Generalized non-metric multidimensional scaling
Research output: Contribution to journal › Conference article › Research › peer-review
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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
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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