Mining Biclusters of Similar Values with Triadic Concept Analysis

Biclustering numerical data became a popular data-mining task in the beginning of 2000's, especially for analysing gene expression data. A bicluster reflects a strong association between a subset of objects and a subset of attributes in a numerical object/attribute data-table. So called biclusters of similar values can be thought as maximal sub-tables with close values. Only few methods address a complete, correct and non redundant enumeration of such patterns, which is a well-known intractable problem, while no formal framework exists. In this paper, we introduce important links between biclustering and formal concept analysis. More specifically, we originally show that Triadic Concept Analysis (TCA), provides a nice mathematical framework for biclustering. Interestingly, existing algorithms of TCA, that usually apply on binary data, can be used (directly or with slight modifications) after a preprocessing step for extracting maximal biclusters of similar values.Comment: Concept Lattices and their Applications (CLA) (2011

Lattice-based biclustering using Partition Pattern Structures

International audienceIn this work we present a novel technique for exhaustive bicluster enumeration using formal concept anal-ysis (FCA). Particularly, we use pattern structures (an ex-tension of FCA dealing with complex data) to mine similar row/column biclusters, a specialization of biclustering when attribute values have coherent variations. We show how bi-clustering can benefit from the FCA framework through its ro-bust theoretical description and efficient algorithms. Finally, we evaluate our bicluster mining approach w.r.t. a standard biclustering technique showing very good results in terms of bicluster quality and performance

Mining bi-sets in numerical data

Thanks to an important research effort the last few years, inductive queries on set patterns and complete solvers which can evaluate them on large 0/1 data sets have been proved extremely useful. However, for many application domains, the raw data is numerical (matrices of real numbers whose dimensions denote objects and properties). Therefore, using efficient 0/1 mining techniques needs for tedious Boolean property encoding phases. This is, e.g., the case, when considering microarray data mining and its impact for knowledge discovery in molecular biology. We consider the possibility to mine directly numerical data to extract collections of relevant bi-sets, i.e., couples of associated sets of objects and attributes which satisfy some user-defined constraints. Not only we propose a new pattern domain but also we introduce a complete solver for computing the so-called numerical bi-sets. Preliminary experimental validation is given. © Springer-Verlag Berlin Heidelberg 2007.status: publishe

Mining bi-sets in numerical data

International audienc

Mining bi-sets in numerical data

International audienc