Data Analysis with the Morse-Smale Complex: The msr Package for R

Abstract

In many areas, scientists deal with increasingly high-dimensional data sets. An important aspect for these scientists is to gain a qualitative understanding of the process or system from which the data is gathered. Often, both input variables and an outcome are observed and the data can be characterized as a sample from a high-dimensional scalar function. This work presents the R package msr for exploratory data analysis of multivariate scalar functions based on the Morse-Smale complex. The Morse-Smale complex provides a topologically meaningful decomposition of the domain. The msr package implements a discrete approximation of the Morse-Smale complex for data sets. In previous work this approximation has been exploited for visualization and partition-based regression, which are both supported in the msr package. The visualization combines the Morse-Smale complex with dimension-reduction techniques for a visual summary representation that serves as a guide for interactive exploration of the high-dimensional function. In a similar fashion, the regression employs a combination of linear models based on the Morse-Smale decomposition of the domain. This regression approach yields topologically accurate estimates and facilitates interpretation of general trends and statistical comparisons between partitions. In this manner, the msr package supports high-dimensional data understanding and exploration through the Morse-Smale complex.