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Boolean Matrix Factorization with Missing Values


Yadava,  Prashant
Databases and Information Systems, MPI for Informatics, Max Planck Society;

Weikum,  Gerhard
Databases and Information Systems, MPI for Informatics, Max Planck Society;

Miettinen,  Pauli
Databases and Information Systems, MPI for Informatics, Max Planck Society;

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Yadava, P. (2012). Boolean Matrix Factorization with Missing Values. Master Thesis, Universität des Saarlandes, Saarbrücken.

Cite as:
Is it possible to meaningfully analyze the structure of a Boolean matrix for which 99% data is missing? Real-life data sets usually contain a high percentage of missing values which hamper structure estimation from the data and the difficulty only increases when the missing values dominate the known elements in the data set. There are good real-valued factorization methods for such scenarios, but there exist another class of data "Boolean data", which demand a different handling strategy than their real-valued counterpart. There are many application which find logical representation only via Boolean matrices, where real-valued factorization methods do not provide correct and intuitive solutions. Currently, there exists no method which can factorize a Boolean matrix containing a percentage of missing values usually associated with non-trivial real-world data set. In this thesis, we introduce a method to fill this gap. Our method is based on the correlation among the data records and is not restricted by the percentage of unknowns in the matrix. It performs greedy selection of the basis vectors, which represent the underlying structure in the data. This thesis also presents several experiments on a variety of synthetic and real-world data, and discusses the performance of the algorithm for a range of data properties. However, it was not easy to obtain comparison statistics with existing methods, for the reason that none exist. Hence we present indirect comparisons with existing matrix completion methods which work with real-valued data sets.