Development of an Agreement Metric Based Upon the RAND Index for the Evaluation of Dimensionality Reduction Techniques, with Applications to Mapping Customer Data

Authors:
Stephen France;Douglas Carroll
Affiliations:
Rutgers University, Graduate School of Management, Newark, New Jersey, 07102-3027,;Rutgers University, Graduate School of Management, Newark, New Jersey, 07102-3027,
Venue:
MLDM '07 Proceedings of the 5th international conference on Machine Learning and Data Mining in Pattern Recognition
Year:
2007

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Abstract

We develop a metric 茂戮驴, based upon the RAND index, for the comparison and evaluation of dimensionality reduction techniques. This metric is designed to test the preservation of neighborhood structure in derived lower dimensional configurations. We use a customer information data set to show how 茂戮驴can be used to compare dimensionality reduction methods, tune method parameters, and choose solutions when methods have a local optimum problem. We show that 茂戮驴is highly negatively correlated with an alienation coefficient K that is designed to test the recovery of relative distances. In general a method with a good value of 茂戮驴also has a good value of K. However the monotonic regression used by Nonmetric MDS produces solutions with good values of 茂戮驴, but poor values of K.