Can unbounded distance measures mitigate the curse of dimensionality?. (1st January 2012)

• Record Type: Journal Article
• Authors: Jayaram, Balasubramaniam; Klawonn, Frank
• Is Part Of: International journal of data mining, modelling and management. Volume 4:Number 4(2012)
• Page Start: 361
• Page End: 383
• Publication Date: 2012-01-01
• Subjects: curse of dimensionality -- CoD -- nearest neighbour classifier -- cluster analysis; Data mining -- Periodicals; Information science -- Periodicals; Databases -- Periodicals; 005.7
• Languages: English
• ISSNs: 1759-1163

Abstract

In this work, we revisit the curse of dimensionality, especially the concentration of the norm phenomenon which is the inability of distance functions to separate points well in high dimensions. We study the influence of the different properties of a distance measure, viz., triangle inequality, boundedness and translation invariance and on this phenomenon. Our studies indicate that unbounded distance measures whose expectations do not exist are to be preferred. We propose some new distance measures based on our studies and present many experimental results which seem to confirm our analysis. In particular, we study these distance measures w.r.t. indices like relative variance and relative contrast and further compare and contrast these measures in the setting of nearest neighbour/proximity searches and hierarchical clustering.