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Deep orthogonal matrix factorization as a hierarchical clustering technique

Deep orthogonal nonnegative matrix factorization (deep ONMF) is a constrained deep low-rank matrix approximation model which decomposes a data matrix through several layers of factorizations. Deep ONMF imposes that each data point is assigned to a single cluster at each layer. In this paper, we first explain why deep ONMF can be interpreted as a bottom-up hiearchical clustering technique. Then our main contribution is to provide a simple yet effective greedy initialization strategy for deep ONMF. We show on synthetic data sets that it performs competitively with other initialization strategies, and apply it on the decomposition of a hyperspectral image into its constitutive materials.