Learning Multi-level Sparse Representations for Identifying Neuronal Activity

Bilinear approximation of a matrix is a powerful paradigm of unsupervised learning. In some applications, however, there is a natural hierarchy of concepts that ought to be reflected in the unsupervised analysis, e.g. neurosciences image sequences. Therefore, we propose a decomposition of the matrix of observations into a product of more than two sparse matrices allowing for both hierarchical and heterarchical relations of lower-level to higher-level concepts. In addition, we learn the nature of these relations rather than imposing them. Finally, the proposed model yields plausible interpretations of the experimental neurosciences data (pixel → neuron → assembly), and fully recovers the structure from synthetic data that was modeled after the experiment.