Deepness Analysis of Learned Factors in Multilayer NMF
Résumé
Hierarchical structures are known since decades for their outstanding properties that make them ideal for representing data and has been suggested as a particularly important method for organizing concepts. This paper fills a big gap between Multilayer Nonnegative Matrix Factorization and hierarchical structures. We prove that this prototype based model is a deep architecture. We prove mathematically and by experiments that each layer depends on the preceding layers, even being trivial it doesn’t exist any stated proof of this. We conclude that different layers in Multilayer Nonnegative Matrix Factorization are not only dependant but also the order of construction is prominent. In other words, Multilayer NMF is indeed a hierarchical dimensionality reduction and clustering method. It involves learning multiple levels of representation, corresponding to different levels of abstractions.
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