Gaussian Pyramid for Nonlinear Support Vector Machine

Abstract

Support vector machine (SVM) is one of the most efficient machine learning tools, and it is fast, simple to use, reliable, and provides accurate classification results. Despite its generalization capability, SVM is usually posed as a quadratic programming (QP) problem to find a separation hyperplane in nonlinear cases. This needs huge quantities of computational time and memory for large datasets, even for moderately sized ones. SVM could be used for classification tasks whose number of samples is limited but does not scale well to large datasets. The idea is to solve this problem by a smoothing technique to get a new smaller dataset representing the original one. This paper proposes a fast and less time and memory-consuming algorithm to solve the problems represented by a nonlinear support vector machine tool, based on generating a Gaussian pyramid to minimize the size of the dataset. The reduce operation between dataset points and the Gaussian pyramid is reformulated to get a smoothed copy of the original dataset. The new dataset points after passing the Gaussian pyramid will be closed to each other, and this will minimize the degree of nonlinearity in the dataset, and it will be 1/4 of the size of the original large dataset. The experiments demonstrate that our proposed techniques can reduce the classical SVM tool complexity, more accurately, and are applicable in real time.