. . . "Proceedings of 2013 IEEE 13th International Conference on Data Mining" . "B\u011Blohl\u00E1vek, Radim" . "Los Alamos" . "RIV/61989592:15310/13:33147956!RIV14-GA0-15310___" . . "978-0-7685-5108-2" . "Beyond Boolean Matrix Decompositions: Toward Factor Analysis and Dimensionality Reduction of Ordinal Data" . "15310" . "1550-4786" . "2"^^ . . . "2"^^ . "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 . "[85CED6FAA5FE]" . "6"^^ . . "IEEE Computer Society Press" . . . "Krmelov\u00E1, Mark\u00E9ta" . "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." . "RIV/61989592:15310/13:33147956" . "Beyond Boolean Matrix Decompositions: Toward Factor Analysis and Dimensionality Reduction of Ordinal Data"@en . . . . . "2013-12-07+01:00"^^ . . "Dallas" . . . . . "10.1109/ICDM.2013.127" . "Beyond Boolean Matrix Decompositions: Toward Factor Analysis and Dimensionality Reduction of Ordinal Data" . "P(GAP103/11/1456)" . "Ordinal Data; Reduction; Dimensionality; Factor; Boolean Matrix Decomposition"@en . "Beyond Boolean Matrix Decompositions: Toward Factor Analysis and Dimensionality Reduction of Ordinal Data"@en . "63157" . . .