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BBN, ADTree and MLP Comparison in Separating Quasars from Large Survey Catalogues

We compare the performance of Bayesian Belief Networks (BBN), Multilayer Perceptron (MLP) networks and Alternating Decision Trees (ADtree) on separating quasars from stars with the database from the 2MASS and FIRST survey catalogs. Having a training sample of sources of known object types, the classifiers are trained to separate quasars from stars. By the statistical properties of the sample, the features important for classification are selected. We compare the classification results with and without feature selection. Experiments show that the results with feature selection are better than those without feature selection. From the high accuracy, it is concluded that these automated methods are robust and effective to classify point sources, moreover they all may be applied for large survey projects (e.g. selecting input catalogs) and for other astronomical issues, such as the parameter measurement of stars and the redshift estimation of galaxies and quasars.

important problem. Due to the large size of the databases, it is impossible to manually analyze the data for knowledge discovery. Therefore the automated extraction of useful knowledge from huge amounts of data is widely recognized now, and leads to a rapidly developing market of automated analysis and discovery tools. Data mining and knowledge discovery are techniques to identify valid, novel, potentially useful, and ultimately understandable patterns hidden in very large databases. Automated discovery tools can provide the potential and advantages to mine the raw data and obtain the extracted high level information to the analyst or astronomers.
Just like statistics, the diversity of tasks and techniques in data mining is broad. For example, Fayyad et al. (1996) divided data mining tasks into six flavors: (i) classification; (ii) regression; (iii) clustering; (iv) summarization; (v) dependency modelling (structural and quantitative); and (vi) change modelling (changes from previous or normative values). In astronomy, the automatic classification of objects from catalogues is a common issue encountered in many surveys (Zhang & Zhao 2003;. From a list of values of variables associated with a celestial object, it is desired to identify the object's type (eg. star, galaxy). In this paper we apply three automated methods: Bayesian Belief Networks (BBN), Multilayer Perceptron (MLP) networks and Alternating Decision Trees (ADtree) to classify objects as quasars or non-quasars using the cross-matched results of a radio survey and a near infrared survey. Such classification is helpful to preselect quasar candidates for large survey projects.
The structure of this paper is as follows: Section 2 presents the data collection and attribute selection. Section 3 gives a brief introduction of BBN, MLP and ADTree. The procedure to get the classifiers and the classification results are presented in section 4.
Section 5 summarizes and concludes the present work.

DATA SAMPLE AND CHOSEN ATTRIBUTES
We describe here near infrared, radio and known catalogs as follows. Table 1 summarizes the characteristics of the two surveys.
The Two Micron All Sky Survey (2MASS) project (Cutri et al. 2003 The Faint Images of the Radio Sky at Twenty centimeters (FIRST) began in 1993. It uses the VLA (Very Large Array, a facility of the National Radio Observatory (NRAO)) at a frequency of 1.4 GHz, and it is slated to 10,000 deg 2 of the North and South Galactic Caps, to a sensitivity of about 1 mJy with an angular resolution of about 5 arcsec. The images produced by an automated mapping pipeline have pixels of 1.8 arcsec, a typical rms of 0.15 mJy, and a resolution of 5 arcsec; the images are available on the Internet (see the FIRST home page at http://sundog.stsci.edu/ for details). The source catalogue is derived from the images. A new catalog (Becker et al. 2003)    Tycho-2 is much bigger and slightly more precise, owing to a more advanced reduction technique. Components of double stars with separations down to 0.8 arcsec are included.
Proper motions precise to about 2.5 mas/yr are given.
We firstly positionally cross-matched the 2MASS catalogue with the FIRST catalogue within 5 arcsecond radius, then crossed out the one-to-many entries and got 153135 oneto-one entries. Secondly the entries were cross-matched with qso.dat of the Véron-Cetty & Véron 2006 catalog and the Tycho-2 catalog within 5 arcsecond radius, respectively.
Similarly not considering the one-to-many entries, we obtained 2389 quasars and 1353 stars from the 2MASS and FIRST catalogues. The chosen attributes from different bands are logF peak (F peak: peak flux density at 1.4 GHz), logF int (F int: integrated flux density at 1.4 GHz), f maj (fitted major axis before deconvolution), f min (fitted minor axis before deconvolution), f pa (fitted position angle before deconvolution), j − h (near infrared index), h−k (near infrared index), k+2.5logF int, k+2.5logF peak, j+2.5logF peak, j + 2.5logF int. To see the statistical properties of this sample, the mean values of parameters are listed in Table 2. Meanwhile the distributions of parameters are shown in  Table 2, some mean values have rather large scatters. The values of logF peak, logF int, k + 2.5logF int, k + 2.5logF peak, j + 2.5logF peak, j + 2.5logF int for quasars are obviously bigger than those of stars. This means that quasars are generally stronger radio emitters than stars. In addition, the values of j − h and h − k of quasars are larger than those of stars, i.e. quasars are redder than stars. Moreover Table 1 and

Bayesian Belief Networks
The Bayesian Belief Network (BBN) is a powerful knowledge representation and reasoning tool under conditions of uncertainty. BBN is defined by two components. The first is a direct acyclic graph, where each node represents a random variable and each arc represents a probabilistic dependence (Pearl 1988;Neapolitan 1990;Han & Kamber 2001). If an arc is drawn from a node Y to a node Z, then Y is a parent or immediate predecessor of Z, and Z is a descendent of Y . Each variable is conditionally independent of its nondescendents in the graph, given its parents. The variables may be discrete or continuous-valued. They may correspond to actual attributes given in the data or to hidden variables believed to form a relationship. The second consists of one conditional probability table (CPT). The CPT for a variable Z specifies the conditional distribution P (Z|P arent(Z)), where parent(Z) are the parents of Z. The joint probability of any tuple (z 1 , ..., z n ) corresponding to the variables or attributes Z 1 , ...Z n is computed by where the values for P (z i |P arents(Z i )) correspond to the entries in the CPT for Z i . A node within the network can be selected as an output node, representing a class label attribute. There may be more than one output node. Inference algorithms for learning can be applied on the network. The classification process, rather than returning a single class label, can return a probability distribution for the class label attribute, that is predicting the probability of each class.

Multilayer Perceptron Networks
The Multilayer Perceptron (MLP) network is one of the most widely applied and investigated Artificial Neural Network model. MLP networks have been applied successfully to solve some difficult and diverse problems in training them in a supervised manner with a highly popular algorithm, known as the error back-propagation algorithm. The algorithm is based on the error-correction learning rule. MLP network model consists of a network of processing elements or nodes arranged in layers. Typically, it requires three or more layers of processing nodes: an input layer which accepts the input variables used in the classification procedure, one or more hidden layers, and an output layer with one node for one class. In fact, a network with just two hidden units using the tanh function can fit the data quite well. The fit can be further improved by adding yet more units to the hidden layer. However, that having too large a hidden layer -or too many hidden layerscan degrade the network's performance. In general, one shouldn't use more hidden units than necessary to solve a given problem. One way to ensure this is to start training with a very small network. If gradient descent fails to find a satisfactory solution, grow the network by adding a hidden unit, and repeat. MLP network is a general-purpose, Neural Networks is presented by Sarle (1994a), and on multilayer Perceptron by Bailer-Jones et al. (2001) and Sarle (1994b). A comprehensive treatment of feed-forward neural networks is provided by Bishop (1995).

Alternating Decision Tree
The alternating decision tree (ADTree) is a generalization of decision trees, voted decision trees and voted decision stumps. A general alternating tree defines a classification rule as follows. An instance defines a set of paths in the alternating tree. As in standard decision trees, when a path reaches a decision node it continues with the child which corresponds to the outcome of the decision associated with the node. However, when reaching a prediction node, the path continues with all of the children of the node. More precisely, the path splits into a set of paths, each of which corresponds to one of the children of the prediction node. We call the union of all the paths reached in this way for a given instance the "multi-path" associated with that instance. The sign of the sum of all the prediction nodes which are included in a multi-path is the classification which the tree associates with the instance. The principle of the algorithm is explained in Freund & Mason (1999).

EXPERIMENTS AND RESULTS
Our experiments were done with the WEKA machine learning package (Witten & Frank 2005). In the process of experimenting, the default configurations of BBN, MLP and ADTree are used. The computer used in this effort was a PC with a 3.4 GHZ Pentium 4 and CPU 1 GB memory. The operating system was Microsoft Windows XP. Here we use 10-fold cross-validation to evaluate the different accuracy of different models for this database. By comparing the accuracy of the classification and time taken to build models, we try to compare the efficiency and effectiveness of the models.

Cross-Validation
Cross-validation is the statistical practice of partitioning a sample of data into subsets such that the analysis is initially performed on a single subset, while the other subset (

Results
Using the 10-fold cross-validation method, we found the classification accuracy achieved with the different algorithms. The results are shown in Tables 3-6. Here MLP employs a three-layer topology, i.e. it includes one input layer, one hidden layer and one output layer. Applying ADTree technique on the two samples, the total number of nodes is 31 and the number of predictor nodes is 21. For any algorithm, the accuracy of quasars and stars is more than 88.0%. Considering the sample 1 (S1), correctly classified instances for BBN, MLP and ADTree are 3524, 3579 and 3553, respectively; as shown by Table   6, the corresponding whole accuracy for BBN, MLP and ADTree amounts to 94.17%, 95.64% and 94.95%, respectively; the running time to build models is 0.34 s, 25.14 s and 1.25 s, respectively. Similarly, given the sample 2 (S2), correctly classified instances for BBN, MLP and ADTree are 3531, 3585 and 3562, respectively; Table 6 shows that the corresponding whole accuracy for BBN, MLP and ADTree is 94.36%, 95.80% and 95.19%, respectively; the running time to build models is 0.28 s, 19.23 s and 0.86 s, respectively.
From the results, we conclude that BBN, MLP and ADTree are feasible to separate quasars from stars only considering the accuracy. When only considering the running time, BBN is the fastest, ADTree runs faster than MLP. If considering both accuracy and time, ADTree is the best approach. Tables 3-6 also indicate that compared to the S1, the accuracy and the speed to building the models for S2 all improve for different algorithms. This fact clearly shows that the effectiveness and efficiency of these models with feature selection are a little better than those without feature selection. In addition, the classification results indicate that it is applicable to preselect quasar candidates from the 2MASS and FIRST survey catalogues. The classifiers trained by these methods can be used to classify the unclassified sources.

CONCLUSIONS
Survey data are one important source of information for astronomers. By classification techniques, we can extract lots of information from the raw data. Here we analyzed a sample and compare the results with and without feature selection. When these algorithms with feature selection are applied, the accuracy all improves, and the speed to build models also accelerates, comparing to the results without feature selection.
Clearly appropriate feature selection may improve the effectiveness and efficiency of classifiers. For the given problem, BBN, MLP and ADTree models on this sample achieve higher accuracy, more than 94.0%. Only taking the accuracy into account, BBN, MLP and ADTree performed comparably. But BBN classifier has fast speed when applied to large databases, especially its speed is much faster than those of MLP and ADTree.
But in terms of both accuracy and speed, ADTree shows its superiority. In conclusion, these algorithms are robust and efficient methods for solving the classification problems faced in astronomy. The classifiers obtained by these methods may be used to preselect source candidates in which astronomers are interested. These techniques may be used on other types of astronomical data, such as spectral data and image data. Moreover they are also applied on other issues, for example star parameter measurement, redshift estimation of galaxies and quasars, morphology classification of galaxies. With the quantity, quality and complexity of astronomical data improving and the number of features increasing, selecting appropriate models and training the classifiers efficiently, as well as feature selection methods, is a challenging study for future research. Especially faced with large and multiwavelength sky surveys, automated methods can not only reduce astronomer's efforts, but also improve the efficiency of astronomers and high-cost telescopes; moreover effective feature selection methods reduce the dimensionality of space and improve the efficiency and effectiveness of automated classification algorithms, meanwhile they can make it possible for the application of some methods only employed in low dimensional spaces. The successful application of data mining in astronomical databases is the catalyzer to find unusual, rare or unknown objects and phenomenon.
Especially clustering analysis and outlier finding algorithms can facilitate class discovery in astronomy.