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Coclustering algorithms are an alternative to classic one-sided clustering algorithms. Because of its ability to simultaneously cluster rows and columns of a dyadic data matrix, coclustering offers a higher value-added information: it offers column clusters besides row clusters, and the relationship between them in terms of coclusters. Different structures of coclusters are possible, and those that overlap in terms of rows or columns still represent an open question with room for improvements. In addition, while most related literature cites coclustering as a means of producing better results from one-side clustering, few initiatives study it as a tool capable of providing higher quality descriptive information about this clustering. In this paper, we present a new coclustering algorithm - OvNMTF, based on triple matrix factorization, which properly handle overlapped coclusters, by adding degrees of freedom for matrix factorization that enable the discovery of specialized column clusters for each row cluster. As a proof of concept, we modeled text analysis as a coclustering problem with column overlaps, assuming that given words (data matrix columns) are associated with over one document cluster (row cluster) because they can assume different semantic relationships in each association. Experiments on synthetic data sets show the OvNMTF algorithm reasonableness; experiments on real-world text data show its power for extracting high quality information.

Co-clustering is being given increasing attention by data scientists because it reveals a priori hidden information in data, through an analysis of item clusters along with attribute clusters. The use of co-clustering methods based on non-negative matrix factorization is considered to be advantageous for contexts in which data is positive matrices. However, there are limitations in these methods when co-clusters are characterized by columns overlapping (or attributes) – a common situation in several application contexts. In this paper, we have formalized the problem of Columns Overlapping Co-clustering and introduced BinOvNMTF (Binary Overlapped Non-negative Matrix Tri-Factorization), a new algorithm to analyze attribute clusters independently for each item cluster. This analysis is particularly useful for discovering information embedded in attribute clusters. We tested the BinOvNMTF algorithm in synthetic and real (textual) datasets; BinOvNMTF achieved superior results than those obtained by correlated algorithms.