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On Boolean Representation of Continuous Data Biclustering

Michalak Marcin, Ślęzak Dominik

Fundamenta Informaticae

2019

Vol. 167, nr 3

193--217

Biclustering is considered as the method of finding two-dimensional subgroups in a matrix of scalars. The paper introduces a new approach to biclustering continuous matrices on the basis of boolean function analysis. We draw the strong relation between inclusion-maximal (maximal with respect to inclusion) biclusters of the assumed maximal difference between the data in a bicluster and prime implicants of a boolean function describing the data. These biclusters are called similarity biclusters. In the opposition to them, a new notion of dissimilarity biclusters was also introduced in the paper.

Boolean Representation for Exact Biclustering

Michalak M., Ślęzak D.

Fundamenta Informaticae

2018

Vol. 161, nr 3

275--297

Biclustering is a branch of data analysis, whereby the goal is to find two–dimensional subgroups in a matrix of scalars. We introduce a new approach for biclustering discrete and binary matrices on the basis of boolean function analysis. We draw the correspondence between non–extendable (maximal with respect to inclusion) exact biclusters and prime implicants of a discernibility function describing the data. We present also the results of boolean-style clustering of the artificial discrete image data. Some possibilities of utilizing basic image processing techniques for this kind of input to the biclustering problem are discussed as well.