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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.

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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