From preferences over objects to preferences over concepts
We present an approach to preference modeling and learning preferences from data based on formal concept analysis. We consider techniques to derive preferences over attribute subsets from preferences over objects, including ceteris paribus preferences.
A novel approach to triclustering of a three-way binary data is proposed. Tricluster is defined in terms of Triadic Formal Concept Analysis as a dense triset of a binary relation Y , describing relationship between objects, attributes and conditions. This definition is a relaxation of a triconcept notion and makes it possible to find all triclusters and triconcepts contained in triclusters of large datasets. This approach generalizes the similar study of concept-based biclustering.
The problem of detecting terms that can be interesting to the advertiser is considered. If a company has already bought some advertising terms which describe certain services, it is reasonable to find out the terms bought by competing companies. A part of them can be recommended as future advertising terms to the company. The goal of this work is to propose better interpretable recommendations based on FCA and association rules.
Formal Concept Analysis (FCA) is a mathematical technique that has been extensively applied to Boolean data in knowledge discovery, information retrieval, web mining, etc. applications. During the past years, the research on extending FCA theory to cope with imprecise and incomplete information made significant progress. In this paper, we give a systematic overview of the more than 120 papers published between 2003 and 2011 on FCA with fuzzy attributes and rough FCA. We applied traditional FCA as a text-mining instrument to 1072 papers mentioning FCA in the abstract. These papers were formatted in pdf files and using a thesaurus with terms referring to research topics, we transformed them into concept lattices. These lattices were used to analyze and explore the most prominent research topics within the FCA with fuzzy attributes and rough FCA research communities. FCA turned out to be an ideal metatechnique for representing large volumes of unstructured texts.
The paper is the preface to the special issue of the Fundamenta Informaticae journal on concept lattices and their applications. It is focused on recent developments in Formal Concept Analysis (FCA), as well as on applications in closely related areas such as data mining, information retrieval, knowledge management, data and knowledge engineering, and lattice theory.
This book constitutes the proceedings of the 14th International Conference on Formal Concept Analysis, ICFCA 2017, held in Rennes, France, in June 2017. The 13 full papers presented in this volume were carefully reviewed and selected from 37 submissions. The book also contains an invited contribution and a historical paper translated from German and originally published in “Die Klassifkation und ihr Umfeld”, edited by P. O. Degens, H. J. Hermes, and O. Opitz, Indeks-Verlag, Frankfurt, 1986. The field of Formal Concept Analysis (FCA) originated in the 1980s in Darmstadt as a subfield of mathematical order theory, with prior developments in other research groups. Its original motivation was to consider complete lattices as lattices of concepts, drawing motivation from philosophy and mathematics alike. FCA has since then developed into a wide research area with applications much beyond its original motivation, for example in logic, data mining, learning, and psychology.
A vast amount of documents in the Web have duplicates, which is a challenge for developing efficient methods that would compute clusters of similar documents. In this paper we use an approach based on computing (closed) sets of attributes having large support (large extent) as clusters of similar documents. The method is tested in a series of computer experiments on large public collections of web documents and compared to other established methods and software, such as biclustering, on same datasets. Practical efficiency of different algorithms for computing frequent closed sets of attributes is compared.
This paper addresses the important problem of efficiently mining numerical data with formal concept analysis (FCA). Classically, the only way to apply FCA is to binarize the data, thanks to a so-called scaling procedure. This may either involve loss of information, or produce large and dense binary data known as hard to process. In the context of gene expression data analysis, we propose and compare two FCA-based methods for mining numerical data and we show that they are equivalent. The first one relies on a particular scaling, encoding all possible intervals of attribute values, and uses standard FCA techniques. The second one relies on pattern structures without a priori transformation, and is shown to be more computationally efficient and to provide more readable results. Experiments with real-world gene expression data are discussed and give a practical basis for the comparison and evaluation of the methods.