Can Shared-Neighbor Distances Defeat the Curse of Dimensionality?

Abstract

Abstract. The performance of similarity measures for search, indexing, and data mining applications tends to degrade rapidly as the dimensionality of the data increases. The effects of the so-called 'curse of dimensionality' have been studied by researchers for data sets generated according to a single data distribution. In this paper, we study the effects of this phenomenon on different similarity measures for multiplydistributed data. In particular, we assess the performance of sharedneighbor similarity measures, which are secondary similarity measures based on the rankings of data objects induced by some primary distance measure. We find that rank-based similarity measures can result in more stable performance than their associated primary distance measures.

Vector Space Information Retrieval Techniques for Bioinformatics Data Mining

“…Regardless of the symbol set employed, it is clear that the approach described can lead to sparse elements embedded in high dimensional vector spaces. While data sets of this kind can be potentially problematic Beyer et al (1999); Hinneburg et al (2000); Houle et al (2010); Steinbach et al (2003), subspace dimension reduction techniques are derivable from LSI approaches such as the SVD. The IR techniques introduced above are readily applicable in any setting where bioinformatics data (sequence, structural, symbolic, etc) can be encoded.…”

Subspace Nearest Neighbor Search - Problem Statement, Approaches, and Discussion

“…This principle of a common set of N N in different dimensions is similar to the concept of the shared nearest neighbor distance [6] or consensus methods. The intuition is that the member dimensions of a subspace agree (to a certain minimum threshold) in their N N rankings, when considered individually.…”

A k-Deviation Density Based Clustering Algorithm

“…According to [14], the shared nearest neighborhood (SNN) method can be used due to its robustness in high dimension dataset. However, SNN is not efficient because of its complexity.…”