Dimension reduction by a novel unified scheme using divergence analysis and genetic search

In this study, a unified scheme using divergence analysis and genetic search is proposed to determine significant components of feature vectors in high-dimensional spaces, without having to deal with singular matrix problems. In the literature it is observed that three main problems exist in the feature selection process performed in a high-dimensional space. These problems are high computational load, local minima, and singular matrices. In this study, feature selection is realized by increasing the dimension one by one, rather than reducing the dimension. In this sense, the recursive covariance matrices are formulated to decrease the computational load. The use of genetic algorithms is proposed to avoid local optima and singular matrix problems in high-dimensional feature spaces. Candidate strings in the genetic pool represent the new features formed by increasing the dimension. The genetic algorithms investigate the combination of features which give the highest divergence value. In this study, two methods are proposed for the selection of features. In the first method, features in a high-dimensional space are determined by using divergence analysis and genetic search (DAGS) together. If the dimension is not high, the second method is offered which uses only recursive divergence analysis (RDA) without any genetic search. In Section 3 two experiments are presented: Feature determination in a two-dimensional phantom feature space, and feature determination for ECG beat classification in a real data space.