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

Mansouri, Jafar; Khademi, Morteza

doi:10.1007/s10115-014-0813-4

Cited by 6 publications

(4 citation statements)

References 39 publications

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“…This holds for any distribution used to sample Z, X i . This result, first presented in Beyer et al (1998) and subsequently discussed in a number of papers (Hinneburg et al 2000;Aggarwal et al 2001;François et al 2007;Durrant and Kabán 2009;Radovanović et al 2010;Mansouri and Khademi 2015;Flexer and Schnitzer 2015), appears to jeopardize all of the material presented in this survey, and much more beyond. The phenomenon leading to the result is known as distance instability and concentration of distances.…”

Section: Distance Instabilitymentioning

confidence: 64%

“…(48) is not verified, and propose them as "good" examples of where k-means can help. In Mansouri and Khademi (2015), the authors propose multiplicative functions and show that they are robust with respect to distance instability. In Radovanović et al (2010), distance instability is related to "hubness", i.e., the number of times a point appears among the k nearest neighbors of other points.…”

Section: Related Resultsmentioning

confidence: 99%

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Distance geometry and data science

Liberti

2020

TOP

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Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in vectorial form. In this survey, we discuss the fundamental problem of mapping graphs to vectors, and its relation with mathematical programming. We discuss applications, solution methods, dimensional reduction techniques, and some of their limits. We then present an application of some of these ideas to neural networks, showing that distance geometry techniques can give competitive performance with respect to more traditional graph-to-vector mappings.

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Section: Distance Instabilitymentioning

confidence: 64%

Section: Related Resultsmentioning

confidence: 99%

Distance geometry and data science

Liberti

2020

TOP

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“…( 48) is not verified, and propose them as "good" examples of where k-means can help. In [128], the authors propose multiplicative functions dist and show that they are robust w.r.t. distance instability.…”

Section: Related Resultsmentioning

confidence: 99%

“…This holds for any distribution used to sample Z, X i . This result, first presented in [27] and subsequently discussed in a number of papers [86,3,73,64,157,128,70], appears to jeopardize all of the material presented in this survey, and much more beyond. The phenomenon leading to the result is known as distance instability and concentration of distances.…”

Section: Distance Instabilitymentioning

confidence: 88%

Distance Geometry and Data Science

Liberti¹

2019

Preprint

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Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in vectorial form. In this survey we discuss the fundamental problem of mapping graphs to vectors, and its relation with mathematical programming. We discuss applications, solution methods, dimensional reduction techniques and some of their limits. We then present an application of some of these ideas to neural networks, showing that distance geometry techniques can give competitive performance with respect to more traditional graph-to-vector mappings.

show abstract