Geometric goodness of fit measure to detect patterns in data point clouds
Fecha
2019
Tipo
artículo preliminar
Autores
Hernández Alvarado, Alberto José
Solís Chacón, Maikol
Zúñiga Rojas, Ronald Alberto
Título de la revista
ISSN de la revista
Título del volumen
Editor
Resumen
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.
Descripción
Palabras clave
Goodness of fit, R2, Vietoris-Rip complex, Manifolds, Area estimation