This can be done in two main ways: (i) with the help of examples or prototypes (supervised classification); and (ii) taking into account only relationships between the properties of the objects (unsupervised classification or clustering). Though seemingly simple, pattern recognition often turns out to be a challenging activity. This is mainly a consequence of overlap between different groups in the data, i.e. objects in a class have similar properties as those in other classes. However, several other issues such as choice of features, noise, and sampling, also impose further problems while classifying data [7], [8], [10]. Even when the features are well-chosen and the data has good quality (e.g. properly sampled and without noise), the results of the classification will frequently vary with the choice of different pattern recognition methods and respective parameters. This situation is typically more critical for sparse data, presence of noise, or non-discriminative features. In an attempt to circumvent such problem and to obtain more robust and versatile classifiers, a number of pattern recognition methods have been proposed in the literature [11]–[13]. Yet, despite the long tradition of pattern recognition research [10], there are no definite guidelines for choosing classifiers. So, those faced with the need to apply pattern recognition are left with the difficult task of choosing among several alternative methods.
There are many works in the literature describing which classifiers are more suitable for specific tasks (see e.g. [14]–[16]), but only a few consider a more systematic quantitative analysis of their performance. Typical datasets employed to compare the performance of different methods include real world and/or artificial data. Advantages of using real datasets include the presence of non-trivial relationships between variables, which may strongly influence the performance of a classifier, the fact that the obtained results will usually be of high confidence when used for samples obtained in the same domain and using a similar criteria, and the presence of noise or unavailable information about the samples (hidden variables). But there is a main drawback associated with using real-world data. Even if one manages to consistently compare the results obtained with hundreds of real world datasets, the results still remain specific to the datasets being used. Trying to extend the information gained in such analyses to a different dataset can be ineffective. Furthermore, obtaining more real data to evaluate other classifier characteristics represents sometimes an arduous task. This is the case of applications whose data acquisition process is expensive. For these reasons, here we chose synthetic datasets. Although such datasets are often not representative of specific real-world systems, they can still be used as representations of large classes of data. For example, we can define that all variables in the dataset will have a given Pearson correlation, and study the behavior of the classifiers when setting this as the main data constrain. In addition, artificial datasets allow a systematic variation of respective parameters, and also provide exact ground truths. A natural choice of distribution for the variables in the dataset is the multivariate normal distribution. This choice is related to the central limit theorem [17], which states that, under certain conditions, the mean of a large number of independent random variables will converge to a normal distribution. All in all, we believe that the adoption of the multivariate normal density is capable of modeling a representative number of real cases. Nevertheless, we observe that the comparative performance of the methods present in this paper may change for other databases or conditions.
Since one of our main concerns is conducting an accessible practical study of the classifiers, we decided to consider the classifiers implemented by the Weka software [18], which is available at http://www.cs.waikato.ac.nz/ml/weka. In particular, we decided to use Weka because of its popularity among researchers. In addition, since the software is open-source, any researcher can check the code of any specific classifier. Since Weka includes many classifiers, we decided to select a subset of those most commonly used [19].
One distinctive feature of the present work is the procedure we use to compare classifiers. Many works in the literature try to find the best accuracy that a classifier can give and then present this value as the quality of the classifier. However, finding the highest accuracy for a classifier is usually not straightforward. Additionally, if this high accuracy can only be achieved for very specific data and values of the classifier parameters, it is likely that for a different dataset the result will be worse, since the parameters were tuned for the specific data analyzed. Therefore, besides giving a high accuracy, it is desirable that the classifier performs well without being too sensitive to parameter changes. That is, a good classifier should provide a robust classification for a reasonably large range of values of its parameters.
This work is organized as follows. We start by describing the generation of synthetic datasets and justifying its respective parameters. Next, we introduce the measurements used to quantify the classifiers performance. The comparative analysis involves the following three approaches. First, we compare the performance of the classifiers when using the default parameters set by Weka. This is probably the most common way researchers use the software. This happens because changing the classifier parameters in order to find the best classification value is a cumbersome task. Then, we address the variation of single parameters of the classifiers, while maintaining other parameters at their default values. That is, we study how the classification results are affected when changing each parameter, given that some parameters are more critical for the performance. Finally, in order to estimate the optimum accuracy of the classifier, as well as to verify its sensitivity to simultaneous changes of its parameters, we randomly sample the sets of parameter values to be used in the classifier.
Related works
Typical works in the literature dealing with comparison between classifiers can be organized into two main groups: (a) comparing among a relatively few methods for the purpose of validation and justification of a new approach (e.g. [20]–[24]); and (b) systematic qualitative and quantitative comparison between many representative classifiers. Examples of qualitative analysis in (b) can be for example found in [19], [25], [26]. These studies perform a comprehensive analysis of several classifiers, describing the drawbacks and advantages of each method. A quantitative analysis of classifiers was performed in [27], where 491 papers comparing quantitatively at least two classification algorithms were analyzed.
Some studies in the literature are devoted to devising novel methodologies to analyze statistically the results obtained from the comparison of classifiers. The suitability of traditional measures was investigated in [28], which concluded that the simplest traditional accuracy indices should be preferred when the comparison is not focused on specific classes. Some studies show that many of the papers aiming at comparing the performance of different classifiers are limited in the sense that they compare several methods with respect to relatively few datasets [29], [30]. Most importantly, the investigation carried out in [31] warns that invalid conclusions can be drawn if specific statistical tests are not applied.
Many comparative studies are specific to a given problem or task. Perhaps this is a consequence of the "No Free Lunch theorem", which states that, without any prior, no single method can be preferred [32]–[34]. A comparison of three representative learning methods (Naive Bayes, decision trees and SVM) was conducted in [35], concluding that Naive Bayes is significantly better than decision trees if the area under curve is employed as a performance measurement. Other quantitative studies compare, for example, artificial neural networks with other methods [36]. An extensive comparison of a large set of classifiers over many different datasets performed in [37] showed that SVMs perform well on classification tasks. Quantitative comparisons between classifiers can be also found in specific domain problems, such as in Bioinformatics [38], Computer Science [39]–[42], Medicine [43], [44], Civil Engineering [45] and Chemistry [46].
Some studies have investigated the influence of parameters on the performance of classifiers. In [47] the authors studied the sensitivity of parameters in accuracy-based learning systems, concluding that particular thresholds should be taken into account in order to prevent critical decreases in performance. A common topic related to the study of classifiers sensitivity concerns the optimization of parameters via heuristic methods. In [48] the authors propose a method to optimize both the parameter values and feature set for a SVM applied to the task of pedestrian detection. A general framework for the parameter selection problem employing Grid Search and Experiment Design is detailed in [49]. Although Grid Search strategies tend to yield better results, genetic methods can provide good results at a smaller computational cost. For this reason, some papers deal with the problem of optimizing the initial conditions of genetic algorithms to improve their accuracy [50]. Finally, parameter optimization has been studied in specific tasks, such as in biological and textual applications [51], [52].
Materials and Methods
In this section we present a generic methodology to construct artificial datasets modeling the different characteristics of real data. In addition, we describe the measurements used to evaluate the quality of the classifiers.
Artificial Data
Here we present an adapted method for generating random datasets with a given ensemble of covariance matrices, which was based on the study made by Hirschberger et al. [54]. We aim at generating classes of data with features for each object, with the additional constraint that the number of objects per class is given by the vector . This problem is mathematically restated as finding sets comprising -dimensional vectors, where each set has a number of elements specified by . Furthermore, we aimed at generating data complying with the three following constraints:
- Constraint 1: the variance of the -th feature of each class is drawn from a fixed distribution, .
- Constraint 2: the correlation between the -th and -th dimension of each class are drawn from another fixed distribution, .
- Constraint 3: we can freely tune the expected separation between the classes, given by parameter , which is explained below.
Traditionally, constraints 1 and 2 are not fully satisfied to generate the data. Many studies impose that all the classes display approximately the same variances and correlations, by defining an ensemble of covariance matrices with a fixed spectrum constraint [55], [56]. Unfortunately, this approach is somewhat artificial to generate realistic data, since the assumption that all data classes share similar relationships between their features is quite unlikely. Our approach is more general because, given the shape of the correlation distribution (e.g. U-shaped), the classes can exhibit all kinds of correlations.
In order to generate the data with the parameters , and complying with constraints 1, 2 and 3, we need covariance matrices (one for each class), where each diagonal and off-diagonal element is drawn, respectively, from and . The most common approach is to randomly draw the mentioned matrix elements from probability density distributions given by and in order to construct the desired matrices. Unfortunately, this process does not guarantee a valid covariance matrix because every covariance matrix must be positive and semi-definite [57]. To overcome this problem we use a well-known property stating that for every matrix , the matrix is positive and semi-definite [57]. This property allows us to create a random matrix that will generate a valid covariance matrix. The matrix is known as root matrix. Next, it is necessary to define a convenient root matrix so that follows constraints 1, 2 and 3. Hirschberger et al. [54] came up with an elegant demonstration on how to create a covariance matrix following constraints 1 and 2. Using their algorithm, modified in order to specify the separation between the classes (parameter ), it is possible to create datasets having the following parameters:
- Number of objects per class : The number of instances in each class can be drawn according to a given distribution. The most common distributions to use are the normal, power-law and exponential distributions. Nevertheless, in order to simplify our analysis, here we use classes having an equal number of instances, , which varies from to elements.
- Number of classes : This parameter is varied from to .
- Number of features : The case represents the simplest case, since it permits the easy visualization of the data. In order to improve the discriminability of the data, real world datasets oftentimes are described by a larger number of features. Here we vary in the range [2], [50]. Hereafter, we refer to the dataset described by features as DBF.
- Standard deviation of the features: For each class, the standard deviation of each feature is drawn according to a given distribution . The process is repeated for each class, using the same distribution .
- Correlation between features: For each class, the correlations between the features are drawn according to a given distribution . The process is repeated for each class using the same distribution. This means that each class of our dataset will show different values of correlation. For example, instances from one class may be described by redundant features, while the same features may be much more efficient in describing samples from other classes. The most common choices for are: (a) uniform, to represent heterogeneous data; (b) zero mean normal, for mostly uncorrelated data; and (c) U-shaped, for data with strong correlations. Here we chose a uniform distribution for the correlations.
- Separation between the data (): It is a parameter to be varied throughout the experiments, quantifying how well-separated are the classes, compared to their standard deviation. This parameter is simply a scaling of the standard deviation of the features for each class, i.e., the values drawn from the distribution are divided by . Since we randomly draw the mean, , for each class in the range , can be used to define an expected separation between the classes. If is large, the classes are well-localized and will present little overlap. Otherwise, if is small, the opposite will happen. Clearly, the separation given by depends on the dimension of the space. Nevertheless, there is no need to define a normalization for , because we are just comparing classifiers and not different configurations of the data.
In Figure 1 we show some examples of the data that can be generated by varying in a two-dimensional dataset.
It is possible to note that different classes have different correlations between the features. The separation between the classes are (a) , (b) and (c) .
Evaluating the performance of the classifiers
A fundamental aspect that should be considered when comparing the performance of classifiers is the proper definition of what quality means. It is impossible to define a single metric that will provide a fair comparison in all possible situations. This means that quality is usually specific to the application and, consequently, many measurements have been proposed [53]. Nevertheless, there are some measurements that have widespread use in the literature, the most popular being the accuracy rate, f-measure (sometimes together with precision and recall), Kappa statistic, ROC area under curve and the time spent for classification (see [53] for a comprehensive explanation of such measurements). Because we are mostly interested in a more practical analysis of the classifiers, we use only the accuracy rate, which is defined as the number of true positives plus the number of true negatives, divided by the total number of instances.
To measure the performance of the classifiers, we generate artificial datasets using the method presented in the previous section and calculate some statistics. The principal quantity extracted from each dataset is the average accuracy rate. In addition, we also compute the variation of accuracy across datasets, as this quantity is useful to quantify the confidence of the classifier when the dataset is changed. The standard deviation of accuracy rate computed over instantiations of the classifier with distinct parameters is useful to quantify the sensitivity with respect to a given parameter.
Results and Discussion
The performance of the classifiers was evaluated according to three methodologies. The default values provided by Weka were used first. We then examined the influence of each classifier parameter on the discriminability of the data. Finally, we study the performance when all classifier parameters are varied jointly. The classifiers considered in the analysis are presented in Table 1.
Comparison of classifiers using their default parameters
The default values of the classifiers are often adopted by non-expert users, and provide a logical starting point for expert researchers. In order to provide a comprehensive comparison between classifiers, we employed the following parameters on the aforementioned algorithm to create the artificial datasets. The number of classes take the values , the number of features are and the number of elements for each class is . One possible drawback of studying such distinct scenarios is that depending on the value of the separation, , between the classes the accuracy of the classifiers might "saturate". For example, when increasing the number of features, if the values of remains fixed, we expect all classifiers to provide accuracies close to 100%. Therefore, for each combination of the parameters , and we performed a grid search to find the value of such that the accuracy rate of the Naive Bayes classifier is as close as possible to 70%. The idea behind this procedure is that fixing the accuracy rate of one classifier will likely avoid other classifiers from reaching too extreme values. The Naive Bayes classifier has been chosen because, during the experiments, it provided an accuracy close to the mean accuracy of all classifiers. In order to explore the behavior of the classifiers for accuracies close to 70%, but also to study what happens for larger or smaller class separations, we generated datasets taking the following values of class separability: . Considering all four parameter combinations, we have a total of different parameter configurations. For each configuration, we take the mean value of 10 generated datasets.
The performance of each classifier over the 810 datasets, considering Weka's default parameters, is summarized in Tables 2 and 3. In Table 2, we show the percentage of parameter configurations where the classifier in row outperformed the classifier in column . The last column shows the percentage of configurations where the classifier reached the best rank. It is clear that the Multilayer Perceptron classifier outperformed the Bayesian Network, C4.5, Simple CART and SVM when considering the default parameters. Surprisingly, the Multilayer Perceptron was only outperformed by the kNN, which is a much simpler and faster classifier. Actually, on average the kNN outperformed all classifiers, even cutting-edge classifiers like SVM and C4.5. Another classifier known for its simplicity, the Naive Bayes, also provided interesting results, showing an almost equal or better ranking than all other classifiers besides the Multilayer Perceptron. Since it is widely known that the Multilayer Perceptron usually requires a longer execution time, these results indicate that if the researcher has no a priori knowledge of the classifier parameters, the Naive Bayes and kNN classifiers could represent a good all-around option for using on his data. Nevertheless, it is also important to note that one reason that cutting-edge classifiers might not provide good results for the default parameters is that they are conceived to be versatile enough to be able to adapt to specific properties of the dataset. Therefore, their parameters can be optimized to the task at hand by using methods like grid search or simulated annealing. The drawback is that such optimization is not always straightforward, and needs an adequate training dataset.
The relative rankings of the classifiers provide concise information about the fraction of times a classifier can be considered better than the others. Nevertheless, an additional information needed to provide a fairer comparison of classifiers is the difference of their mean accuracies. This is necessary because the relative ranking indicates whether the accuracy of a classifier is higher than the other, but not how large the difference in accuracy is. In Table 3 we show the mean difference in accuracy between the classifiers for the 81 parameter configurations. Also shown on the last column is the mean accuracy of each classifier over all configurations. By comparing Tables 2 and 3 it is clear that although the Multilayer Perceptron usually outperforms other classifiers, it is not always by a large margin. For example, although the Multilayer Perceptron is 72% of the time better ranked than the Random Forest, on average the improvement is only 2.4%. Another interesting result is that the kNN provided the highest mean accuracy. Comparing the kNN with the Multilayer Perceptron the situation is as follows. The kNN usually provides a larger accuracy than the Multilayer Perceptron, but in cases where the Multilayer Perceptron is better than the kNN, it becomes the best classifier. This means that in the scenario where the default parameters are to be used, when the accuracy given by the kNN is not satisfactory, it may be worth using the Multilayer Perceptron instead.
Another interesting issue to be investigated concerns the assessment of the discriminability of the classifiers as the number of features increases continually from two to ten features. To perform this analysis, we assessed the accuracy of the classifiers in datasets having , and . The increase in the number of features tends to result in higher accuracies. Therefore, in order to avoid a trivial result of all classifiers providing better results when including more features, for each dataset we set . In Figure 2 we show the variation of the average accuracy as the number of features describing the dataset is incremented. Three distinct behaviors can be clearly observed: (i) the accuracy increases; (ii) the accuracy is nearly constant; and (iii) the accuracy decreases. The only classifier in which the pattern (i) was observed was the kNN classifier. The behavior (ii) is the most common trend. Finally, the third effect is more prominent in the case of the C4.5, Simple CART and Bayesian Network. All in all, these results suggest that the kNN performs significantly better than others classifiers in higher () dimensions.
As more attributes are taken into account, the kNN becomes significantly better than the other pattern recognition techniques.
Varying parameters: One-dimensional analysis
An alternative scenario in typical classification tasks arises when the researcher or practitioner wants to improve the performance of the classification by changing the values of the parameters. In this case, we turn to the concept of sensitivity of the classification with regard to the parameters. In other words, if a good classification is achieved only for a very small range in the parameter space, then for many applications it will be very difficult to achieve the best accuracy rate provided by the classifier. Conversely, if the classifier provides high accuracy rates for many different configuration of parameters, then one expects that it will consistently yield high-quality classifications irrespectively to the chosen parameters.
To probe the sensitivity of the classifiers with regard to distinct values or parameters, we analyzed the behavior of the accuracy rate curves when each parameter is varied separately while keeping the remaining parameters set at their default values. This one-dimensional analysis is illustrated in Figure 3. Since the analysis of varying the classifiers parameters for all generated datasets would be impossible, here we use only two datasets. Both datasets have and , the dataset we call DB2F has and , and the dataset called DB10F has and . The behavior of the accuracy with the adoption of values different from the default for some parameters is shown in Figures S1 and S2 in File S1. For the sake of completeness, tables S1–S3 in File S1 show the accuracy rates obtained for the case where default parameters were employed in the same database.
of the kNN classifier. Panel (a) illustrates the default value of the parameter () with a red vertical dashed line. The accuracy rate associated with default values of parameters is denoted by and the best accuracy rate observed in the neighborhood of the default value of is represented as . The difference between these two quantities is represented by . Panel (b) shows how the accuracy rates vary with the variation of in DB2F (each line represent the behavior of a particular dataset in DB2F). Finally, panel (c) displays the distribution of in DB2F.
An extensive analysis comparing the quality achieved with the parameters set with default and non-default values is provided in Table 3 for classifications obtained in DB2F. For each parameter, we provide the average , the standard deviation and the maximum value of , where and are respectively the maximum accuracy observed when the parameter varies and the accuracy rate obtained with all the parameters set at their default values. Therefore, the statistic computed over quantifies how much the accuracy of the classification is influenced when each parameter is set to a value different from the default. Table 3 shows that for almost all parameters, with the only exceptions being the number of seeds () of the kNN and the type () of SVM used. This result suggests that the default parameters usually provide a classification performance that is close to the optimum. Interestingly, even the maximum gain in accuracy is usually small, as they do not exceed 6.25% in any particular dataset (aside from the kNN and SVM classifiers).
Similarly to Table 4, Table 5 shows the results for single parameter variation for classifications performed in DB10. We note that a proper analysis of this table must consider the accuracy rate obtained with default parameters (see Table S2 in File S1), because the latter has a large variation across classifiers. Therefore, if a classifier performs very well with parameters set with their default values, one expects that a significant improvement through one-dimensional variation of parameters will be less probable. This effect becomes evident when one analyzes, for example, the kNN. The default configuration of parameters yields high accuracy rates (), while the average improvement through one-dimensional analysis is only . A significant improvement in the discriminability was observed for the Multilayer Perceptron through the variation of the size of the hidden layers (H). In a similar manner, a significant increase of accuracy was observed when we varied the number of trees (I) of the Random Forest. As for the SVM classifier, six of its parameters allowed an increase of about 20%, which led to accuracy rates higher than 94% in many cases. This result suggests that appropriate parameter tuning in SVM might improve significantly its discriminability.
Varying parameters: Multidimensional analysis
Although the one-dimensional analysis is useful to provide relevant information regarding the variability of accuracy with regard to a given parameter, this type of analysis deliberately disregards the influence of possible mutual interdependencies among parameters on the performance of the classifiers. In order to consider this interdependence, we randomly sample the values of parameters in a bounded range. More specifically, random configurations of parameters for each classifier were generated and each classifier was applied to discriminate the classes in DB2F and DB10F. Note that the Naive Bayes and Bayesian Net classifiers were not included in the multidimensional analysis, since they only have binary parameters. In the next step, we compared the performance of the best random configuration with the performance achieved with the default parameters. An example of the procedures adopted in the multidimensional analysis is provided in Figure 4. A more 'efficient' possibility could be based on the search of the best accuracy rates (considering all configuration of parameters) through an optimization heuristic. Nevertheless, we decided to avoid optimization heuristics because this would imply many problems caused by the different kinds of parameters used in distinct classifiers (e.g., nominal, binary, integer, etc). Moreover, it would be difficult to avoid local extremes which are typical of such approaches.
We use one of the artificial datasets and the kNN classifier. (a) By randomly drawing 1,000 different parameter combinations of kNN we construct a histogram of accuracy rates. The red dashed line indicates the performance achieved with default parameters. (b) The accuracy rate for the default parameters are subtracted from the values obtained for the random drawing. The normalized area of the histogram for values that are above zero indicates how easy is to improve the performance with a random tuning of parameters.
In Figure 5, we show the histograms of the accuracy rates obtained with the random choice of parameters of the classifiers, which were evaluated in DB2F. In order to summarize the main characteristics observed in these histograms, in Table 6 we show some statistics taken over the histograms. The -value quantifies the percentage of realizations in which a random configuration of parameters improved the performance obtained with the default configuration. Considering the cases where an improvement was observed, we can summarize the values of accuracy in terms of their average, standard deviation and maximum value. It is noteworthy that the random choice of parameters usually reduces the accuracy (i.e. -value) for Simple CART, Multilayer Perceptron, C4.5 and Logistic. This means that one should be aware when choosing parameters other than the default configuration, since most of the random configurations impact the performance negatively. Surprisingly, in almost every random choice of parameters (96.89% of the cases) the accuracy of the SVM increases. In the case of the kNN, the improvement is less likely (-value = 76.15%). The Random Forest shows a typical small improvement in 52% of the realizations, in comparison with SVM and kNN. Whenever the computing time for each dataset is not very high, it is possible to generate many random configurations and select that providing the highest accuracy. In this case, the most important parameter extracted from Table 6 becomes the maximum accuracy. This scenario is particularly useful for SVM, kNN and Random Forest, since the performance can be improved in 16%, 13% and 10%, respectively. Actually, SVM and kNN emerge as the best classifiers when we consider only the best realization among the 1,000 random configurations for each dataset (see Table 7).
(a) kNN; (b) C4.5; (c) Multilayer Perceptron; (d) Logistic; (e) Random Forest; (f) Simple CART; (g) SVM. Note that, in the case of kNN and SVM classifiers, most of the random configurations yield better results than the default case.
Repeating the above analysis for the classifications performed in DB10F, one observes some differences in the results, which are shown in Table 8. From the analysis of the means (third column), it is clear that, apart from SVM, a significant improvement in accuracy is much less likely. These results reinforce the premise that default parameters generally provide an accuracy that is near to the optimum. However, as we found for DB2F, the performance of SVM can be significantly improved by the suitable configuration of parameters. Note that the average improvement of 20.35% is equivalent to that found with a one-dimensional variation in the complexity parameter (see parameter C in Table 5). Therefore, the best configuration of the SVM can be achieved by varying only one parameter. Again, if we consider only the best configuration among the 1,000 random configurations for each dataset, the SVM and kNN performs better than the other methods (see Table 9).
Machine learning methods have been applied to recognize patterns and classify instances in a wide variety of applications. Currently, several researchers/practitioners with varying degrees of expertise have employed computational tools such as Weka to study particular problems. Since the appropriate choice of parameters requires certain knowledge of the underlying mechanisms behind the algorithms, oftentimes these methods are applied with their default configuration of parameters. Using the Weka software, we evaluated the performance of classifiers using distinct configurations of parameters in order to verify whether it is feasible to improve their performance. We should highlight here that results obtained from the comparison of different classification methods on the artificial dataset are not universal. This means that, in particular cases, the rank of classifiers may assume different configurations for distinct datasets, as it is widely known that machine learning methods are case-based learning. Nevertheless, we believe that our multivariate normal dataset encompasses a wide variety of real problems.
The analysis of performance with default parameters in the artificial dataset revealed that the kNN usually outperforms the other methods. The Multilayer Perceptron performed better than Bayesian Network, C4.5, SVM and Simple CART in most datasets. Unfortunately, this average gain is not significative and could not be justifiable in practical applications as the computational cost of the Multilayer Perceptron is higher than the cost of the other methods. The Naive Bayes also outperformed the Bayesian Network, C4.5, SVM and Simple CART. Surprisingly, the SVM implemented by Weka displayed an overall performance lower than the other methods when default parameters were employed in the analysis. When just one parameter was allowed to vary, there was not a large variation in the accuracy compared with the classification achieved with default parameters. The only exceptions were the parameter K of the kNN and parameter S of SVM (with Puk kernel). In these cases, the appropriate choice of the parameters enabled an average increase of 6% in accuracy. Surprisingly, we found that when the same analysis is performed with a ten-dimensional dataset, the improvement in performance surpasses 20% for the SVM. Finally, we developed a strategy in which all the configuration of parameters are chosen at random. Despite its outward simplicity, this strategy is useful to optimize SVM performance especially in higher dimensions (), since the average increase provided by this strategy is higher than 20%.
Another important result arising from the experiments is the strong influence of the number of features on the performance of the classifiers. While small differences across distinct classifiers were found in 2–3 dimensions, we observed significant differences in performance when increasing the number of features. When assessing the performance of the classifiers in higher dimensions, kNN and SVM turned out to be the most accurate techniques when default and alternative parameters were considered, respectively. In addition, we found that the behavior of the performance with the number of features follows three distinct patterns (for the considered interval): (i) almost constant (Multilayer Perceptron); (ii) monotonic increase (kNN), and (iii) monotonic decrease (Bayesian Network). These results suggest that the number of features of the problem plays a key role on the choice of algorithms and, therefore, it should be considered in practical applications. In addition, for low dimension classification tasks, Weka's default parameters provided accuracy rates close to the optimal value, with a few exceptions. The highest discrepancies occurred when the performance of the SVM was assessed in higher dimensions, suggesting additional care while choosing the parameters in these conditions.
It is possible to perform further research to probe the properties of classifiers with regard to other factors such as number of classes, number of instances per class and overlap between classes. It is also important to probe the performance of supervised classifiers in problems where the number of training instances is limited because of their cost.
Supporting Information
Author Contributions
Conceived and designed the experiments: LdFC CHC DRA. Performed the experiments: CHC DRA DC. Analyzed the data: CHC DRA LdFC OMB GT FAR. Wrote the paper: CHC DRA DC LdFC OMB GT FAR.
- 1.
Mayer-Schonberger V, Cukier K (2013) Big Data: a revolution that will transform how we live, work, and think. Eamon Dolan/Houghton Mifflin Harcourt.
- 2.
Sathi A (2013) Big Data analytics: disruptive technologies for changing the game. Mc Press.
- 3. Pers TH, Albrechtsen A, Holst C, Sorensen TIA, Gerds TA (2009) The validation and assessment of machine learning: a game of prediction from high-dimensional data. PLoS ONE 4 (8) e6287.
- 4. Marquand AF, Filippone M, Ashburner J, Girolami M, Mourao-Miranda J, et al. (2013) Automated, high accuracy classification of parkinsonian disorders: a pattern recognition approach. PLoS ONE 8 (7) e69237.
- 5. Montavon G, Rupp M, Gobre V, Vazquez-Mayagoitia A, Hansen K, Tkatchenko A, Mller K-R, Lilienfeld OA (2013) Machine learning of molecular electronic properties in chemical compound space. New Journal of Physics 15: 095003.
- 6. Amancio DR, Altmann EG, Oliveira ON Jr, Costa LF (2011) Comparing intermittency and network measurements of words and their dependence on authorship. New Journal of Physics 13: 123024.
- 7.
Bishop CM (2007) Pattern recognition and machine learning. Springer.
- 8.
Murphy KP (2012) Machine Learning: a probabilistic perspective. The MIT Press.
- 9. Wu Xindong, Kumar Vipin, Quinlan J Ross, Ghosh Joydeep, Yang Qiang, et al. (2008) Top 10 algorithms in data mining. Knowledge and Information Systems 14: 1–37.
- 10.
Duda RO, Hart PE, Stork DG (2000) Pattern Classification. Wiley-Interscience.
- 11. Jain AK, Mao J, Mohiuddin KM (1996) Artificial neural networks: a tutorial. Computer 29: 31–44.
- 12. Wood J (1996) Invariant pattern recognition: a review. Pattern Recognition 29: 1 1–17.
- 13. Smetanin YG (1995) Neural networks as systems for pattern recognition: a review. Pattern Recognition and Image Analysis 5: 254–293.
- 14. Howell AJ, Buxton H (2002) RBF network methods for face detection and attentional frames. Neural Processing Letters 15: 197–211.
- 15.
Darrell T, Indyk P, Shakhnarovich F (2006). Nearest neighbor methods in learning and vision: theory and practice. MIT Press.
- 16. Huang L-C, Hsu S-E, Lin E (2009) A comparison of classification methods for predicting Chronic Fatigue Syndrome based on genetic. Journal of Translational Medicine 7: 81.
- 17.
Rice JA (2007) Mathematical statistics and data analysis. Cengage Learning, Belmont, CA.
- 18.
Witten IH, Frank E, Hall MA (2011) Data mining: practical machine learning tools and techniques. Morgan Kaufmann, Burlington.
- 19. Jain AK, Duin RPW, Mao J (2000) Statistical pattern recognition: a review. IEEE Trans. Pattern Analysis and Machine Intelligence 22: 4–37.
- 20. Yang J, Frangi AF, Yang JY, Zhang D, Jin Z (2005) KPCA plus LDA: a complete kernel fisher discriminant framework for feature extraction and recognition. IEEE Transactions Pattern Analysis and Machine Intelligence 27: 230–244.
- 21. Bezdek JC, Chuah SK, Leep D (1986) Generalized k-nearest neighbor rules. Fuzzy Sets and Systems 18: 237–256.
- 22. Seetha H, Narasimha MM, Saravanan R (2011) On improving the generalization of SVM classifier. Communications in Computer and Information Science 157: 11–20.
- 23. Fan L, Poh K-L (1999) Improving the Naïve Bayes classifier. Encyclopedia of Artificial Intelligence 879–883.
- 24. Tsang IW, Kwok JT, Cheung P-K (2005) Core vector machines: Fast SVM training on very large data sets. Journal of Machine Learning Research 6: 363–392.
- 25.
Wu X, Kumar V, Quinlan JR, Ghosh J (2007) Top 10 algorithms in data mining. Springer-Verlag.
- 26. Kotsiantis SB (2007) Supervised machine learning: A review of classification techniques. Informatica 31: 249–268.
- 27. Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. Journal of Machine Learning Research 7: 1–30.
- 28.
Labatut V, Cherifi H (2012) Accuracy measures for the comparison of classifiers. http://arxiv.org/abs/1207.3790
- 29. Prechelt L (1996) A quantitative study of experimental evaluations of neural network algorithms: current research practice. Neural Networks 9 (3) 457–462.
- 30. Flexer A (1996) Statistical evaluation of neural network experiments: minimum requirements and current practice. European Meeting on Cybernetics and Systems Research 1005–1008.
- 31. Salzberg SL (1997) On comparing classifiers: pitfalls to avoid and a recommended approach. Data Mining and Knowledge Discovery 1 (3) 317–328.
- 32. Wolpert DH (1996) The lack of a priori distinctions between learning algorithms. Neural Computation 8 (7) 1341–1390.
- 33. Wolpert DH, Macready WG (2005) Coevolutionary free lunches. IEEE Transactions on Evolutionary Computation 9 (6) 721–735.
- 34. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1 (1) 67–82.
- 35. Huang J, Ling CX (2005) Using AUC and accuracy in evaluating learning algorithms. IEEE Transactions Knowledge and Data Engineering 17: 299–310.
- 36. Ripley BD (1994) Neural networks and related methods for classification. Journal of the Royal Statistical Society Series B 56: 409–456.
- 37. Meyera D, Friedrich L, Hornik K (2003) The support vector machine under test. Neurocomputing 55: 169–186.
- 38. Tavares LG, Lopes HS, Lima CRE (2008) A Comparative Study of Machine Learning Methods for Detecting Promoters in Bacterial DNA Sequences. International Conference on Intelligent Computing 5227: 959–966.
- 39. Mico L, Oncina J (1998) Comparison of fast nearest neighbor classifiers for handwritten character recognition. Pattern Recognition Letters 19: 351–356.
- 40. Pérez O, Piccardi M, Garca J, Molina JM (2007) Comparison of classifiers for human activity recognition. Lecture Notes in Computer Science 4528: 192–201.
- 41. Becq G, Charbonnier S, Chapotot F, Buguet A, Bourdon L, Baconnier P (2005) Comparison between five classifiers for automatic scoring of human sleep recordings. Studies in Computational Intelligence 4: 113–127.
- 42. Cufoglu A, Lohi M, Madani K (2009) A Comparative Study of Selected Classifiers with Classification Accuracy in User Profiling. World Congress on Computer Science and Information Engineering 708–712.
- 43. Conrad C, Ere H, Warnat P, Daigle N, Lrch T, et al. (2004) Automatic identification of subcellular phenotypes on human cell arrays. Genome Research 14: 1130–136.
- 44. Kuramochi M, Karypis G (2005) Gene classification using expression profiles: a feasibility study. International Journal on Artificial Intelligence Tools 14: 641–660.
- 45. Sayed T, Abdelwahab W (1998) Comparison of fuzzy and neural classifiers for road accidents analysis. Journal of Computing in Civil Engineering 12 (1) 42–47.
- 46. Berrueta LA, Alonso-Salces RM, Hberger K (2007) Supervised pattern recognition in food analysis. Journal of Chromatography A 1158: 196–214.
- 47. Wada A, Takadama K, Shimohara K, Katai O (2007) Analyzing parameter sensitivity and classifier representations for real-valued XCS. Lecture Notes in Computer Science 4399: 1–16.
- 48. Cao XB, Xu YW, Chen D, Qiao H (2009) Associated evolution of a support vector machine-based classifier for pedestrian detection. Information Sciences 179 (8) 1070–1077.
- 49. Zhuang L, Honghua D (2006) Parameter optimization of kernel-based one-class classifier on imbalance learning. Lecture Notes in Computer Science Volume 4099 434–443.
- 50. Reif M, Shafait F, Dengel A (2012) Meta-learning for evolutionary parameter optimization of classifiers. Machine Learning 87 (3) 357–380.
- 51. Gaspar P, Carbonell J, Oliveira JL (2012) On the parameter optimization of Support Vector Machines for binary classification. Journal of Integrative Bioinformatics 9 (3) 201.
- 52. Moschitti A (2003) A study on optimal parameter tuning for Rocchio text classifier. Proceedings of the 25th European Conference on IR Research 420–435.
- 53.
Ian H, Frank E (2005) Data mining: pratical machine learning tools and techiniques. Morgan Kaufmann.
- 54. Hirschberger M, Qi Y, Steuer RE (2007) Randomly generating portfolio-selection covariance matrices with specified distributional characteristics. European Journal of Operational Research 177: 1610–1625.
- 55. Lin SP, Bendel RB (1985) Algorithm AS 213: Generation of population correlation matrices with specified eigenvalues. Journal of the Royal Statistical Society Series C 34: 193–198.
- 56. Marsaglia Gand Olkin I (1984) Generating correlation matrices. SIAM Journal on Scientific and Statistical Computing 5: 470–475.
- 57.
Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, Cambridge.


text:
Bill Auberlen
2020: With his illustrious history racing in BMWs, Auberlen continued his success in the SRO GT4 SprintX series, pushing the team into third overall for the season while also earning third in driver standings. He also helped the team score first place after starting from the back in the first-ever SRO Intercontinental GT Challenge Indianapolis 8-Hour Endurance Race to finish off the season.
Previously: Auberlen comes to the BimmerWorld team with a long history with the BMW brand. He has driven BMW cars in more races than any other driver in the world to become the all-time winningest American driver in a leading series. Having claimed six professional championships (four with BMW power) and competed in over 500 professional races to date, Auberlen is the most decorated and prolific BMW driver in the world. His results include over 90 race victories, 190 podium finishes, 55 pole positions, 80 fastest race laps, and 110 lap records.

subset: commoncrawl


text: BIFoR FACE Research In 'BIFoR FACE' FACE ResearchFACE TeamFACE PublicationsFACE Arrays & experimental designFlux Tower and Met MastsCanopy AccessFACE access - use / collaborate nowQUINTUSFACE UndergroundGet involvedBIFoR FACEBack to Research homepage Back to 'Birmingham Institute of Forest Research' We have tried to map projects into different research themes but as the research is related to whole forest ecosystems, there is naturally overlap between the areas. To see the University of Birmingham staff and students involved in each of the research areas please go to our "Research Team" webpage. An overview of the emerging results from the research underway at BIFoR FACE, is available to listen to in a podcast interview of Director, Prof Rob Mackenzie by Tonia Clark from Birmingham Tree People. Research council funded projects underway at BIFoR FACE The following are examples of research council funded projects underway at BIFoR FACE: QUINTUS (2018 -2024) - a £3.7m NERC funded large grant project, Quinquennial (half-decadal) carbon and nutrient dynamics in temperate forests: Implications for carbon sequestration in a high carbon dioxide world, led by Prof Rob MacKenzie (University of Birmingham) FACE Underground (2020 - 2023) - a standard NERC funded project. This project will use the FACE experiment to determine whether mature temperate forests will be able to access more soil nutrients under elevated carbon dioxide (eCO2), led by Dr Sami Ullah (University of Birmingham) Disentangling mechanisms of co-adaption between trees and soil food webs in response to environmental perturbations (2019 - 2022) - a NERC funded project, led by Prof David Johnson (University of Manchester) Distributed Real Time Soil (DiRTS) Monitoring (2020 - 2022) a NERC funded project led by Dr Sami Ullah (University of Birmingham). NI: Network for Monitoring Canopy Temperature of Forests (netCTF) - a 2020 NERC funded project led by Dr Sophie Fauset (University of Plymouth). This project will increase the global network for IR monitoring of forest canopy temperatures (netCTF). As part of that award an instrument will be placed on our 40m flux tower collecting important continuous measurements. The information to follow regarding measurements at BIFoR FACE is separated into: Core measurements - these measurements have been taken continuously over a long period and are made in most cases by the Research Technician staff at the FACE Facility Project specific measurements - these might have been taken just for a shorter undergraduate/postgraduate research project. If you have an idea for research at the BIFoR FACE facility, we'd really like to hear from you, we've a team of people willing to talk to any future collaborators, please do 'contact us' if you would like an initial conversation or if you have an idea developed already you can complete a short form to start the process. Aboveground vegetation processes Core measurements Green chromatic coordinate (GCC) and red chromatic coordinate (RCC) – Phenocam Phenology and biodiversity observations, including bryophyte, deadwood surveys Tree stem growth – LIDAR surveys (includes tree height), dendrometers (manual and automated) Tissue samples of green leaves taken from the top/middle/bottom of canopy for oak trees and also tissue samples from the other 3 key species of tree (hazel, hawthorn & sycamore) biobanked for chemical analysis Tissue samples of buds & catkins bio banked for future research Leaf Area measurements of green leaves sampled from top/middle/bottom of canopy for the four key species of tree (oak, hazel, hawthorn & sycamore) Leaf litter trap samples - samples are separated into up to 9 different categories including a 'woody material' archive and 'reproductive output' archive Leaf Area Index – both hemispherical and direct method Each tree is identified and has its own ID number and is mapped. Projects specific measurements Leaf temperature Leaf-level gas exchange Tree stem respiration Canopy spread Tree stem xylem sap flux Stem wood characteristics from core and slice samples Physiological performance in naturally regenerated trees Carbon isotope analysis of tree cores Sulphur measurements from tree discs Poplar seedlings under elevated CO2 Wood compositional analysis Dry and wet deposition fluxes Sub-canopy Photosynthetically Active Radiation (PAR) Imaging of leaves from leaf litter traps for leaf area Acorn collection and some hazel nuts Examples of research projects QUINTUS a £3.7m NERC funded large grant - Quinquennial (half-decadal) carbon and nutrient dynamics in temperate forests: Implications for carbon sequestration in a high carbon dioxide world Physiological performance of seedlings in a temperate FACE forest - post-doctoral research fellow, Dr Carolina Mayoral. Presentation 2019 Introduction to and analysis of the green chromatic coordinate of BIFoR FACE (Poster 2022) High rainfall disturbs soil microbial structure and function in a mature temperate forest under elevated carbon dioxide (Poster 202) Tree Growth in an Oak Woodland Exposed to Elevated Atmospheric CO2 (Poster 2022) Monitoring the Carbon Dioxide levels in the BIFoR FACE baseline areas (Poster 2022) From branch to forest to globe: how do tree choices regarding growth change forest response to eCO2? (Poster 2022) Do elevated CO2, ozone (O3) and diesel fumes alter the volatile organic compound (VOC) emissions of plants under insect attack? (Poster 2022) Weighing trees non-destructively from terrestrial LiDAR point cloud data - Dr Eric Casella, Forest Research. Poster 2019 Earthwatch Institute - How does CO2 enrichment influence within season growth? Poster 2019 Old Growth oaks: the effect of elevated CO2- PhD student, Anna Gardner. Poster 2021 Early responses of leaf level assimilation to elevated CO2 in a mature oak forest - Dr Sabine Tausz. Poster 2018 Belowground vegetation, litter and soil processes Core measurements Fine Root development Soil CO2, H20 Fluxes N mineralization and N2O source partitioning studies. Soil sampling and lab analysis for nutrients (cations, anions), particle size distribution at least three times a year pH, soil type, organic matter content, CEC, bulk density Leaf litter Hyphal growth and turnover Project specific measurements CH4 and N20 Leaf litter decomposition Fine root production and chemistry: Hyphal growth and turnover Root and hyphal control over decomposition rates, microbial functional activity and nutrient availability Production and turnover of extra-radical mycelium of symbiotic mycorrhizal fungi Dissolved Organic Matter (DOM). Examples of research projects QUINTUS - Quinquennial (half-decadal) carbon and nutrient dynamics in temperate forests: Implications for carbon sequestration in a high carbon dioxide world Disentangling mechanisms of co-adaption between trees and soil food webs in response to environmental perturbations. A University of Manchester led project - Prof D Johnson Biological nitrogen fixation (BNF) and nitrogen mineralization in forest soils under elevated CO2 by Manon Rumeau. Poster 2022 FACE Underground will use the FACE experiment to determine whether mature temperate forests will be able to access more soil nutrients under elevated carbon dioxide (eCO2)Deciduous Woodlands under eCO2 and Nitrogen Deposition: Biogeochemical tradeoffs and the fate of soil carbon Poster 2022 Soil Bioavailable Nitrogen at BIFoR FACE, by PhD student Angeliki Kourmouli. Poster 2019 Resistance and resilience of forest soil microbial communities to extreme weather eventsin a high CO2 world - University of Warwick, Katy Faulkner Poster 2021 Does wood grown under elevated CO2 decompose at a different pace than wood grown under ambient conditions? - ETH Zurich Prof Tom Crowther At the interface of soil and air: What happens under future climate? - by Nine Douwes-Dekker. Poster 2022 Getting to the root of the problem - PhD student Clare Ziegler, Dr Iain Johnston and Dr Rosemary Dyson. Poster 2019. Soil Water Cation Chemistry Under Elevated CO2 Conditions at BIFoR FACE, by masters student Samuel Walrond. Poster 2019 Ionophore-based sensors in BIFoR; results and opportunities (Poster) and Low cost chemical sensors for monitoring soil nutrients: progress and opportunities University of Keele, Dr A Radu. Presentation 2019. Animals (especially invertebrates) Core Measurements Camera traps are installed through the woodland - take a look at some images in our "Gallery" Project specific measurements Invertebrate sampling including the following trapping: Malaise, pitfall, pan, funnel, beating (canopy, field layers), Robinson trap Image analysis of green leaves and senesced leaves for herbivory Leaf mines Winter active lepidoptera specific study Saproxylic activity and wood decay Example Projects Mines bigger than yours - PhD student Liam Crowley. Poster 2021 Investigating the effects of elevated carbon dioxide on forest arthropods - PhD student Liam Crowley. Presentation 2019. Listen to Dr Scott Hayward's 2021 talk from our Annual Meeting. A collaborative project with the University of Lund Assessing the functional contribution of saproxylic invertebrates to wood decay and carbon cycling under changing C02 conditions. - University of Leicester led project by Dr Moya Burns, a long term study commenced in 2019. Atmospheric processes Please also look at our webpage "Flux Tower and Met Masts" for further information. Core Measurements Wind speed CO2,H2O,CH4, fluxes Solar and net radiation Air temperature and relative humidity profile Project Specific Measurements Plant Metabolites Volatile Organic Compounds (VOC) concentrations eg nitrous acid (HONO), peroxynitrate (NO4), dinitrogen pentoxide(N205 ), BBCEAS, NOx and Ozone (O3) Micro-meteorological measurements (using sensors mounted directly on to the central rigger mast): air temperature, photosynthetically active radiation (PAR), relative humidity and wind speed and direction Bioaerosol particles Example Projects Wind flow across a forest edge - PhD student Ed Bannister. Presentation 2020 Finding a needle in a haystack' – Monitoring pollen with low-cost sensors and machine learning Eddy Covariance Fluxes and Footprints at BIFoR FACE - a collaborative project with the Met Office and Swansea University. Poster 2019 Open University's Kadmiel Maseyk et al's project UAV-based measurements of solar induced fluorescence (SIF) to investigate photosynthetic responses to elevated CO2. Poster 2020 How will forests smell in the future? - University of Lancaster, PhD Student Tom King. Poster 2020 Bioaerosols at BIFoR FACE by Aileen Baird. Poster 2021 (see also Aileen's presentation under Microbial Processes tab below). Which volatile organic compounds (VOCs) are emitted by trees, or show significant increases or decreases, under herbivory? How is this moderated by exposure to elevated CO2, O3, or both? A systematic review and meta analysis. - PhD student Laura James. Poster 2021 Laura James Dispersion inside woodland using CO2 data measured at Mill Haft - by student Jinxiu Han, Dr Xiaoming Cai and Dr Rick Thomas. Poster 2018 VOCs, their role in mapping ecosystem changes under high CO2 - PhD student Anthony Hyacinth. Poster 2018. Water FACE arrays core measurements Throughfall precipitation (ground level) Groundwater levels Field precipitation (ground level) FACE arrays project specific measurements Tree stem xylem sap flux Isotopic composition of branches Soil water isotopic composition Soil pore water samples Soil temperature profile Leaf water potential Leaf transpiration and water vapour exchange Across site project specific measurements · Resarzurin-resorufin(Raz/Rru) · Dissolved Oxygen · Conductivity Temperature and Depth (CTD) · Stream Stage · pH/electrical conductivity/dissolved oxygen/turbidity/temp/chromophoric dissolved organic matter/Tryptophan · NO3, NO2, Chemical Oxygen Demand (COD), Total Organic Carbon (TOC) · Stream pore water samples · Stream surface water samples · Precipitation · Air pressure Example projects in FACE arrays / across the woodland site The plant-water conundrum: root-xylem-stomatal response of Quercus robur (pedunculate oak) to elevated CO2 in a temperate futureforest experiment. Xylem sapflow at BIFoR FACE: early results of Tree-Soil-Water Relations- PhD Sue Quick. Presentation 2022 Wrangling Plant-Water data: an update - PhD Sue Quick, Poster 2021 Trends in soil moisture and temperature dynamics in juvenile forests align to those of mature forest from the time of canopy closure. Andrea Rabbi Poster 2021 ADTS for high resolution monitoring of soil moisture at the field scale - Dr Giulio Curioni. Poster 2020 The dependency of Hyporheic Nutrient Cycling on Season and Sediment Type - S Comer-Warner, D Gooddy and S Krause. Poster 2019 Temperature and Turbidity Effects on the Fluorescence Intensity of Uranine, Resazurin and Resorufin- Nicolai Brekenfeld. Poster 2019 High frequency monitoring of catchment nutrient exports - Dr Phil Blaen. Poster 2018 Modelling the Spatiotemporal Dynamics of Stream Temperature in a Mixed-Use Farmland Catchment - Han Qui, Philip Blaen, David Hannah, Stefan Krause and Manthan Phanikumar. Poster 2018 Microbial Processes & Biomarkers Project specific measurements soil fungal metagenomics macrofungi surveys n-alkanes Example projects Fungi of the future - PhD student Aileen Baird. Presentation 2020 Bioeaorsoals at BIFoR FACE - PhD student Aileen Baird. Poster 2021 Leaf waxes: tracking past climate and plant metabolism - PhD student Bridget Warren. Poster 2021 Listen to Bridget talk about her research Bridget Warren Future climate: Future pollen and spores by Sophie Mills. Poster 2021 Plant health and plant diseases Visit our Forest Health Research page for further information. Some example projects follow: The transgenerational impact of elevated CO2 on oak progeny growth and development by Mark Raw. Poster 2021 Investigating the effect of mixed plantations in resistance to ash dieback disease by Iwan Evans. Poster 2020 Everyone completing research at BIFoR FACE needs to read & agree to the BIFoR FACE Intellectual Property and Data Protocol in advance of starting research. In summary the maximum scientific exploitation of BIFoR FACE depends on the collaborative utilisation of all data collected at BIFoR FACE for research. The BIFoR FACE science community believe and advocate transparency in science assured through open data after an agreed period of privileged use. All data acquired through BIFoR FACE projects will be deposited in a shared database in good time and with appropriate accompanying metadata after consultation with the BIFoR Data Manager. A scientist sharing data does not relinquish ownership of that data but recognises that all BIFoR FACE data will become open data, with due care taken to record data provenance, in a timely manner in order to ensure transparency, to be compatible with the requirements of funding agencies, and to accelerate scientific advance. Inside a FACE array - Dr Rick Thomas and Anna Gardner describe some of the experiments Research here Add your own research experiment /how to use BIFoR FACE data already gathered "Research here" BIFoR FACE Back to the BIFoR FACE home page


text:
SCC is responsible for approving administering organizations that accept responsibility for the management of one or more mirror committees on behalf of SCC. Approval as an administering organization demonstrates that the organization is competent, credible and reliable to administer mirror committees.
Once an organization has been approved as an administering organization, the administering organization can submit applications to administer mirror committees on behalf of SCC.
Document date:


text:
- The Rev. Arianne Rice
This is the Voice!
Easter 4, 4/25/21
The voice of the Lord is a powerful voice. The voice of the Lord breaks the cedars. The voice of the Lord is over the waters. The God of glory thunders.
That's my paraphrase of some of Psalm 29. This morning we heard the more familiar Psalm 23. Both of which were written at least 500 years before Jesus.
And, it seems to me – that in this morning's Good Shepherd gospel – on Good Shepherd Sunday – when we hear the Good Shepherd psalm – Jesus is giving a fresh take on both.
The voice of the Lord – who is the Good Shepherd.
So I wonder – why? Why does Jesus use this image of the Good Shepherd – and what is it about the voice that Jesus wants us to know?
I'll tell you one thing – when I was in seminary – our chaplain told us – y'all better memorize some scripture – specifically – memorize Psalm 23 – because you will go into rooms and places and you won't have a prayer book. And that was good and true advice.
I can say it right now – and you'd know most of it – the Lord is my shepherd I shall not want – he makes me lie down in green pastures and leads me besides still waters – he revives my soul and guides me along right pathways for his namesake – yea, though I walk through the valley of the shadow of death I shall fear no evil – for you are with me – your rod and your staff they comfort me – you spread a table before me in the presence of my enemies and my cup is running over.
Surely – your goodness and mercy shall follow me all the days of my life and I will dwell in the house of the Lord forever.
What is it about that psalm? I have prayed it with people who are making that journey and yes – they are asleep – but then their lips move – or then they start to speak – or whisper – or just give some indication that they are taking in those words.
What is it about that psalm? I could tell you the prayer book history of it – and when it came into use – but – the lord is my shepherd I shall not be in want – that is why we all know that psalm. Because it resonates with something we don't just want, we need.
A friend of mine in DC – who is healthy as can be – a few years ago hiked the Applachain trail – and this week – this week was supposed to start hiking the Pacific Coast Trail – a 5 month excursion – thank you, no thank you. Well, a week ago her arm swelled up – so much so that she went to the hospital – and they found a clot and she had it removed twice – and she has another surgery – and it's all been a trying experience. And we were talking this week and she was telling me how when she had to go back to the hospital she was fine – but then the nurse came in and started using all the medical speak – and my friend started freaking out – and then the doctor came in all cheery and ready to get to work – and she was sobbing – and she couldn't stop.
Because – it doesn't matter if it's normal operating procedure – or if it's standard practice – or done all the time. When it's you – and this thing is happening to you and your body – that you cannot in anyway fix or control – and you're alone in that reality – it's overwhelming.
The Lord is my shepherd – he is with me – rod and staff they will comfort me.
This is why we all know that Psalm. I know what it is like to feel abandoned and alone. Jesus reminds us – not on my watch. Say the words – and listen for my voice – I abide in you and you in me – I am the Good Shepherd.
How do we listen? How do we know that voice? First question first. We hear the voice – when we choose to listen.
The voice of the Good Shepherd does not compete with the other voices. "The word of the Lord is very near, it is on your lips and it is written on your heart." The voice of the Good Shepherd is within us. It is deeper than the voices on the surface. The ones that compete for attention.
It is not our consciousness – not our metacognition. The voice that analyzes who we are and what we do. It is not our inner critic – or our inner coach. In other words – the voice is not our inner voice – that's nature, and nurture and an amalgamation.
If you think about the metaphor – sheep don't talk, right? There has to be something in the sheep that resonates with the shepherd. That's how I think about what Jesus is saying. Like when Paul says the Spirit prays on our behalf with sighs too deep for words.
The voice of the Good Shepherd is a resonance. If you walk down the sidewalk with a two-year old child – where everything they happen upon is a curiosity and delight – that is the voice of the Good Shepherd.
It's that feeling within us when we know we need to pay attention to something we don't want to pay attention to – I can't breathe. Say her name. There are too many names.
The resonance of that voice challenges, encourages, invites, heals, helps us do hard things. Resonance doesn't bargain or compete to trick us into listening.
Why did Jesus use this metaphor? Well, I don't know since I'm not Jesus or a Jewish prophet from the 1st century – but, from my experience I believe – Jesus wants us to know we are not alone.
Like a shepherd cares for the sheep – God cares for us.
God cares for us as a flock – and God cares for each and every one of us – goes after us when we get lost.
I believe Jesus wants us to listen for what resonates deep in our heart and soul – as truth – truth that sets us free. Free to live without fear for being who God made me to be.
I believe Jesus wants us to use our voice to do the same. To build people up in love. To pay attention to the things in our world that are hard to pay attention to – but when we do – we use our voice to amplify hope and healing – because we do have the ability to make that a reality.
The Lord is my shepherd – I shall not be in want.
The voice of the Lord is a powerful voice.
Surely God's goodness and mercy shall follow me all the days of my life and I will dwell in the house of the Lord forever.
How is the Good Shepherd inviting you to listen? How is the Good Shepherd inviting you to use your voice?


text:
Brown Leather Briefcase
- In Stock
Classic Chanel briefcase crafted in supple brown leather with large 'CC' logo embroidery on front, finished with two rolled leather top handles and silver-tone hardware.
- Two Leather Top Handles
- Top Zip Closure
- Two Slip Compartments, Interior Zip And Two Pouch Pockets
- Leather
- Fabric Lining
- Silver Hardware
- Length: 16" (40 cm)
- Height: 11" (27 cm)
- Depth: 4" (10 cm)
- Strap Drop: 4" (10 cm)
- Made in Italy
- 2005-2006
Very Good Condition. Moderate slouching to structure, light creasing throughout leather and handles
Shipping & Returns:
$10 Ground Shipping & Free Returns on most items.
If for any reason you are not satisfied with your purchase it may be returned within 7 days after delivery for a refund (unless the item is marked as final sale). You can read more about our return policy here.
This item is guaranteed authentic by What Goes Around Comes Around.


text:
unit 6
B6 level
Main Aims
To provide carification and practice of two part verbs, requests, requests with modals and apologies
Subsidiary Aims
To provide listening, speaking and writing skill practice
Procedure (82-145 minutes)
In this stage I will give ss dices to roll and write the number they get on a paper. Ss should hide the their papers so other students can't know them. I will ask students to write down things that happened the them the past couple weeks ( since we haven't met for two weeks) For instance if a student gets number 5 they will share 5 things. I will ask student to fold the papers and throw them in the middle of the classroom. then each student should pick a paper share it with the classroom and guess who wrote it.
Since the last lesson was about two part verbs, I will ask ss to give me examples of phrasal verbs and the different ways to place them in a sentence. I will also ask them to make requests and respond to them using the phrasal verbs. In pairs I will ask students to come up with a short conversation using the target language then share with Wc;
First thing first I will ask SS about the meaning of "household chores" then elicit the meaning from Ss. Part A : I will read the nouns and ask students to repeat to practice then I will ask them to match the nouns with the verbs and come up with other nouns that go with each verb. I'll correct this part as WCF. Part B and C : I will ask ss to work in pairs and brain storm some requests that can be made in each of the following rooms ( the kitchen, the living room, the bathroom and the bedroom) after brain storming they should buildconversation usin the requests and give excuses as in the example on page 38
I will ask SS " do you think men and women share housework equally? who does more work around the house? why ?" I will ask ss to listen to the results of a surey (an examination of opinions, behaviour, etc) about family life and answer the four qhuestions they have on part A.then share results as WCF For part B: I will ask students to take notes of women, men , boys and girls tasks. ss compair their answers after the first time they listen to the audio, then after the second time I will elicit SS answers. For part C: in groups of 3, I'll ask ss to discuss who does the housework in their families and share with WC
Mr Omar promised to give a presentation about marriage. so Mr Omar will give a resentation and then we will discuss it and ask SS if they have anything else to add concerning the subject.
in large 2 groups I will ask students to think of 10 items that fit particular criteria. For example: Jobs where you have to wear a uniform football clubs Sports that are played with a ball Foods that contain egg Animals that lay eggs Three letter parts of the body – eye, arm, leg, hip, ear, toe jaw, rib, lip, gum
I will use this activity ad a dictation activity. ss should work in pairs. one of the students should sit in their desk and have a pen and a paper, the other ss should read from the paper haug on the wall and dictate it to thei partner. when they finish they should match the sentences and listen to the audio and check their answers. we will discuss as wc which requests are not reasonable and why. I will ask ss if they made similar requests or others to their neighbors. after the discussion I will elicit 4 kinds of requests from the exercise to introduce the grammar focus.
From the examples I will ask SS to compair between the requests they learned previously ( informal) and the ones with modal ( formal ) I will also elicit the from of the requests. For "would you mind ....?" I will underline the gerund to hilight the form of the verb after the expression both in affirmative and negative requests. I will ask students to come up with their own requests using the target language. and share with WC. I will ask ss to match the requests with the appropriate responses in part A and check their answers together then share with wc Part C: I will ask Ss to brain storm some unusual requests individually and go around the class ask their classmates. ss should keep the record of who could do what they were asked and who couldn't.
I will ask ss to write down three complaints they have about neighbors, the have some suggestion on the book in part A for part B students will take turns making requests and they should respond with an apology along with an excuse, promise or an offer. at the end of the activity we will do a role play.


text:
Introduction: MATLAB Robotic Mixologist
Ever wish to have your drinks mixed perfectly for you in a matter of seconds? Well look no further the Robotic Mixologist is here to take away the time it takes to stir your drinks. This project utilizes the RobotGeek Snapper Arm to function as your very own bartender. All you have to do is put the desired beverage of your choice in a glass and let the MATLAB code do the rest.
Step 1: Project Parts
5x Metal Gear 9G Servos
1x RobotGeek Small Workbench
1x RobotGeek Sensor Shield
Assembly Hardware
Tools Needed: 2.5mm Hex Driver
1.5mm Hex Driver
Step 2: Assembly
We will be using the gripper as a transport system for ice and also as a stirring mechanism to mix drinks to your desired flavor. Pictured is an aerial and horizontal view of the final assembly for the arm snatcher. Our micro controller came assembled already for the most part other than having to print out a new arm piece that was broken. For a general assembly guide follow the attached link to get your arm snatcher up and running.
Arm Snatcher Assembly Link: http://learn.robotgeek.com/projects/237-robotgeek-snapper-assembly-guide-v3.html
Step 3: Wiring
Wiring is the hardest part next to the MATLAB code so make sure that all of your wires are in the correct place. The main thing is to plug in the usb into your computer to connect the circuit board to your MATLAB code(grey usb pictured). Once you have it connected, all you need to do is make sure the servos are in the right inputs. Each servo is designed to move a specific part(i.e. elbow, shoulder, base). Once you connect the servos to the designated spots on the circuit you can plug in the wires into any of the (+) and (-), for more details look at the picture above to get an idea.
Step 4: MATLAB Code
Each servo, as mentioned before, is connected to a specific part. In order for these parts to move one would need to write code, we chose to operate through MATLAB. We used a for loop in a move function which we would recall in our main function to move the specific parts. For example, in the code we have servos connected to pins on the board ranging from D3-D7 and to generate movement we just typed in degrees of rotation for each part. We also used delays in our function in order for the robot to operate smoothly. For more code related problems just visit MATLABs general help page.


text:
The research report provides valuable insights into demand drivers, geographical outlook, and competitive landscape of the Traction Battery for the Traction Battery forecast period. Further, it throws light on restraints as well discusses opportunities at length that are likely to come to the fore over the forecast period. The analysis thus provided helps stakeholders with business planning and to gauge scope of expansion in the Traction Battery over the forecast period.
The report discusses the structure, including prevailing trends, size of the vis-à-vis revenue and volume, and finally forecasts values. Vital information, facts, and statistical figures provided for the Traction Battery are based on extensive primary and secondary research. Analysts also reached out to industry experts for their insightful inputs on the Traction Battery .
Planning To Lay Down Strategy For The Next Few Years? Our Report Can Help Shape Your Plan Better.
Further, the report provides a comparative analysis of historical and current trends prevailing in the Traction Battery . This helps to estimate growth trends in the Traction Battery over the assessment period. Such comparative analysis is provided using an exhaustive collection of tables and graphical representations.
The report delves into the vendor landscape of the Traction Battery . The research report on the Traction Battery provides valuable insights on the competitive landscape of the Traction Battery . Besides this, the research report provides deep insights into growth strategies employed by key players, along with impact of these strategies on future business growth.
The SWOT analysis of key vendors along with a detailed profile of key vendors based on business overview, financial status, and product portfolio helps to gauge competitive dynamics in the Traction Battery . This analysis helps to gauge growth strategies to be employed by prominent vendors in the Traction Battery , and scope of collaborations and partnerships between these players
The report includes an exhaustive list of top players in the Traction Battery :
Johnson Controls, Exide, Hitachi, Samsung, BYD Company, LG Chem, Mutlu, Enersys, Panasonic Systems Sunlight, Amara Raja Batteries, Hoppecke Batteries, GS Yuasa, Haze Batteries, Midac and Banner Batterien.
Further, share projections and changing competitive hierarchy in the Traction Battery until the end of the forecast period are vital offerings of this report.
To Obtain All-Inclusive Information On Forecast Analysis Of Global , Request A PDF Brochure Here.
Key Questions Answered in the Traction Battery Report
- What is the revenue projections in the Traction Battery over the forecast period?
- Which product segment is likely to garner maximum share in the Traction Battery over the forecast period?
- Which regional segment is likely to hold the leading share in the Traction Battery over the assessment period?
- What are winning strategies adopted by leading players in the Traction Battery to consolidate their foothold?
- What are some prominent developments observed in the Market ?


text:
The Villa Finder Concierge team takes care of guest experiences! We are your personal assistants on the ground and help you with anything and everything from the moment you book with us, at no extra charge.
This fabulous award-winning 3-bedroom villa is an amazing place to spend your holiday near the beach in Goa. Gorgeous teak wooden pavilions with two-tiered high high-pitched rooftops, full-length glass windows and doors and a sprawling garden with a spectacular swimming pool - this place is heavenly! Villa Summertime sits on the slopes of a hill just outside Calangute and it boasts magnificent views of rice paddies and gardens. This splendid holiday home sits on 2 acres of sprawling land and spending your holiday here is like residing in some sort of luxury paradise for a little while. It's impossible not to love your stay!
This tropical luxury estate houses 3 master bedrooms and it sleeps up to 7 people. The master rooms are very spacious and each of them features a stylish individual interior design. The rooms come with large dressing areas, comfortable beds, seating areas, AC and opulent bathrooms with rain showers. The rooms also have TV with Amazon Fire TV Stick for watching Amazon Prime, Netflix and Hotstar and verandas with lovely views to wake up to in the morning. The Koi Suite features French windows overlooking a tranquil koi fish pond. The coral suite is very romantic with a beautifully draped canopied four-poster bed. This heavenly suite enjoys fantastic views of the rice paddy valley below in the valley. The Sunflower Suite has got an all-yellow colour-theme and it's got somewhat of a colonial air. This room features king-size single beds.
Ever dreamt of residing in paradise, or a heavenly Garden of Eden? You have found it here at Villa Summertime. Sitting on 2 acres of sprawling tropical land overlooking valleys and rice paddies of Goa the garden is home to ponds, fountains and waterfalls. Furthermore, Villa Summertime boasts a stunning private infinity pool - a definite highlight! - overlooking the tropical nature and rice paddy valleys. Breathtaking! By the poolside, there are sunbeds to work on that tan and there is an open-air living lounge pavilion to soak up the views, enjoy a delicious meal or drinks in the company of your loved ones. Villa Summertime has got its very own orchard where you can pick bananas, mangos, tamarind, corn and lots of herbs. If this isn't paradise-like, I don't know what is!
The living room features a double-height ceiling and glass doors opening up to breezy verandas where you can sit to enjoy the views and the tranquil ambience. The living space is soaked in natural sunlight and there is a natural rice paddy breeze flowing through. Villa Summertime is furnished elegantly with wooden furniture from Bali and India, rustic and sophisticated. Cushioned rattan sofas and armchairs, chandeliers, a handsome teak timber dining table and a modern kitchen, Villa Summertime has got everything you could wish.
Villa Summertime is fully staffed with a cook, housekeeping staff, gardener and pool cleaner. One of the staff members stays onsite in a private room for security purposes.
Villa Summertime is located in the hills just outside of a village called Calangute in the north of Goa. The villa enjoys a peaceful location surrounded by nature and away from traffic. Just a short drive away from the villa you will find beautful beaches, shops and restaurants. It takes approximately 1 hour to drive to Goa's airport.
|Minimum stay
|3 bedrooms
|01/10/2023 15/12/2023
|High season
|3 nights
|15/12/2023 08/01/2024
|Peak season
|7 nights
|08/01/2024 01/06/2024
|High season
|3 nights


text:
All Shook Up by Joe DiPietro
– Equity Submissions
Ivoryton Playhouse Ivoryton, CT SPT $420.
First rehearsal: June 17; First performance: July 2; Close: July 27.
Executive/Artistic Director: Jacqueline Hubbard
Director/Choreographer: Richard Amelius
Please send a headshot and resume with relevant experience to email@example.com
Video submissions are welcomed and songs from the show are encouraged.
Looking for:
CHAD (25-35 – baritone): a great-lookin', motorcycling, guitar-playing, leather-jacketed roustabout.
JIM HALLER (mid 40's-50's – baritone): Natalie's widowed father.
Theatre's mailing address: Ivoryton Playhouse, PO Box 458, Ivoryton CT 06442.


text:
AJ Dillon shoved by police officer, chief apologizes
GREEN BAY, Wis. - Packers running back AJ Dillon has received an apology from the Green Bay police chief for the way an officer treated him during an exhibition soccer match at Lambeau Field.
Chris Davis issued the apology Friday and said the police department directed "appropriate corrective action" to the officer involved as it completed an internal review of the July 23 incident.
Video posted on social media showed Dillon in the end zone greeting fans in the stands during a soccer match between FC Bayern Munich and Manchester City FC. Dillon appeared to be on the verge of doing a Lambeau leap into the crowd when the video showed an officer grabbing him by the back of his collar and giving him a shove.
RELATED: Check out the new and improved FOX Sports app
After fans booed and Dillon appeared to offer an explanation, the officer allowed Dillon to jump into the stands.
Davis said in a statement that he had "sustained two allegations of GBPD policy violations by the officer involved and directed appropriate corrective action to be taken." Davis said the department doesn't provide additional details on personnel matters "out of respect for the employee's due process rights."
His statement didn't name the officer involved.
"I apologize to Mr. Dillon for the way he was treated," Davis said. "We appreciate the strong relationship we have with the Packers organization, and the GBPD remains committed to working with them along with the entire Green Bay community to provide the best and most professional police service possible."
SIGN UP TODAY: Get daily headlines, breaking news emails from FOX6 News
The Packers issued a statement saying they appreciated that the police department followed up on the matter.
"We respect their process in reviewing the situation and its conclusions," the Packers said. "We value our partnership with the Department and appreciate all they do in working with the Packers to ensure public safety at Lambeau Field events, including gamedays.
FREE DOWNLOAD: Get breaking news alerts in the FOX6 News app for iOS or Android.
"Additionally, we appreciate AJ Dillon's professionalism in handling the matter."
When the video circulated on social media, Dillon tweeted out a statement giving his account of the incident and describing it as "just miscommunication between parties."
"The @GBPolice are great people and I'm glad we have them down for our games to keep us safe," Dillon tweeted at the time "Standing there in the pouring rain with all those people, it's hard to know what's going on with just one. All good."


text:
Because the radio frequency (RF) circuit is a distributed parameter circuit, skin effect and coupling effect are prone to occur in the actual work of the circuit, so in the actual PCB design, it will be found that the interference radiation in the circuit is difficult to control, Such as: mutual interference between digital circuit and analog circuit, noise interference of power supply, interference caused by unreasonable ground wire, etc. Because of this, how to weigh the pros and cons in the PCB design process to find a suitable compromise, to reduce these interferences as much as possible, and even to avoid the interference of some circuits, is the key to the success or failure of the RF PCB design. From the perspective of PCB LAYOUT, this article provides some processing skills, which are of great use to improving the anti-interference ability of radio frequency circuits.
1.RF layout
What we discussed here is the layout of the components of the multilayer board. The key to the layout of components is to fix the components on the RF path. By adjusting its direction, the length of the RF path is minimized, and the input is far away from the output, and the high-power circuit and the low-power circuit are separated as far as possible. The signal is far away from high-speed digital signals and RF signals.
The following techniques are often used in the layout.
1.1 One-line layout
The components of the RF main signal are arranged in a straight line as much as possible, as shown in Figure 1. However, due to the limitation of PCB board and cavity space, it cannot be laid out in a straight shape in many cases. At this time, L-shaped layout can be used. It'd be better not to use U-shaped layout (as shown in Figure 2). When it is unavoidable, it'd be better to increase the distance between input and output to at least 1.5cm.
Figure 1 One-line layout
Figure 2 L-shaped and U-shaped layout
In addition, when using an L-shaped or U-shaped layout, the turning point should not turn as soon as it enters the interface, as shown on the left in Figure 3, but after a slight straight line, as shown on the right in Figure 3.
Figure 3 Two options
1.2 Same or symmetrical layout
The same modules should be made into the same layout or symmetrical layout as much as possible, as shown in Figure 4 and Figure 5.
Figure 4 The same layout
Figure 5 Symmetrical layout
1.3 Cross-shaped layout
The feed inductance of the bias circuit is placed perpendicular to the RF channel, as shown in Figure 6, mainly to avoid mutual inductance between inductive devices.
Figure 6 Cross-shaped layout
1.4 45° layout
In order to use the space reasonably, the devices can be arranged in a 45-degree direction to make the RF line as short as possible, as shown in Figure 7.
Figure 7 45° layout
2.RF Routing
The overall requirements for wiring are: RF signal traces are short and straight, reduce line abrupt changes, drill fewer holes, and do not intersect with other signal lines, and add as many ground vias as possible around the RF signal line.
The following are some commonly used optimization methods:
2.1 Gradient line processing
In the case that the RF line width is much larger than the width of the IC device pin, the line width of the contact chip adopts a gradual method, as shown in Figure 8.
Figure 8 Gradient line
2.2 Arc line processing
If the radio frequency line cannot be straight, treat it as an arc line, which can reduce the external radiation and mutual coupling of the RF signal. Experiments have shown that the corners of the transmission line are bent at right angles, which can minimize return loss. As shown in Figure 9.
Figure 9 Arc line
2.3 Ground wire and power supply
The ground wire should be as thick as possible. If it is possible, each layer of the PCB should be grounded as much as possible, and the ground should be connected to the main ground. More ground vias should be made to reduce the ground impedance as much as possible.
The power supply of the RF circuit should not be divided into planes as much as possible. The entire power plane not only increases the radiation of the power plane to the RF signal, but also is easily interfered by the RF signal. Therefore, the power cord or plane generally adopts a long strip shape and is processed according to the size of the current. It is as thick as possible under the premise of meeting the current capacity, but it cannot be widened without limit. When handling power lines, be sure to avoid loops.
The direction of the power line and the ground line must be parallel to the direction of the RF signal but not overlap. It is best to use a vertical cross where there is a cross.
2.4 Cross processing
The RF signal and the IF signal should be crossed with a ground if it is possible.
When RF signals cross other signal traces, try to arrange a layer of ground connected to the main ground along the RF traces between them. If it is not possible, make sure they are crossed. Other signal traces here also include power lines.
2.5 Coplanar impedance
Coplanar impedance of radio frequency signals, interference sources, sensitive signals and other important signals can not only improve the anti-interference ability of the signal, but also reduce the interference of the signal to other signals. As shown in Figure 10.
Figure 10 Coplanar impedance
2.6 Copper foil treatment
The copper foil processing requires smooth, no long lines or sharp corners are allowed. If it is unavoidable, fill a few ground vias at the edges of sharp corners, slender copper foil or copper foil.
2.7 Spacing
The RF line must be at least 3W wide from the edge of the adjacent ground plane, and there must be no non-ground vias within the 3W range.
Figure 11 Spacing
The radio frequency lines of the same layer should be have coplanar impedance, and ground vias should be added to the ground copper. The hole spacing should be less than 1/20 of the wavelength (λ) corresponding to the signal frequency, and they should be evenly arranged.
3.Cavity treatment
For the entire RF circuit, the radio frequency units of different modules should be isolated with a cavity, especially between sensitive circuits and strong radiation sources. In high-power multi-stage amplifiers, the isolation between stages should also be guaranteed.
After the branch of the entire circuit is placed, it is the treatment of the shielding cavity. The treatment of the shielding cavity has the following points:
The entire shielding cavity should be made into a regular shape as much as possible to facilitate casting. Try to make each shielding cavity rectangular, avoiding square shielding cavities.
The corners of the shielding cavity are arc-shaped, and the shielding metal cavity is generally formed by casting. The arc-shaped corners are convenient for drafting during casting. As shown in Figure 12.
Figure 12 Cavity
The periphery of the shielding cavity is sealed, and the interface line into the cavity is generally a strip line or a microstrip line
Place 3mm metalized holes on the corners of the cavity to fix the shielding shell, and evenly place the same metalized holes on each long cavity to strengthen the support.
The cavity is generally windowed to facilitate welding of the shielding shell. The cavity is generally thicker than 2 mm, and 2 rows of windowed via screens are added to the cavity. The vias are staggered. The distance between the vias in the same row is 150MIL.
In the design of RF circuit PCB, it is very important to reduce circuit radiation, thereby improving anti-interference ability. However, the handling of some problems in the actual layout and wiring is in conflict, so how to find a compromise point to optimize the overall performance of the entire radio frequency circuit is a problem that the designer must consider. This article summarizes some of the design experience in the work, which will help improve the anti-interference ability of the RF circuit PCB, and hope to help beginners in RF circuit design.
PCBWay provide service including PCB Prototype & Batch Production, PCB Assembly (SMT), PCB Design and Electronics Modules Selling. We are committed to meeting the needs of global makers from different industries in terms of quality, delivery, cost-effectiveness and any other demanding requests in electronics.
Enter the year of your birth and check your Chinese Zodiac.


text:
VMware Workstation and Fusion contain a use-after-free vulnerability in VMware NAT service when IPv6 mode is enabled. This issue may allow a guest to execute code on the host. Note: IPv6 mode for VMNAT is not enabled by default.
With Rapid7 live dashboards, I have a clear view of all the assets on my network, which ones can be exploited, and what I need to do in order to reduce the risk in my environment in real-time. No other tool gives us that kind of value and insight.
– Scott Cheney, Manager of Information Security, Sierra View Medical Center