Keyword(s):Non-negative Matrix Factorization, Binary Data, Binary Matrix Factorization, Text Modelling.

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Subjects/Areas/Topics:Artificial Intelligence
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Business Analytics
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Computational Intelligence
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Data Analytics
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Data Engineering
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Evolutionary Computing
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Knowledge Discovery and Information Retrieval
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Knowledge-Based Systems
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Machine Learning
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Mining Text and Semi-Structured Data
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Soft Computing
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Symbolic Systems

Abstract: We propose the Logistic Non-negative Matrix Factorization for decomposition of binary data. Binary data
are frequently generated in e.g. text analysis, sensory data, market basket data etc. A common method for
analysing non-negative data is the Non-negative Matrix Factorization, though this is in theory not appropriate
for binary data, and thus we propose a novel Non-negative Matrix Factorization based on the logistic link
function. Furthermore we generalize the method to handle missing data. The formulation of the method
is compared to a previously proposed logistic matrix factorization without non-negativity constraint on the
features. We compare the performance of the Logistic Non-negative Matrix Factorization to Least Squares
Non-negative Matrix Factorization and Kullback-Leibler (KL) Non-negative Matrix Factorization on sets of
binary data: a synthetic dataset, a set of student comments on their professors collected in a binary termdocument
matrix and a sensory dataset. We find that choosing the number of components is an essential part
in the modelling and interpretation, that is still unresolved.(More)

We propose the Logistic Non-negative Matrix Factorization for decomposition of binary data. Binary data are frequently generated in e.g. text analysis, sensory data, market basket data etc. A common method for analysing non-negative data is the Non-negative Matrix Factorization, though this is in theory not appropriate for binary data, and thus we propose a novel Non-negative Matrix Factorization based on the logistic link function. Furthermore we generalize the method to handle missing data. The formulation of the method is compared to a previously proposed logistic matrix factorization without non-negativity constraint on the features. We compare the performance of the Logistic Non-negative Matrix Factorization to Least Squares Non-negative Matrix Factorization and Kullback-Leibler (KL) Non-negative Matrix Factorization on sets of binary data: a synthetic dataset, a set of student comments on their professors collected in a binary termdocument matrix and a sensory dataset. We find that choosing the number of components is an essential part in the modelling and interpretation, that is still unresolved.

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Larsen, J. and Clemmensen, L. (2015). Non-negative Matrix Factorization for Binary Data.In Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1 KDIR: SSTM, (IC3K 2015) ISBN 978-989-758-158-8, ISSN 2184-3228, pages 555-563. DOI: 10.5220/0005614805550563

@conference{sstm15, author={Jacob Søgaard Larsen. and Line Katrine Harder Clemmensen.}, title={Non-negative Matrix Factorization for Binary Data}, booktitle={Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1 KDIR: SSTM, (IC3K 2015)}, year={2015}, pages={555-563}, publisher={SciTePress}, organization={INSTICC}, doi={10.5220/0005614805550563}, isbn={978-989-758-158-8}, }

TY - CONF

JO - Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1 KDIR: SSTM, (IC3K 2015) TI - Non-negative Matrix Factorization for Binary Data SN - 978-989-758-158-8 AU - Larsen, J. AU - Clemmensen, L. PY - 2015 SP - 555 EP - 563 DO - 10.5220/0005614805550563