Dependence maps, a dimensionality reduction with dependence distance for high-dimensional data

Authors:
Kichun Lee;Alexander Gray;Heeyoung Kim
Affiliations:
Industrial Engineering, Hanyang University, Seoul, Republic of Korea 133-791;College of Computing, Georgia Institute of Technology, Atlanta, USA 30332-0205;Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA 30332-0205
Venue:
Data Mining and Knowledge Discovery
Year:
2013

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Abstract

We introduce the dependence distance, a new notion of the intrinsic distance between points, derived as a pointwise extension of statistical dependence measures between variables. We then introduce a dimension reduction procedure for preserving this distance, which we call the dependence map. We explore its theoretical justification, connection to other methods, and empirical behavior on real data sets.