document: Model order selection for boolean matrix factorization Matrix factorizations -- where a given data matrix is approximated by a product of two or more factor matrices -- are powerful data mining tools . Among other tasks , matrix factorizations are often used to separate global structure from noise . This , however , requires solving the ` model order selection problem ' of determining where fine-grained structure stops , and noise starts , i.e. , what is the proper size of the factor matrices . Boolean matrix factorization ( BMF ) -- where data , factors , and matrix product are Boolean -- has received increased attention from the data mining community in recent years . The technique has desirable properties , such as high interpretability and natural sparsity . But so far no method for selecting the correct model order for BMF has been available . In this paper we propose to use the Minimum Description Length ( MDL ) principle for this task . Besides solving the problem , this well-founded approach has numerous benefits , e.g. , it is automatic , does not require a likelihood function , is fast , and , as experiments show , is highly accurate . We formulate the description length function for BMF in general -- making it applicable for any BMF algorithm . We extend an existing algorithm for BMF to use MDL to identify the best Boolean matrix factorization , analyze the complexity of the problem , and perform an extensive experimental evaluation to study its behavior .
doc_bio_tags: B I I O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O