Topological data analysis as a tool for classification of digital images

Abstract

Topological data analysis, as a branch of applied mathematics, is one of the newer areas that enable data analysis. The basic tool of this field is persistent homology, the main method of topological data analysis and it is used to process the data set in this article. Persistent homology is a method that detects the topological features of a space reconstructed from a data set. The application is illustrated on simple synthetic generated sets. In this article, we proposed and evaluated a new model that includes topological features into the classification process in real data sets composed of digital images. We got results in which there are some improvements in most of the statistical values for the classification performance over a model that does not include these topological features.