Local multidimensional scaling

Authors:
Jarkko Venna;Samuel Kaski
Affiliations:
Adaptive Informatics Research Centre, Helsinki University of Technology, TKK, Finland;Adaptive Informatics Research Centre, Helsinki University of Technology, TKK, Finland
Venue:
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Year:
2006

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Abstract

In a visualization task, every nonlinear projection method needs to make a compromise between trustworthiness and continuity. In a trustworthy projection the visualized proximities hold in the original data as well, whereas a continuous projection visualizes all proximities of the original data. We show experimentally that one of the multidimensional scaling methods, curvilinear components analysis, is good at maximizing trustworthiness. We then extend it to focus on local proximities both in the input and output space, and to explicitly make a user-tunable parameterized compromise between trustworthiness and continuity. The new method compares favorably to alternative nonlinear projection methods.