Formal Concept Analysis 12th International Conference, ICFCA 2014, C
This book constitutes the refereed proceedings of the 12th International Conference on Formal Concept Analysis, ICFCA 2014, held in Cluj-Napoca, Romania, in June 2014.The 16 regular papers presented together with 3 invited talks were carefully reviewed an
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To cite this version: Aleksey Buzmakov, Sergei O. Kuznetsov, Amedeo Napoli. Scalable Estimates of Concept Stability. Cynthia Vera Glodeanu, Mehdi Kaytoue, Christian Sacarea 12th International Conference on Formal Concept Analysis (ICFCA 2014), 2014, Cluj-Napoca, Romania. Springer, 8478, pp.157 - 172, Formal Concept Analysis. .
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Scalable Estimates of Concept Stability Aleksey Buzmakov1,2 , Sergei O. Kuznetsov2 , and Amedeo Napoli1 1
LORIA (CNRS – Inria NGE – U. de Lorraine), Vandœuvre-l`es-Nancy, France National Research University Higher School of Economics, Moscow, Russia [email protected], [email protected], [email protected]
2
Abstract. Data mining aims at finding interesting patterns from datasets, where “interesting” means reflecting intrinsic dependencies in the domain of interest rather than just in the dataset. Concept stability is a popular relevancy measure in FCA. Experimental results of this paper show that high stability of a concept for a context derived from the general population suggests that concepts with the same intent in other samples drawn from the population have also high stability. A new estimate of stability is introduced and studied. It is experimentally shown that the introduced estimate gives a better approximation than the Monte Carlo approach introduced earlier. Keywords: formal concept analysis, stability, pattern selection, experiment
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Introduction
Given a dataset, data mining methods may reveal a huge number of patterns, so filtering patterns w.r.t. some relevancy measures can be necessary. The question of how much a pattern is interesting arises in many areas of data mining, including those that employ tools of Formal Concept Analysis (FCA). FCA is a mathematical formalism having many applications in data analysis [1]. It aims at computing concepts and their lattices from a formal context, a triple (G, M, I) where G is a set of objects (experiments or elements of a dataset), M is a set of attributes used to build the description of every object, and I ⊆ G × M is a relation between objects and attributes. The number of concepts for a given context can be exponential w.r.t. the size of the context, and thus, a special procedure for selecting the most relevant concepts is needed. Two options can be distinguished. The first one is to introduce background knowledge into the procedure for computing concepts [2–6]. Background knowledge allows
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