Deflating the dimensionality curse using multiple fractal dimensions

Pagel, Bernd-Uwe; Korn, Flip; Faloutsos, Christos

doi:10.1109/icde.2000.839457

Cited by 71 publications

(47 citation statements)

References 28 publications

(36 reference statements)

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“…For spatial queries, the observation that the intrinsic dimensionality of a data set in many cases is lower than the representational dimensionality (due to interdependencies among attributes) is often presented as a justification of strategies for obviating the curse of dimensionality [31][32][33][34]. It should be noted that there are scenarios where correlations among attributes do exist, but the problem of discrimination of distances still applies [1].…”

Section: Problem 3: Presence Of Redundant Attributes Similarly As Witmentioning

confidence: 99%

Can Shared-Neighbor Distances Defeat the Curse of Dimensionality?

Houle

Kriegel

Kröger

et al. 2010

Lecture Notes in Computer Science

213

153

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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.

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Section: Problem 3: Presence Of Redundant Attributes Similarly As Witmentioning

confidence: 99%

Can Shared-Neighbor Distances Defeat the Curse of Dimensionality?

Houle

Kriegel

Kröger

et al. 2010

Lecture Notes in Computer Science

213

153

View full text Add to dashboard Cite

show abstract

“…In general, none of these definitions readily lend themselves to measurement; however, for self-similar sets, the fractal dimension provides a reasonable estimation method. The fractal dimension has been shown to facilitate selectivity estimation, range queries [4,8], nearest-neighbor queries [2,3,6], similarity searches [2], dimensionality reduction [10], outlier detection [7], and other applications.…”

Section: Introductionmentioning

confidence: 99%

Fast estimation of fractal dimension and correlation integral on stream data

Wong

Gibbons

et al. 2005

Information Processing Letters

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“…Numerous methods have been proposed for finding cost models for high dimensional index structures with different focus from our work [1,4,16,29,12,21,10,20,25,18].…”

Section: Related Workmentioning

confidence: 99%