Framework Of Formal Concept Analysis Research Articles

위키피디아 기반의 3차원 텍스트 표현모델을 이용한 개념망 구축 기법

A concept network is an essential knowledge base for semantic search engines, personalized search systems, recommendation systems, and text mining. Recently, studies of extending concept representation using external ontology have been frequently conducted. We thus propose a new way of building 3-dimensional text model-based concept networks using the world knowledge-level Wikipedia ontology. In fact, it is desirable that 'concepts' derived from text documents are defined according to the theoretical framework of formal concept analysis, since relationships among concepts generally change over time. In this paper, concept networks hidden in a given document collection are extracted more reasonably by representing a concept as a term-by-document matrix.

Characterizing functional dependencies in formal concept analysis with pattern structures

Computing functional dependencies from a relation is an important database topic, with many applications in database management, reverse engineering and query optimization. Whereas it has been deeply investigated in those fields, strong links exist with the mathematical framework of Formal Concept Analysis. Considering the discovery of functional dependencies, it is indeed known that a relation can be expressed as the binary relation of a formal context, whose implications are equivalent to those dependencies. However, this leads to a new data representation that is quadratic in the number of objects w.r.t. the original data. Here, we present an alternative avoiding such a data representation and show how to characterize functional dependencies using the formalism of pattern structures, an extension of classical FCA to handle complex data. We also show how another class of dependencies can be characterized with that framework, namely, degenerated multivalued dependencies. Finally, we discuss and compare the performances of our new approach in a series of experiments on classical benchmark datasets.

Deep first formal concept search.

The calculation of formal concepts is a very important part in the theory of formal concept analysis (FCA); however, within the framework of FCA, computing all formal concepts is the main challenge because of its exponential complexity and difficulty in visualizing the calculating process. With the basic idea of Depth First Search, this paper presents a visualization algorithm by the attribute topology of formal context. Limited by the constraints and calculation rules, all concepts are achieved by the visualization global formal concepts searching, based on the topology degenerated with the fixed start and end points, without repetition and omission. This method makes the calculation of formal concepts precise and easy to operate and reflects the integrity of the algorithm, which enables it to be suitable for visualization analysis.

Greedy Modifications of OAC-triclustering Algorithm

In this paper we propose several possible modifications to the OAC-triclustering algorithms based on the prime operators. This method based on the framework of Formal Concept Analysis showed some rather promising results in the previous research. But while it is fast and efficient with respect to such measures as average density of the output, diversity, coverage, and noise- tolerance, it produces rather large number of triclusters. This makes it almost impossible for the expert to manually check the results. We show that the proposed post-processing techniques not only reduce the size of the output for this approach and keep the good values for the measures, but also keep the time complexity of the original algorithm.

Formal concept analysis based on the topology for attributes of a formal context

Formal concept analysis (FCA) concerns the hierarchical structures induced by a binary relation between a pair of sets, it is widely applied in data analysis, information retrieval, and knowledge discovery. Within the framework of FCA, computing all formal concepts is the main challenge due to its exponential complexity. It has be proved that all formal concepts is a closure system on objects, hence, the closure operator on objects are general used to generate all formal concepts of a formal context. In the lexicographic tree approach, a base on objects is used to generate extensions of all formal concepts and construct the formal concept lattice. Inspired from the approach, we concentrate a base on attributes and generate intensions of all formal concepts in this paper. To this end, we firstly analyze an example, the lexicographic tree approach is used to generate all formal concepts, from the time complexity point of view, we present that it is not trivial to generate the base on attributes by a simple symmetrical way from the methods based on objects. Then, we deduce a set-valued mapping from attributes to the power set of attributes in a formal context and define a binary relation on attributes by the set-valued mapping. Using the binary relation on attributes, we construct an approximation space and a topology for attributes, respectively, and obtain a base for the topology. We prove that intensions of all formal concepts are included in the topology for attributes, this means that the base can be used to generate intensions of all formal concepts of the formal context and construct the formal concept lattice. More general, our results represent relationships and the hierarchical structures among attributes of the formal context, we present some typical applications, in which the topology for attributes and the base for the topology are applied for association rules discovery from a formal context and linguistic concept analysis.

Analysis of a Vector Space Model, Latent Semantic Indexing and Formal Concept Analysis for Information Retrieval

Abstract Latent Semantic Indexing (LSI), a variant of classical Vector Space Model (VSM), is an Information Retrieval (IR) model that attempts to capture the latent semantic relationship between the data items. Mathematical lattices, under the framework of Formal Concept Analysis (FCA), represent conceptual hierarchies in data and retrieve the information. However, both LSI and FCA use the data represented in the form of matrices. The objective of this paper is to systematically analyze VSM, LSI and FCA for the task of IR using standard and real life datasets.