International Journal of Computer Applications (0975 – 8887) Volume 64– No.18, February 2013 9 Fuzzy Weighted Gaussian Mixture Model for Feature Reduction Charles.S Assistant Professor Department of Computer Science St. Joseph’s College, Tiruchirappalli L. Arockiam Associate Professor Department of Computer Science St. Joseph’s College, Tiruchirappalli ABSTRACT Feature reduction is one kind of pattern recognition and decision making technique, which can be achieved by using Fuzzy Weighted Gaussian Mixture Model (FWGMM) based on the Gaussian Mixture Model. This model helps to find relevant features by using Fuzzy ordered weighted average, which leads to determine the similarity of the density mixture. The salient feature of this approach is to find the relevant features simultaneously by employing fuzzy weighted approach. By applying Ordered Weighted Average (OWA), the feature weights are calculated and they are ordered using the membership values (oring criterion). Hence the feature weights are used as a regulator to determine the relevant features in feature reduction process. Maximum Ordered Weighted Average Likelihood (MOWAL) Framework adopts the Fuzzy Weighted – Gaussian Mixture Model (FW-GMM) for finding the component, which helps to discriminate the relevance of the features and improve the accuracy of density mixture. Keywords : GMM, OWA, FW-GMM 1. INTRODUCTION In feature reduction, a number of techniques are proposed to select the relevant features from the datasets. In this paper, the features are selected based on weight w i є[0,1] using Maximum Weighted Likelihood framework. It is one of the promising techniques to identify the features which are relevant. In review of literature, the common weight finding mechanism is not available for selecting the relevance of features in GMM. So the features are selected using Ordered Weighted Average (OWA) approach by applying fuzzy decision technique. Fuzzy decision making process is an efficient method compared with other estimation approaches under incomplete or uncertain information. The OWA based ordered weighting can be applied to weigh the features by using membership values. Hence, Gaussian Mixture Model also plays a vital role in the form clustering initialization and it is trained by the Expectation Maximization Technique. The process stops until the relative log-likelihood is obtained by applying the preset threshold. The density of component Mixture is improved by applying fuzzy weighted approach and thereby identifying relevant features and reducing the feature subset. 2. REVIEW OF LITERATURE In feature reduction, various approaches are employed for reducing the features by using the filter, wrapper and hybrid approach. One of the approaches is called Semi Supervised which identifies the features. In this approach, information theory analysis was employed and symmetry cross entropy distance measure was used to measure the difference of two random variables. The average symmetry cross entropy was used to measure the difference in degree of a multi-class problem [1]. Various methods were employed for the classification problem and seven feature selection techniques were used for evaluating imbalanced data sets. The receiver operating characteristic and area under the precision-recall curve metric can be used for finding the average performance for all classes. The likelihood metric was used to predict the performance of the model. The results revealed that very small number of features are selected using this approach for prediction [2].The wrapper approach was applied to evaluate the feature subset. And the performance was good compared to the earlier approaches but, the searching strategy of finding the feature subset stops with local maxima [3,4]. The feature saliency was measured in the form of relevance by applying the unequal weights. The likelihood criterion optimized the feature reduction by using weights in Expectation Maximization algorithm [5].The weights were introduced in the Maximum Weighted Likelihood framework, which yielded the component mixture and discriminated the features based on the relevance in the feature space [6]. The OWA optimization can be used into a mixed integer programming problem with monotonic weights, which were employed for higher dimensions [7]. 3. MOTIVATION 3.1 Weighted likelihood Estimation (WLE) The different weights are assigned to different samples, which are merged as relevant information into WLE function. The WLE for implication on α is defined as, WL (α) = L 1 ( x 1 , x 2 ,……x n ; α) λ1 L 1 ( x 1 , x 2 ,……x n ; α) λ2 (1) where λ1 and λ2 are weights and they are used for finding the relevance of the likelihood. The non-negative weights are used for the experiment which is optimum. L1(x1, x2,...xn; α) can be used instead of L2 ( x1, x2,……xn; β), which defines WL(α). This value is used as a marginal distribution of X’s and Y’s. The WL value depends on the X’s and it doesn’t depend on Y’s distributions. The value of X’s and Y’s are not independent and the weights of the likelihood function are modelled as the dependent one, which are not expressed in the marginals. Maximum Weighted Likelihood Estimator is obtained from likelihood function by maximizing the weights λ1 and λ2.