Cubical Homology-Based Machine Learning: An Application in Image Classification

Persistent homology is a powerful tool in topological data analysis (TDA) to compute, study, and encode efficiently multi-scale features being increasingly used digital image classification. The represent number of connected components, cycles, voids that describe the shape data. extracts birth death these through filtration process. lifespan can be represented using persistent diagrams (topological signatures). Cubical more efficient method for extracting from 2D uses collection cubes compute homology, which fits structure grids. In this research, we propose cubical homology-based algorithm images generate their signatures. Additionally, novel score measure, measures significance each sub-simplices terms persistence. addition, gray-level co-occurrence matrix (GLCM) contrast limited adapting histogram equalization (CLAHE) are as supplementary methods features. Supervised machine learning models trained on selected datasets study efficacy extracted Among eight tested with six published varying pixel sizes, classes, distributions, our experiments demonstrate deep residual network (ResNet 1D) Light Gradient Boosting Machine (lightGBM) shows promise