Generalized non-metric multidimensional scaling

Research output: Contribution to journal › Conference article › Research › peer-review

Standard

Generalized non-metric multidimensional scaling. / Agarwal, Sameer; Lanckriet, Gert; Wills, Josh; Kriegman, David; Cayton, Lawrence; Belongie, Serge.

In: Journal of Machine Learning Research, Vol. 2, 2007, p. 11-18.

Research output: Contribution to journal › Conference article › Research › peer-review

Harvard

Agarwal, S, Lanckriet, G, Wills, J, Kriegman, D, Cayton, L & Belongie, S 2007, 'Generalized non-metric multidimensional scaling', Journal of Machine Learning Research, vol. 2, pp. 11-18.

APA

Agarwal, S., Lanckriet, G., Wills, J., Kriegman, D., Cayton, L., & Belongie, S. (2007). Generalized non-metric multidimensional scaling. Journal of Machine Learning Research, 2, 11-18.

Vancouver

Agarwal S, Lanckriet G, Wills J, Kriegman D, Cayton L, Belongie S. Generalized non-metric multidimensional scaling. Journal of Machine Learning Research. 2007;2:11-18.

Author

Agarwal, Sameer ; Lanckriet, Gert ; Wills, Josh ; Kriegman, David ; Cayton, Lawrence ; Belongie, Serge. / Generalized non-metric multidimensional scaling. In: Journal of Machine Learning Research. 2007 ; Vol. 2. pp. 11-18.

Bibtex

@inproceedings{2f18ad85a23f44338c4dfb3fa9600e8a,
title = "Generalized non-metric multidimensional scaling",
abstract = "We consider the non-metric multidimensional scaling problem: given a set of dissimilarities Δ, find an embedding whose inter-point Euclidean distances have the same ordering as Δ In this paper, we look at a generalization of this problem in which only a set of order relations of the form d ij < d kl are provided. Unlike the original problem, these order relations can be contradictory and need not be specified for all pairs of dissimilarities. We argue that this setting is more natural in some experimental settings and propose an algorithm based on convex optimization techniques to solve this problem. We apply this algorithm to human subject data from a psychophysics experiment concerning how reflectance properties are perceived. We also look at the standard NMDS problem, where a dissimilarity matrix Δ is provided as input, and show that we can always find an order-respecting embedding of Δ.",
author = "Sameer Agarwal and Gert Lanckriet and Josh Wills and David Kriegman and Lawrence Cayton and Serge Belongie",
year = "2007",
language = "English",
volume = "2",
pages = "11--18",
journal = "Journal of Machine Learning Research",
issn = "1533-7928",
publisher = "MIT Press",
note = "11th International Conference on Artificial Intelligence and Statistics, AISTATS 2007 ; Conference date: 21-03-2007 Through 24-03-2007",

}

RIS

TY - GEN

T1 - Generalized non-metric multidimensional scaling

AU - Agarwal, Sameer

AU - Lanckriet, Gert

AU - Wills, Josh

AU - Kriegman, David

AU - Cayton, Lawrence

AU - Belongie, Serge

PY - 2007

Y1 - 2007

N2 - We consider the non-metric multidimensional scaling problem: given a set of dissimilarities Δ, find an embedding whose inter-point Euclidean distances have the same ordering as Δ In this paper, we look at a generalization of this problem in which only a set of order relations of the form d ij < d kl are provided. Unlike the original problem, these order relations can be contradictory and need not be specified for all pairs of dissimilarities. We argue that this setting is more natural in some experimental settings and propose an algorithm based on convex optimization techniques to solve this problem. We apply this algorithm to human subject data from a psychophysics experiment concerning how reflectance properties are perceived. We also look at the standard NMDS problem, where a dissimilarity matrix Δ is provided as input, and show that we can always find an order-respecting embedding of Δ.

AB - We consider the non-metric multidimensional scaling problem: given a set of dissimilarities Δ, find an embedding whose inter-point Euclidean distances have the same ordering as Δ In this paper, we look at a generalization of this problem in which only a set of order relations of the form d ij < d kl are provided. Unlike the original problem, these order relations can be contradictory and need not be specified for all pairs of dissimilarities. We argue that this setting is more natural in some experimental settings and propose an algorithm based on convex optimization techniques to solve this problem. We apply this algorithm to human subject data from a psychophysics experiment concerning how reflectance properties are perceived. We also look at the standard NMDS problem, where a dissimilarity matrix Δ is provided as input, and show that we can always find an order-respecting embedding of Δ.

UR - http://www.scopus.com/inward/record.url?scp=84862296204&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:84862296204

VL - 2

SP - 11

EP - 18

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

SN - 1533-7928

T2 - 11th International Conference on Artificial Intelligence and Statistics, AISTATS 2007

Y2 - 21 March 2007 through 24 March 2007

ER -

ID: 302051565