Clustering is one of the most commonly used data exploration tools, but data often hold interesting geometric structure for which generic clustering objectives are too coarse. Subspace clustering is a simple generalization that tries to fit each cluster with a low-dimensional subspace (ie, each cluster has a low-dimensional covariance structure). This is a very useful model for many problems in computer vision and computer network topology inference. Our group has developed state-of-the-art approaches for subspace clustering when the data matrix is incomplete and in the active clustering context.
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Eriksson, Brian, Laura Balzano, and Robert Nowak. 2012. “High Rank Matrix Completion.” In Proc. of Intl. Conf. on Artificial Intell. and Stat. http://jmlr.csail.mit.edu/proceedings/papers/v22/eriksson12/eriksson12.pdf. 1
Balzano, Laura, Arthur Szlam, Benjamin Recht, and Robert Nowak. 2012. “K-Subspaces with Missing Data.” In Statistical Signal Processing Workshop (SSP), 2012 IEEE, 612–615. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6319774.