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The application of cat swarm optimisation algorithm in classifying small loan performance

It is common for banking system to analyse the feasibility of credit application before its approval. Although this process has been carefully done, there is no warranty that all credits will be repaid smoothly. This study aimed to know the accuracy of Cat Swarm Optimisation (CSO) algorithm in classifying small loans’ performance that is approved by Bank Rakyat Indonesia (BRI), one of several public banks in Indonesia. Data collected from 200 lenders were used in this work. The data matrix consists of 9 independent variables that represent profile of the credit, and one categorical dependent variable reflects credit’s performance. Prior to the analyses, data was divided into two data subset with equal size. Ordinal logistic regression (OLR) procedure is applied for the first subset and gave 3 out of 9 independent variables i.e. the amount of credit, credit’s period, and income per month of lender proved significantly affect credit performance. By using significantly estimated parameters from OLR procedure as the initial values for observations at the second subset, CSO procedure started. This procedure gave 76 percent of classification accuracy of credit performance, slightly better compared to 64 percent resulted from OLR procedure.


Introduction
Extracting valuable information such as recognising pattern from hidden data is one aim of data mining technique. This technique belongs to multidisciplinary field that intersects statistical methods, machine learning, pattern recognition, and data visualisation. One purpose in data mining technique is classifying objects based on their attribute(s). The classification problem can be veiewed as a problem to classify objects into a set of clusters without any priori knowledge [1].
To classify an object into its appropriate group can be done by several methods. Among these methods, K -means algorithm is very popular. Despite of its popularity, refers to [2], the major drawback of this algorithm is frequently found it gets stuck at local minima and classification results is heavily depended on the choice of initial cluster center. To overcome this limitation, some alternative techniques in classifying objects were developed. Metaheuristic algorithms such as genetic algorithm as well as particle swarm optimisation had been operationalised to classify objects regarding their attribute(s) [3] [4].
This work implements Cat Swarm Optimisation (CSO) algorithm in classifying small loans performance were approved by Bank Rakyat Indonesia, one of several public bank in Indonesia. CSO is belonged to swarm intelligence method that models cats behavior in solving optimisation problem [5]. Researchers  but to our best knowledge, CSO is rarely used to classify financial data. In addition, to elaborate its performance, we used Ordinal Logistic Regression (OLR) to predicts loan's classification from the loan's attributes. Chu and Tsai [5] propose CSO as a new metaheuristic technique in optimisation problems by observing the behavior of cats. Basically, CSO algorithm consists of two states of cats, namely (a) seeking mode, represents cats during a resting period but being alert, and (b) tracing mode, represents mode of cats while tracing their target. According to [5], cats which are awake spend most of their time resting and spend very little time to chase target. The proportion on cats in tracing mode is defined as mixture ratio (MR).

Research Method
The small loan data from 200 lenders for this work were acquired from Bank Rakyat Indonesia, Melati branch office at Denpasar. The data consists of 9 independent variables represent credit's profile and one categorical dependent variable represents the performance of credit. The operational definition of the variables is listed on Table 1.
Prior to analysis stage, the data is randomly divided into two subset with equal size. In order to make fair comparison, before OLR and CSO algorithm were applied, we check the proportion of loans are classified as smoothly paid, less smoothly, and doubtful in each of data subset. The maximum proportion differences is allowed for same classification between subset is five percent. The first subset is analysed with OLR technique to identify influential variables in determining performance of credit, and the second subset is analysed using CSO algorithm with number of dimensions to move is determined by the number of influential variables that is identified with the OLR. The last stage is to compare the classification accuracy is resulted from both techniques. Classification accuracy of both methods were counted through the Apparent Correct Classification Rate (ACCR) measure [6], which is stated by equation In equation (1), N represents total observation numbers, n i is the number of observations were correctly classified in class i, and c represents number of class.

OLR Analysis
OLR is an extension of binary logistic regression (BLR). OLR as well as BLR utilised maximum likelihood method to estimate the parameters of regression model [5]. Using STATA to analyse the first subset data, we obtained three out of nine predictor variables significantly affect small loan performance. The OLR's result is listed on Table 2. The Nagelkerke pseudo R 2 showed the variance of loan's performance can be explained by its predictors as much as 61.5 per cent while the rest is unexplained.
The number of small loan performance were predicted correctly by using this OLR model as smoothly, less smoothly, and doubtful credits are 34, 24, and 6 observation respectively. By applying eq. (1), the classification accuracy is resulted from OLR method as much as 64 per cent.

CSO Analysis
Arbitrary, we create 30 cats in our work. In initialisation stage, these cats were randomly assigned between tracing and seeking mode according to MR value. As aforementioned explain, in seeking mode where cats are in resting period, four factors have to be considered and defined as follows [  The computational steps of cat in seeking mode can be listed as follows [5][6]: (i) Create n copies of current position of cat i , n = SMP. If SPC = 1 then n = n -1; (ii) For each of dimension according to CDC's value, replace the SR's old value for each cat with randomly plus or minus x percent of the old value; (iii) Randomly select point to move to from the candidates points and replace the position of cat i .
Once cat i goes into tracing mode, its steps can be listed as follows: (i) Update its velocities for every dimension to consider (CDC) according to equation (2) v

CSO Result
To make fair comparison with OLR technique, we position each cat in five dimensional space (R 5 ). These dimensions represents two constants and three significant variables according to OLR analysis. The values from OLS analysis were applied as initial positions in each dimensions of cat. In applying CSO algorithm to classify the loan performance, we set the minimum, increment, and maximum values for CSO's parameters as follows: After 2000 iterations, for 30 cats and using c 1 = 2 as suggested by [6] we found the best parameter for MR, SR, SMP, and CDC values in our work are 0.20, 0.50, 3, and 0.20 respectively. Refers to Table 3, the classification accuracy result from CSO method as much as 76 percent, slightly greater than 64 percent was obtained from OLR technique.

Conclusion
The application of CSO algorithm in classifying small loan performance by utilizing the significantly estimated parameters from OLR technique proved can increase the classification accuracy. This finding is inline with similar experiment result conducted by [7] in classifying gene expression data. Kumar and Mishra utilised CSO method to update the gene's weight values resulted from Principal Component Analysis (PCA) and Factor Analysis (FA) for high dimensionality of the datasets.
As a metaheuristic algorithm, CSO and other swarm optimisation techniques were known as an efficient and effective global search tehnique. However, CSO has never been investigated its  performance according to the characteristics of object under studied. We showed by eliminating unsignificant variables in small loan classification process, the classification accuracy increase. Despite of its performance to classify small loan data is better than OLR method, CSO as well as other particle swarm optimisation techniques, its theoretical background is rather weak. Refers to [8], PSO algorithm has a limited condition for the particle(s) move stable from the point of math's.