A Convex Approach to Subspace Clustering
2011 (English)In: Proceedings of the 50th IEEE Conference on Decision and Control, 2011, 1467-1472 p.Conference paper (Refereed)
The identification of multiple affine subspaces from a set of data is of interest in fields such as system identification, data compression, image processing and signal processing and in the literature referred to as subspace clustering. If the origin of each sample would be known, the problem would be trivially solved by applying principal component analysis to samples originated from the same subspace. Now, not knowing what samples that originates from what subspace, the problem becomes considerably more difficult. We present a novel convex formulation for subspace clustering. The proposed method takes the shape of a least-squares problem with sum-of-norms regularization over optimization parameter differences, a generalization of the ℓ1-regularization. The regularization constant is used to trade off fit and the identified number of affine subspaces.
Place, publisher, year, edition, pages
2011. 1467-1472 p.
Convex programming, Least squares approximations, Pattern clustering
IdentifiersURN: urn:nbn:se:liu:diva-95597DOI: 10.1109/CDC.2011.6161221ISBN: 978-1-61284-799-3ISBN: 978-1-61284-800-6OAI: oai:DiVA.org:liu-95597DiVA: diva2:636445
50th IEEE Conference on Decision and Control, Orlando, FL, USA, 12-15 December, 2011