Samuel Gerber and Kristin Potter, Data Analysis with the Morse-Smale
Complex: The msr Package for R. Submitted to Journal of Statistical
Software. ABSTRACT: In many ares scientists deal with increasingly high dimensional data sets of increasing dimensionality. An important aspect for the 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 an R package for the 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 which can be exploited for visualization and partition-based regression. The visualization combines Morse-Smale complex with dimension-reduction techniques for visual summary representation serving as a guide for interactive exploration of the high dimensional function. In a similiar fashion, the regression employs a combination of linear models based on the Morse-Samle decomposition of the domain. This 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 use of the Morse-Smale complex. |
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