Abstract
The hierarchical non-negative matrix factorization (HNMF) is a multilayer generative network for decomposing strictly positive data into strictly positive activations and base vectors in a hierarchical manner. However, the standard hierarchical NMF is not suited for overcomplete representations and does not code efficiently for transformations in the input data. Therefore we extend the standard HNMF by sparsity conditions and transformation-invariance in a natural, straightforward way. The idea is to factorize the input data into several hierarchical layers of activations, base vectors and transformations under sparsity constraints, leading to a less redundant and sparse encoding of the input data.
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© 2007 Springer-Verlag Berlin Heidelberg
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Rebhan, S., Eggert, J., Groß, HM., Körner, E. (2007). Sparse and Transformation-Invariant Hierarchical NMF. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds) Artificial Neural Networks – ICANN 2007. ICANN 2007. Lecture Notes in Computer Science, vol 4668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74690-4_91
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DOI: https://doi.org/10.1007/978-3-540-74690-4_91
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74689-8
Online ISBN: 978-3-540-74690-4
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