Published:

Abstract-Data classification is an important area of data mining. Several well known techniques such as Decision tree, Neural Network, etc. are available for this task. In this paper we propose a Kalman Particle Swarm Optimized (KPSO) Polynomial equation for classification for several well known data sets. Our proposed method is derived from some of the findings of the valuable information like number of terms, number and combination of features in each term, degree of the polynomial equation etc. of our earlier work on data classification using Polynomial Neural Network. The KPSO optimizes these polynomial equations with a faster convergence speed unlike PSO. The polynomial equation that gives the best performance is considered as the model for classification. Our simulation result shows that the proposed approach is able to give competitive classification accuracy compared to PNN in many datasets.

Keywords-Polynomial Neural Network, Group Methods Of Data Handling, Particle Swarm Optimization ,Kalman Filter

## 1. Introduction

Different parametric and nonparametric approaches like NN, Decision tree; SVM, etc are used extensively for pattern recognition [1-9]. Quite a few approaches are there which produce mathematical models for pattern recognition/data classification tasks. Group Method of data handling (GMDH) based Polynomial Neural Network (PNN) is a popular approach for evolving a short-term polynomial equation for data classification. The short-term polynomial equation is developed taking into account the features of the data sets as input to the PNN. The degree of the polynomials, the number of terms in the polynomial equations and number of features and type of features are determined based on algorithm used for PNN. We have investigated [10] the approach of PNN with different real world data sets. Although this approach is a suitable one but it involves a great deal of computational complexity in terms of time and memory requirements to evolve the polynomial equations to achieve desired classification performance. In this paper we suggest a suitable approach of developing mathematical models in terms of polynomial equations using Kalman Particle Swarm Optimized (KPSO) techniques which is comparatively less complex than PNN providing competitive performance. The KPSO has a fast convergence time compared to basic PSO. The KPSO is based on the principle of Extended Kalman Filtering (EKF)[11-13]. The degree of polynomials, number of terms in the equation and the variables in the equation (i.e. features) are randomly chosen in suitable ranges for developing the model using PSO technique. The ranges are determined from our experience of developing models using PNN approach [10]. Our derived polynomial equations using KPSO are found to be computationally less expensive and the performance is competitive with PNN approach. We have taken few data sets like Iris, Diabetes etc to justify the above.

The section II describes the PNN approach and the motivation for our proposed model. The basic PSO and KPSO are discussed in section III. Section IV and section V describe our model and simulation results respectively. Finally conclusion and further enhancements are given in the section VI.