Invariant Method in Topological Data Analysis (A Paradigm on Data Shape Approach)

This paper works as a motivation to consider stronger methods in TDA (Topological Data Analysis). We discuss some of the main principles used currently in Big Data analysis. This discussion points became evident while we apply TDA to Big Data. Mathematical formal concepts might be considered, in order, to obtain better results from Data Analysis. Among these arguable principles, it may be considered “data grouping methods”, and also “relation data base-graph and its connection”. We discuss the topological argument, which stands as a powerful tool on Big Data analysis and TDA, from “inverse numbers” methodology, and we present a qualitative description of “Invariant Method” which we think is a strong methodology in order to obtain valuable hidden information from Big Data sets. Furthermore, we propose an algorithm to invariant method