On the effects of dimensionality reduction on high dimensional similarity search

Abstract

The dimensionality curse has profound effects on the effectiveness of high-dimensional similarity indexing from the performance perspective. One of the well known techniques for improving the indexing performance is the method of dimensionality reduction. In this technique, the data is transformed to a lower dimensional space by finding a new axis-system in which most of the data variance is preserved in a few dimensions. This reduction may also have a positive effect on the quality of similarity for certain data domains such as text. For other domains, it may lead to loss of information and degradation of search quality. Recent research indicates that the improvement for the text domain is caused by the re-enforcement of the semantic concepts in the data. In this paper, we provide an intuitive model of the effects of dimensionality reduction on arbitrary high dimensional problems. We provide an effective diagnosis of the causality behind the qualitative effects of dimensionality reduction on a given dat a set. The analysis suggests that these effects are very data dependent. Our analysis also indicates that currently accepted techniques of picking the reduction which results in the least loss of information are useful for maximizing precision and recall, but are not necessarily optimum from a qualitative perspective. We demonstrate that by making simple changes to the implementation details of dimensionality reduction techniques, we can considerably improve the quality of similarity search.