Two Expectation-Maximization algorithms for Boolean Factor Analysis
Methods for the discovery of hidden structures of high-dimensional binary data are one of the most important challenges facing the community of machine learning researchers. There are many approaches in the literature that try to solve this hitherto rather ill-defined task. In the present study, we...
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| Vydáno v: | Neurocomputing (Amsterdam) Ročník 130; s. 83 - 97 |
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23.04.2014
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| ISSN: | 0925-2312, 1872-8286 |
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| Abstract | Methods for the discovery of hidden structures of high-dimensional binary data are one of the most important challenges facing the community of machine learning researchers. There are many approaches in the literature that try to solve this hitherto rather ill-defined task. In the present study, we propose a general generative model of binary data for Boolean Factor Analysis and introduce two new Expectation-Maximization Boolean Factor Analysis algorithms which maximize the likelihood of a Boolean Factor Analysis solution. To show the maturity of our solutions we propose an informational measure of Boolean Factor Analysis efficiency. Using the so-called bars problem benchmark, we compare the efficiencies of the proposed algorithms to that of Dendritic Inhibition Neural Network, Maximal Causes Analysis, and Boolean Matrix Factorization. Last mentioned methods were taken as related methods as they are supposed to be the most efficient in bars problem benchmark. Then we discuss the peculiarities of the two methods we proposed and the three related methods in performing Boolean Factor Analysis. |
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| AbstractList | Methods for the discovery of hidden structures of high-dimensional binary data are one of the most important challenges facing the community of machine learning researchers. There are many approaches in the literature that try to solve this hitherto rather ill-defined task. In the present study, we propose a general generative model of binary data for Boolean Factor Analysis and introduce two new Expectation-Maximization Boolean Factor Analysis algorithms which maximize the likelihood of a Boolean Factor Analysis solution. To show the maturity of our solutions we propose an informational measure of Boolean Factor Analysis efficiency. Using the so-called bars problem benchmark, we compare the efficiencies of the proposed algorithms to that of Dendritic Inhibition Neural Network, Maximal Causes Analysis, and Boolean Matrix Factorization. Last mentioned methods were taken as related methods as they are supposed to be the most efficient in bars problem benchmark. Then we discuss the peculiarities of the two methods we proposed and the three related methods in performing Boolean Factor Analysis. |
| Author | Polyakov, Pavel Y. Husek, Dusan Frolov, Alexander A. |
| Author_xml | – sequence: 1 givenname: Alexander A. surname: Frolov fullname: Frolov, Alexander A. organization: Institute of Higher Nervous Activity and Neurophysiology, Russian Academy of Sciences, Butlerova 5a, 117 485 Moscow, Russia – sequence: 2 givenname: Dusan surname: Husek fullname: Husek, Dusan email: dusan@cs.cas.cz organization: Institute of Computer Science, Academy of Science of the Czech Republic, Pod Vodarenskou vezi 2, 182 07 Prague 8, Czech Republic – sequence: 3 givenname: Pavel Y. surname: Polyakov fullname: Polyakov, Pavel Y. organization: FEI VSB – TU Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic |
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| Cites_doi | 10.1109/TNN.2009.2016090 10.1016/S0925-2312(02)00847-0 10.1109/TKDE.2008.53 10.1007/978-94-011-5014-9_12 10.1016/S0925-2312(02)00512-X 10.1007/978-3-540-77046-6_29 10.1109/TNN.2007.891664 10.1098/rstb.1971.0078 10.1016/j.neucom.2007.09.017 10.1162/089976602320264033 10.1016/j.neucom.2011.05.011 10.1016/j.neucom.2008.11.033 10.1111/j.2517-6161.1977.tb01600.x 10.1088/0954-898X/12/3/301 10.1017/S0033291700031470 10.1038/44565 10.1016/S0893-6080(99)00046-5 10.1162/neco.1995.7.1.51 10.1016/S0925-2312(01)00675-0 10.1016/j.neucom.2007.07.038 10.1017/S0033291700003585 10.1007/BF02331346 10.1016/j.jcss.2009.05.002 10.1098/rspb.1970.0040 |
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| Keywords | Dimension reduction Binary Matrix Factorization Boolean Factor Analysis Binary data model Neural networks Bars problem |
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| SubjectTerms | Algorithms Bars Bars problem Benchmarking Binary data Binary data model Binary Matrix Factorization Boolean algebra Boolean Factor Analysis Dimension reduction Factor analysis Mathematical models Neural networks |
| Title | Two Expectation-Maximization algorithms for Boolean Factor Analysis |
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