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Bsig: evaluating the statistical significance of biclustering solutions. (English) Zbl 1416.62340
Summary: Statistical evaluation of biclustering solutions is essential to guarantee the absence of spurious relations and to validate the high number of scientific statements inferred from unsupervised data analysis without a proper statistical ground. Most biclustering methods rely on merit functions to discover biclusters with specific homogeneity criteria. However, strong homogeneity does not guarantee the statistical significance of biclustering solutions. Furthermore, although some biclustering methods test the statistical significance of specific types of biclusters, there are no methods to assess the significance of flexible biclustering models. This work proposes a method to evaluate the statistical significance of biclustering solutions. It integrates state-of-the-art statistical views on the significance of local patterns and extends them with new principles to assess the significance of biclusters with additive, multiplicative, symmetric, order-preserving and plaid coherencies. The proposed statistical tests provide the unprecedented possibility to minimize the number of false positive biclusters without incurring on false negatives, and to compare state-of-the-art biclustering algorithms according to the statistical significance of their outputs. Results on synthetic and real data support the soundness and relevance of the proposed contributions, and stress the need to combine significance and homogeneity criteria to guide the search for biclusters.

MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62G07 Density estimation
62H35 Image analysis in multivariate analysis
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