Geometrical correlation indices using homological constructions on manifolds

Abstract

Abstract The course of dimensionality is a common problem in statistics and data analysis. Variable sensitivity analysis methods are a well studied and established set of tools designed to overcome these sorts of problems. However, as this work shows, these methods fail to capture relevant features and patterns hidden within the geometry of the enveloping manifold projected into a variable. We propose an index that captures, reflects and correlates the relevance of distinct variables within a model by focusing on the geometry of their projections. The analysis was made with an original R-package called TopSA, short for Topological Sensitivity Anal- ysis. The TopSA R-package is available on the site https://github.com/maikol- solis/TopSA.