Matrix Factorisation with Linear Filters
This work provides a theoretical link between two algorithm families, potentially improving efficiency in high-dimensional tasks like image processing, but it appears incremental as it builds on existing methods.
The paper connects matrix factorization with recursive linear filters by deriving a matrix-variate recursive linear filter from a probabilistic model, enabling efficient high-dimensional inference and interpreting it as a stochastic gradient algorithm, with demonstrations on image restoration.
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation algorithm. Using the probabilistic model, we derive a matrix factorisation algorithm as a recursive linear filter. More precisely, we derive a matrix-variate recursive linear filter in order to perform efficient inference in high dimensions. We also show that it is possible to interpret our algorithm as a nontrivial stochastic gradient algorithm. Demonstrations and comparisons on an image restoration task are given.