Abstract
Learning of objects from complex patterns is a long-term challenge in philosophy, neuroscience, machine learning, data mining, and in statistics. There are some approaches in literature trying to solve this difficult task consisting in discovering hidden structure of high-dimensional binary data and one of them is Boolean factor analysis. However there is no expert independent measure for evaluating this method in terms of the quality of solutions obtained, when analyzing unknown data. Here we propose information gain, model-based measure of the rate of success of individual methods. This measure presupposes that observed signals arise as Boolean superposition of base signals with noise. For the case whereby a method does not provide parameters necessary for information gain calculation we introduce the procedure for their estimation. Using an extended version of the ”Bars Problem” generation of typical synthetics data for such a task, we show that our measure is sensitive to all types of data model parameters and attains its maximum, when best fit is achieved.
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References
Barlow, H.B.: Cerebral cortex as model builder. In: Rose, D., Dodson, V.G. (eds.) Models of the Visual Cortex, pp. 37–46. Wiley, Chichester (1985)
Belohlavek, R., Vychodil, V.: On Boolean factor analysis with formal concepts as factors, pp. 20–24 (2006)
Belohlavek, R., Vychodil, V.: Discovery of optimal factors in binary data via a novel method of matrix decomposition. Journal of Computer and System Sciences 76(1), 3–20 (2010)
Foldiak, P.: Forming sparse representations by local anti-hebbian learning. Biological Cybernetics 64, 165–170 (1990)
Frolov, A.A., Husek, D., Muraviev, I.P., Polyakov, P.Y.: Boolean factor analysis by attractor neural network. IEEE Transactions on Neural Networks 18(3), 698–707 (2007)
Frolov, A.A., Husek, D., Polyakov, P., Rezankova, H.: New Neural Network Based Approach Helps to Discover Hidden Russian Parliament Voting Patterns. In: IEEE International Joint Conference on Neural Networks, pp. 6518–6523 (2006)
Frolov, A.A., Husek, D., Polyakov, P.Y.: Recurrent neural network based Boolean factor analysis and its application to automatic terms and documents categorization. IEEE Transactions on Neural Networks 20(7), 1073–1086 (2009)
Frolov, A.A., Husek, D., Polyakov, P.Y.: Origin and Elimination of Two Global Spurious Attractors in Hopfield-like Neural Network Performing Boolean Factor Analysis. Neurocomputing (2010) (in press)
Frolov, A.A., Húsek, D., Rezanková, H., Snásel, V., Polyakov, P.: Clustering variables by classical approaches and neural network Boolean factor analysis. In: IEEE International Joint Conference on Neural Networks, pp. 3742–3746 (2008)
Lücke, J., Sahani, M.: Maximal causes for non-linear component extraction. The Journal of Machine Learning Research 9, 1227–1267 (2008)
Marr, D.: A Theory for Cerebral Neocortex. Proceedings of the Royal Society of London. Series B, Biological Sciences (1934-1990) 176(1043), 161–234 (1970)
Marr, D.: Simple Memory: A Theory for Archicortex. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences (1934-1990) 262(841), 23–81 (1971)
Mickey, M.R., Mundle, P., Engelman, L.: Boolean factor analysis. In: Dixon, W. (ed.) BMDP Statistical Software, pp. 538–545. University of California Press, Berkeley (1983)
Pelaez, J.R.: Plato’s theory of ideas revisited. Neural Networks 10(7), 1269–1288 (1997)
Veiel, H.O.: Psychopathology and Boolean Factor Analysis: a mismatch. Psychol. Med. 15(3), 623–628 (1985)
Weber, A.C., Scharfetter, C.: The syndrome concept: history and statistical operationalizations. Psychol. Med. 14(2), 315–325 (1984)
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Frolov, A.A., Husek, D., Polyakov, P.Y. (2011). New Measure of Boolean Factor Analysis Quality. In: Dobnikar, A., Lotrič, U., Šter, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2011. Lecture Notes in Computer Science, vol 6593. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20282-7_11
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DOI: https://doi.org/10.1007/978-3-642-20282-7_11
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