CSAIL Event Calendar: Previous Series
Sparse Matrix Factorization
Speaker: Nathan Srebro , MIT AI Laboratory, Laboratory of Computer Science
We present a new unsupervised modeling technique: modeling data via sparse matrix factorization (SMF). Under this approach, one unveils structure in a data matrix A, by approximating it as a product of two matrices C*F, where the rows of C are constrained to be sparse: each row is allowed to have at most m non-zero entries. Setting m=1, we obtain a clustering of the data rows, where the rows of F indicate the cluster centers. At the other extreme, setting m to the width of C, yields a low-rank approximation, specified by the leading components of the singular value decomposition. We focus on small values of m, where the rows of F can be viewed as factors, and each row of A as being approximated by a linear combination of only a few factors.