TY - GEN
T1 - Robust multi-dimensional scaling via outlier-sparsity control
AU - Forero, Pedro A.
AU - Giannakis, Georgios B.
PY - 2011/12/1
Y1 - 2011/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84861302810&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84861302810&partnerID=8YFLogxK
U2 - 10.1109/ACSSC.2011.6190202
DO - 10.1109/ACSSC.2011.6190202
M3 - Conference contribution
AN - SCOPUS:84861302810
SN - 9781467303231
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 1183
EP - 1187
BT - Conference Record of the 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011
T2 - 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011
Y2 - 6 November 2011 through 9 November 2011
ER -