About: Beyond Boolean Matrix Decompositions: Toward Factor Analysis and Dimensionality Reduction of Ordinal Data

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Description	Boolean matrix factorization (BMF), or decomposition, received a considerable attention in data mining research, both for its direct usefulness in data analysis and its fundamental role in understanding Boolean data. In this paper, we argue that research should extend beyond the Boolean case toward more general type of data such as ordinal data. Technically, such extension amounts to replacement of the two-element Boolean algebra utilized in BMF by more general structures, which brings non-trivial challenges. We first present the problem formulation, survey the existing literature, and provide an illustrative example. Second, we present new theorems regarding decompositions of matrices with ordinal data. The theorems helps understand the geometry of decompositions and identify parts of input matrices which are good to focus on when computing factors. Third, we propose two algorithms based on these results along with an experimental evaluation. We conclude the paper with a discussion regarding future research issues. Boolean matrix factorization (BMF), or decomposition, received a considerable attention in data mining research, both for its direct usefulness in data analysis and its fundamental role in understanding Boolean data. In this paper, we argue that research should extend beyond the Boolean case toward more general type of data such as ordinal data. Technically, such extension amounts to replacement of the two-element Boolean algebra utilized in BMF by more general structures, which brings non-trivial challenges. We first present the problem formulation, survey the existing literature, and provide an illustrative example. Second, we present new theorems regarding decompositions of matrices with ordinal data. The theorems helps understand the geometry of decompositions and identify parts of input matrices which are good to focus on when computing factors. Third, we propose two algorithms based on these results along with an experimental evaluation. We conclude the paper with a discussion regarding future research issues. (en)
Title	Beyond Boolean Matrix Decompositions: Toward Factor Analysis and Dimensionality Reduction of Ordinal Data Beyond Boolean Matrix Decompositions: Toward Factor Analysis and Dimensionality Reduction of Ordinal Data (en)
skos:prefLabel	Beyond Boolean Matrix Decompositions: Toward Factor Analysis and Dimensionality Reduction of Ordinal Data Beyond Boolean Matrix Decompositions: Toward Factor Analysis and Dimensionality Reduction of Ordinal Data (en)
skos:notation	RIV/61989592:15310/13:33147956!RIV14-GA0-15310___
http://linked.open...avai/predkladatel	Přírodovědecká fakulta
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GAP103/11/1456)
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Bělohlávek, Radim Krmelová, Markéta
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Palackého v Olomouci / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	63157
http://linked.open...ai/riv/idVysledku	RIV/61989592:15310/13:33147956
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Ordinal Data; Reduction; Dimensionality; Factor; Boolean Matrix Decomposition (en)
http://linked.open.../riv/klicoveSlovo	Boolean Matrix Decomposition Dimensionality Ordinal Data Factor Reduction
http://linked.open...ontrolniKodProRIV	[85CED6FAA5FE]
http://linked.open...v/mistoKonaniAkce	Dallas
http://linked.open...i/riv/mistoVydani	Los Alamos
http://linked.open...i/riv/nazevZdroje	Proceedings of 2013 IEEE 13th International Conference on Data Mining
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Foundations of Similarity-Based Data Processing
http://linked.open...UplatneniVysledku	2013
http://linked.open...iv/tvurceVysledku	Bělohlávek, Radim Krmelová, Markéta
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2013-12-07 (xsd:date)
issn	1550-4786
number of pages	6 (xsd:int)
http://bibframe.org/vocab/doi	10.1109/ICDM.2013.127
http://purl.org/ne...btex#hasPublisher	IEEE Computer Society Press
https://schema.org/isbn	978-0-7685-5108-2
http://localhost/t...ganizacniJednotka	15310

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