NDLI: Multiplicative distance: a method to alleviate distance instability for high-dimensional data

Content Provider	Springer Nature Link
Author	Mansouri, Jafar Khademi, Morteza
Copyright Year	2014
Abstract	Recently, it has been shown that under a broad set of conditions, the commonly used distance functions will become unstable in high-dimensional data space; i.e., the distance to the farthest data point approaches the distance to the nearest data point of a given query point with increasing dimensionality. It has been shown that if dimensions are independently distributed, and normalized to have zero mean and unit variance, instability happens. In this paper, it is shown that the normalization condition is not necessary, but all appropriate moments must be finite. Furthermore, a new distance function, namely multiplicative distance, is introduced. It is theoretically proved that this function is stable for data with independent dimensions (with identical or nonidentical distribution). In contrast to usual distance functions which are based on the summation of distances over all dimensions (distance components), the multiplicative distance is based on the multiplication of distance components. Experimental results show the stability of the multiplicative distance for data with independent and correlated dimensions in the high-dimensional space and the superiority of the multiplicative distance over the norm distances for the high-dimensional data.
Starting Page	783
Ending Page	805
Page Count	23
File Format	PDF
ISSN	02191377
Journal	Knowledge and Information Systems
Volume Number	45
Issue Number	3
e-ISSN	02193116
Language	English
Publisher	Springer London
Publisher Date	2014-12-28
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Distance instability High-dimensional data Minkowski and fractional norms Multiplicative and additive distances Information Systems and Communication Service IT in Business
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Information Systems Human-Computer Interaction Hardware and Architecture Software

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