Name
Abstract | ||
|---|---|---|
We consider the non-metric multidimensional scaling problem: given a set of dissimilarities , find an embedding whose inter-point Eu- clidean distances have the same ordering as . In this paper, we look at a generaliza- tion of this problem in which only a set of order relations of the form dij < dkl are pro- vided. Unlike the original problem, these or- der 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 is provided as input, and show that we can always find an order- respecting embedding of . |
Year | Venue | Keywords |
|---|---|---|
2007 | AISTATS | convex optimization |
Field | DocType | Volume |
Mathematical optimization,Embedding,Multidimensional scaling,Of the form,Computer science,Matrix (mathematics),Euclidean geometry,Reflectivity,Psychophysics,Convex optimization | Journal | 2 |
Citations | PageRank | References |
45 | 2.50 | 8 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sameer Agarwal | 1 | 10328 | 478.10 |
| Josh Wills | 2 | 153 | 6.53 |
| Lawrence Cayton | 3 | 152 | 8.27 |
| Gert R. G. Lanckriet | 4 | 4769 | 296.98 |
| David Kriegman | 5 | 7693 | 451.96 |
| Serge J. Belongie | 6 | 12512 | 1010.13 |