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

Handle URI:
http://hdl.handle.net/10754/596980
Title:
Data Analysis with the Morse-Smale Complex: The msr Package for R
Authors:
Gerber, Samuel; Potter, Kristin
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.
Citation:
Gerber S, Potter K (2012) Data Analysis with the Morse-Smale Complex: The msr Package for R . J Stat Soft 50. Available: http://dx.doi.org/10.18637/jss.v050.i02.
Publisher:
Foundation for Open Access Statistic
Journal:
Journal of Statistical Software
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
2012
DOI:
10.18637/jss.v050.i02
Type:
Article
ISSN:
1548-7660
Sponsors:
We thank Oliver Rubel for early tests and many bug reports as well as helpful discussions on the design of the package and Peter G. Lindstrom for providing us with the optimization data set. We thank the anonymous reviewers for their helpful comments and technical clarifications. This work was funded by the National Institute of Health grants U54-EB005149 and 2-P41- RR12553-08, NSF grant CCF-073222 and CNS-0615194, and Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorGerber, Samuelen
dc.contributor.authorPotter, Kristinen
dc.date.accessioned2016-02-23T13:51:42Zen
dc.date.available2016-02-23T13:51:42Zen
dc.date.issued2012en
dc.identifier.citationGerber S, Potter K (2012) Data Analysis with the Morse-Smale Complex: The msr Package for R . J Stat Soft 50. Available: http://dx.doi.org/10.18637/jss.v050.i02.en
dc.identifier.issn1548-7660en
dc.identifier.doi10.18637/jss.v050.i02en
dc.identifier.urihttp://hdl.handle.net/10754/596980en
dc.description.abstractIn 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.en
dc.description.sponsorshipWe thank Oliver Rubel for early tests and many bug reports as well as helpful discussions on the design of the package and Peter G. Lindstrom for providing us with the optimization data set. We thank the anonymous reviewers for their helpful comments and technical clarifications. This work was funded by the National Institute of Health grants U54-EB005149 and 2-P41- RR12553-08, NSF grant CCF-073222 and CNS-0615194, and Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherFoundation for Open Access Statisticen
dc.rightsThis work is licensed under the licenses Creative Commons Attribution 3.0 Unported Licenseen
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/en
dc.titleData Analysis with the Morse-Smale Complex: The msr Package for Ren
dc.typeArticleen
dc.identifier.journalJournal of Statistical Softwareen
dc.contributor.institutionUniversity of Utahen
kaust.grant.numberKUS-C1-016-04en
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