Compact Matrix Factorization with Dependent Subspaces

Viktor Larsson
(Lund University, Sweden)


Traditional matrix factorization methods approximate high dimensional data with a low dimensional subspace. This imposes constraints on the matrix elements which allow for estimation of missing entries. A lower rank provides stronger constraints and makes estimation of the missing entries less ambiguous at the cost of measurement fit.

In this talk, new factorization model that further constrains the matrix entries is presnted . Our approach can be seen as a unification of traditional low-rank matrix factorization and the more recent union-of-subspace approach. It adaptively finds clusters that can be modeled with low dimensional local subspaces and simultaneously uses a global rank constraint to capture the overall scene interactions. For inference we use an energy that penalizes a trade-off between data fit and degrees-of-freedom of the resulting factorization. We show qualitatively and quantitatively that regularizing both local and global dynamics yields significantly improved missing data estimation.