Classification And Analysis Of Clustered Non-Linear Separable Data Set Using Support Vector Machines

Abstract

The Support Vector Machines is the pre-eminent methodology in supervised machine learning, is adeptly applied to classification tasks and extends its utility to regression challenges. SVMs endeavour to discern the optimal hyperplane for dichotomizing data into distinct classes. When confronted with clustered non-linearly separable data, the Nonlinear mapping function approach emerges as a strategic solution to enhance computational efficiency. By employing mapping functions, data is mapped into a feature space, thus revealing a discernible linear decision boundary for the categorization of non-linear data. In our research, the objective is to transmute clustered non-linearly separable data into a linearly separable format through developing the nonlinear mapping functions. We have illustrated an example in classifying the clustered nonlinear synthetic data which was generated using Generative Adversarial Network (GAN), enabling nonlinear models to adeptly represent the vector similarities within the feature space. Through the identification of nonlinear mapping functions denoted as Φ, the data undergoes transformation into a novel feature space where the discernment of the hyperplane separation becomes apparent. This nuanced approach not only provides a deeper understanding of the internal mechanics of these models but also facilitates the assessment of the pertinence of feature combinations.