Geometric goodness of fit measure to detect patterns in data point clouds
Loading...
Date
Authors
Hernández Alvarado, Alberto José
Solís Chacón, Maikol
Zúñiga Rojas, Ronald Alberto
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The curse of dimensionality is a commonly encountered 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 onto a variable. Here 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. We construct the 2-simplices of a Vietoris-Rips complex
and then estimate the area of those objects from a data-set cloud. The analysis was made
with an original R-package called TopSA, short for Topological Sensitivity Analysis. The
TopSA R-package is available at the site https://github.com/maikol-solis/TopSA.
Description
Keywords
Goodness of fit, R2, Vietoris-Rip complex, Manifolds, Area estimation
Citation
http://jmlr.org/papers/v20/