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

When analyzing 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 factorization and blends their favorable properties: Sparse code shrinkage aims to remove Gaussian noise in a robust fashion; Non-negative matrix factorization extracts sub-structures from the noise filtered inputs. The loop architecture performs robust pattern completion when organized 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.