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

posted Nov 1, 2011, 5:13 PM by Teng-Yok Lee
Samuel Gerber and Kristin Potter, Data Analysis with the Morse-Smale Complex: The msr Package for R. Submitted to Journal of Statistical Software.

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.