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Vol: 58(72) No: 2 / June 2013        

Dimension Reduction by Exploring Conditional Independences
Tamás Szántai
Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem rkp. 3-9, 1111 Budapest, Hungary, phone: (+36-1) 463-1359, e-mail: szantai@math.bme.hu, web: http://www.math.bme.hu/~szantai
Edith Kovács
Department of Methodology, Budapest College of Management, Villányi út 11-13, 1114 Budapest, Hungary, phone: (+36-1) 381-8139, e-mail: kovacs.edith@avf.hu

Keywords: dimension reduction, conditional independence, cherry-tree probability distribution, probabilistic machine learning

One of the main problems of data mining is to find the dependence structure of a dataset. Using simply a dependency graph, in which the dependent features (random variables) are connected, often causes that we have to take into account too many features as the dependency graph usually is an extremely dense graph. Exploring the conditional independences yield a more efficient graph with lower number of edges. This led us to the idea of discovering the Markov network underlying the random variables. For this purpose we developed a greedy algorithm which is based on information theoretical concepts. By using this algorithm we obtain a graph structure which helps us to find those important features (a few features only) which can produce efficient clustering of the data set. We also give a method for determining the probability that a new data point belongs to a given cluster. We test the effectiveness of our method on real datasets and compare it with those of other existing methods.

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