The Danger of Dimensionality Reduction

The problem known as the "curse of dimensionality" (Bellman, 1961) has been given a great deal of attention by researchers in the database and data mining community.  As a counter-measure, many dimensionality reduction techniques have been proposed, and it has been shown that when done properly, the properties or structures of the objects can be well preserved even in the lower dimensions. Nevertheless, naively applying dimensionality reduction can lead to pathological results.
We have prepared some materials to illustrate the dangers of dimensionality reduction. In particular, we have created a simple 3-D dataset that has dramatically different (and visually striking) projections onto various subspaces. In addition, we have a related example that illustrates problems of clustering on subspaces.

(The code/demo provided on this page are made freely available for non-commercial, educational uses; however, if you use them, we would appreciate an email telling us where/when you used them, and we would also appreciate you linking to this site to help others to find this resource.)

View this page in Romanian (Courtesy of azoft)


 Example 1

 Example 2


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Page last updated: Dec 28, 2003