Evaluating a class of distance-mapping algorithms for data mining and clustering

Abstract

A distance-mapping algorithm takes a set of objects and a distance metric and then maps those objects to a Euclidean or pseudoEuclidean space in such a way that the distances among objects are approximately preserved. Distance mapping algorithms are a useful tool for clustering and visualization in data intensive applications, because they replace expensive distance calculations by sum-of-square calculations.This can make clustering in large databases with expensive distance metrics practical.In this paper we present five distance-mapping algorithms and conduct experiments to compare their performance in data clustering applications.These include two algorithms called FastMap and MetricMap, and three hybrid heuristics that combine the two algorithms in different ways. Experimental results on both synthetic and RNA data show the superiority of the hybrid algorithms. The results imply that FastMap and MetricMap capture complementary information about distance metrics and therefore can be used together to great benefit. The net effect is that multi-day computations may be done in minutes. *

A privacy-preserving technique for Euclidean distance-based mining algorithms using Fourier-related transforms

“…However, there exist algorithms as presented in [39] that can accurately map arbitrary distance functions to Euclidean distance domain as a baseline to simplify complicated distance function calculations. Given a set of objects and a distance function that could be non-Euclidean, these algorithms map these objects into a Euclidean space such that the distances between these objects are approximately preserved.…”

“…Given a set of objects and a distance function that could be non-Euclidean, these algorithms map these objects into a Euclidean space such that the distances between these objects are approximately preserved. Experimental results in [39] show that for several data sets, these mapping algorithms preserve distances to a high degree such that the mapping introduces small error (less than 10%) for clustering. Thus, the algorithms presented in this paper can potentially be generalized to -This paper proposes a solution to a centralized database case where coefficient information about a data set is transmitted to a third party mining engine.…”

Indexing Issues in Supporting Similarity Searching

“…In particular, methods have been devised for deriving "features" purely based on the inter-object distances [25,26,27,28]. Thus, given N objects, the goal is to choose a value of k and find a set of N corresponding points in a k-dimensional space so that the distance between the N corresponding points is as close as possible to that given by the distance function for the N objects.…”

Eigensolver Methods for Progressive Multidimensional Scaling of Large Data

“…It was addressed as early as in the 1960s [23], and since then, many approaches to speeding up spring-force computations have been devised [6,16,25,26]. Likewise, methods for speeding up the spectral methods have been proposed [11,31]. Closest to our approach is Landmark MDS [10]; we give an experimental comparison in Sect.…”