132 research outputs found
Revisiting Numerical Pattern Mining with Formal Concept Analysis
In this paper, we investigate the problem of mining numerical data in the
framework of Formal Concept Analysis. The usual way is to use a scaling
procedure --transforming numerical attributes into binary ones-- leading either
to a loss of information or of efficiency, in particular w.r.t. the volume of
extracted patterns. By contrast, we propose to directly work on numerical data
in a more precise and efficient way, and we prove it. For that, the notions of
closed patterns, generators and equivalent classes are revisited in the
numerical context. Moreover, two original algorithms are proposed and used in
an evaluation involving real-world data, showing the predominance of the
present approach
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
On mining complex sequential data by means of FCA and pattern structures
Nowadays data sets are available in very complex and heterogeneous ways.
Mining of such data collections is essential to support many real-world
applications ranging from healthcare to marketing. In this work, we focus on
the analysis of "complex" sequential data by means of interesting sequential
patterns. We approach the problem using the elegant mathematical framework of
Formal Concept Analysis (FCA) and its extension based on "pattern structures".
Pattern structures are used for mining complex data (such as sequences or
graphs) and are based on a subsumption operation, which in our case is defined
with respect to the partial order on sequences. We show how pattern structures
along with projections (i.e., a data reduction of sequential structures), are
able to enumerate more meaningful patterns and increase the computing
efficiency of the approach. Finally, we show the applicability of the presented
method for discovering and analyzing interesting patient patterns from a French
healthcare data set on cancer. The quantitative and qualitative results (with
annotations and analysis from a physician) are reported in this use case which
is the main motivation for this work.
Keywords: data mining; formal concept analysis; pattern structures;
projections; sequences; sequential data.Comment: An accepted publication in International Journal of General Systems.
The paper is created in the wake of the conference on Concept Lattice and
their Applications (CLA'2013). 27 pages, 9 figures, 3 table
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