The majorization approach to multidimensional scaling for Minkowski distances

Patrick J.F. Groenen; Rudolf Mathar; Willem J. Heiser

doi:10.1007/BF01202265

The majorization approach to multidimensional scaling for Minkowski distances

Patrick J.F. Groenen^*, Rudolf Mathar, Willem J. Heiser

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

54 Citations (Scopus)

Abstract

The majorization method for multidimensional scaling with Kruskal's STRESS has been limited to Euclidean distances only. Here we extend the majorization algorithm to deal with Minkowski distances with 1≤p≤2 and suggest an algorithm that is partially based on majorization for p outside this range. We give some convergence proofs and extend the zero distance theorem of De Leeuw (1984) to Minkowski distances with p>1.

Original language	English
Pages (from-to)	3-19
Number of pages	17
Journal	Journal of Classification
Volume	12
Issue number	1
DOIs	https://doi.org/10.1007/BF01202265
Publication status	Published - Mar 1995

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title = "The majorization approach to multidimensional scaling for Minkowski distances",

abstract = "The majorization method for multidimensional scaling with Kruskal's STRESS has been limited to Euclidean distances only. Here we extend the majorization algorithm to deal with Minkowski distances with 1≤p≤2 and suggest an algorithm that is partially based on majorization for p outside this range. We give some convergence proofs and extend the zero distance theorem of De Leeuw (1984) to Minkowski distances with p>1.",

author = "Groenen, {Patrick J.F.} and Rudolf Mathar and Heiser, {Willem J.}",

year = "1995",

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T1 - The majorization approach to multidimensional scaling for Minkowski distances

AU - Groenen, Patrick J.F.

AU - Mathar, Rudolf

AU - Heiser, Willem J.

PY - 1995/3

Y1 - 1995/3

N2 - The majorization method for multidimensional scaling with Kruskal's STRESS has been limited to Euclidean distances only. Here we extend the majorization algorithm to deal with Minkowski distances with 1≤p≤2 and suggest an algorithm that is partially based on majorization for p outside this range. We give some convergence proofs and extend the zero distance theorem of De Leeuw (1984) to Minkowski distances with p>1.

AB - The majorization method for multidimensional scaling with Kruskal's STRESS has been limited to Euclidean distances only. Here we extend the majorization algorithm to deal with Minkowski distances with 1≤p≤2 and suggest an algorithm that is partially based on majorization for p outside this range. We give some convergence proofs and extend the zero distance theorem of De Leeuw (1984) to Minkowski distances with p>1.

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U2 - 10.1007/BF01202265

DO - 10.1007/BF01202265

M3 - Article

AN - SCOPUS:0345792347

SN - 0176-4268

VL - 12

SP - 3

EP - 19

JO - Journal of Classification

JF - Journal of Classification

IS - 1

ER -

The majorization approach to multidimensional scaling for Minkowski distances

Abstract

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