Robust multi-dimensional scaling via outlier-sparsity control

Pedro A. Forero, Georgios B. Giannakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


Multidimensional scaling (MDS) seeks an embedding of N objects in a p < N dimensional space such that inter-vector distances approximate pair-wise object dissimilarities. Despite their popularity, MDS algorithms are sensitive to outliers, yielding grossly erroneous embeddings even if few outliers contaminate the available dissimilarities. This work introduces a robust MDS approach exploiting the degree of sparsity in the outliers present. Links with compressive sampling lead to a robust MDS solver capable of coping with outliers. The novel algorithm relies on a majorization-minimization (MM) approach to minimize a regularized stress function, whereby an iterative MDS solver involving Lasso operators is obtained. The resulting scheme identifies outliers and obtains the desired embedding at a computational cost comparable to that of non-robust MDS alternatives. Numerical tests illustrate the merits of the proposed algorithm.

Original languageEnglish (US)
Title of host publicationConference Record of the 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011
Number of pages5
StatePublished - Dec 1 2011
Event45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011 - Pacific Grove, CA, United States
Duration: Nov 6 2011Nov 9 2011

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
ISSN (Print)1058-6393


Other45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011
CountryUnited States
CityPacific Grove, CA

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