Study on proximal support vector machine as a classifier

Abstract

Proximal Support Vector machine based on Least Mean Square Algorithm classi-fiers (LMS-SVM) are tools for classification of binary data. Proximal Support Vector
based on Least Mean Square Algorithm classifiers is completely based on the theory of Proximal Support Vector Machine classifiers (PSVM). PSVM classifies binary pat-
terns by assigning them to the closest of two parallel planes that are pushed apart as far as possible. The training time for the classifier is found to be faster compared to their previous versions of Support Vector Machines. But due to the presence of slack variable or error vector the classification accuracy of the Proximal Support Vector Machine is less. So we have come with an idea to update the adjustable weight vectors at the training phase such that all the data points fall out-side the region of separation and falls on the correct side of the hyperplane and to enlarge the width of the separable region.To implement this idea, Least Mean Square (LMS) algorithm is used to modify the adjustable weight vectors. Here, the error is represented by the minimum distance of data points from the margin of the region of separation of the data points that falls inside the region of separation or makes a misclassification and distance of data points from the separating hyperplane for the data points that falls on the wrong side of the hyperplane. This error is minimized using a modification of adjustable weight vectors. Therefore, as the number of iterations of the LMS algorithm increases, weight vector performs a random walk (Brownian motion) about the solution of optimal hy-perplane having a maximal margin that minimizes the error. Experimental results show that the proposed method classifies the binary pattern more accurately than classical Proximal Support Vector Machine classifiers.