Robust hierarchical image representation using non-negative matrix factorisation with sparse code shrinkage preprocessing

When analysing patterns, our goals are (i) to find structure in the presence of noise, (ii) to decompose the observed structure into sub-components, and (iii) to use the components for pattern completion. Here, a novel loop architecture is introduced to perform these tasks in an unsupervised manner. The architecture combines sparse code shrinkage with non-negative matrix factorisation, and blends their favourable properties: sparse code shrinkage aims to remove Gaussian noise in a robust fashion; non-negative matrix factorisation extracts substructures from the noise filtered inputs. The loop architecture performs robust pattern completion when organised into a two-layered hierarchy. We demonstrate the power of the proposed architecture on the so-called ‘bar-problem’ and on the FERET facial database.