Formal Concept Analysis as Mathematical Theory of Concepts and Concept Hierarchies

2005 ◽  
pp. 1-33 ◽  
Author(s):  
Rudolf Wille
Keyword(s):  
Formal Concept Analysis ◽  
Mathematical Theory ◽  
Concept Analysis ◽  
Formal Concept ◽  
Concept Hierarchies

scholarly journals Visualizing and Interacting with Concept Hierarchies

2015 ◽  
Vol 24 (02) ◽  
pp. 1540006
Author(s):  
Michel Plantié ◽  
Michel Crampes
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Formal Concept ◽  
Visual Interpretation ◽  
Galois Lattices ◽  
Navigation Support ◽  
On Line ◽  
Object Attribute ◽  
Concept Hierarchies

Concept Hierarchies and Formal Concept Analysis (FCA) are theoretically well grounded. They rely on line diagrams called Galois lattices for visualizing and analysing object-attribute sets. Galois lattices are visually seducing and conceptually rich for experts. However they present important drawbacks due to their concept oriented overall structure: analysing what they show is difficult for non experts, navigation is cumbersome, interaction is poor, and scalability is a deep bottleneck for visual interpretation even for experts. In this paper we introduce semantic probes as a means to overcome many of these problems and extend usability and application possibilities of traditional FCA visualization methods. Semantic probes are visual user centred objects which extract and organize reduced Galois sub-hierarchies. They are simpler, clearer, and they provide a better navigation support through a rich set of interaction possibilities. Since probe driven sub-hierarchies are limited to users' focus, scalability is under control and interpretation is facilitated. After some successful experiments, several applications are being developed with the remaining problem of finding a compromise between simplicity and conceptual expressivity.

Lower and Upper Concept Lattices

2014 ◽  
Vol 60 (2) ◽  
pp. 337-352
Author(s):  
Cristian Vaideanu
Keyword(s):  
Formal Concept Analysis ◽  
Mathematical Theory ◽  
Concept Analysis ◽  
Galois Connection ◽  
Knowledge Systems ◽  
Domain Theory ◽  
Formal Concept ◽  
Concept Lattices ◽  
New Models ◽  
Formal Concepts

Abstract Formal Concept Analysis is a mathematical theory of data analysis using formal contexts and concept lattices. In this paper, two new types of concept lattices are introduced by using notions from domain theory (in particular, Hoare and Smyth powerdomains). Based on a Galois connection, we prove the fundamental theorem of the Formal Concept Analysis, as well as other properties of lower and upper formal concepts. In this way, we provide new models to represent and retrieve the information in data and knowledge systems.

scholarly journals Learning Concept Hierarchies from Text Corpora using Formal Concept Analysis

2005 ◽  
Vol 24 ◽  
pp. 305-339 ◽  
Author(s):  
P. Cimiano ◽  
A. Hotho ◽  
S. Staab
Keyword(s):  
Formal Concept Analysis ◽  
Clustering Algorithm ◽  
Special Kind ◽  
Concept Analysis ◽  
Formal Concept ◽  
Agglomerative Clustering ◽  
Text Corpus ◽  
Text Corpora ◽  
The Impact ◽  
Concept Hierarchies

We present a novel approach to the automatic acquisition of taxonomies or concept hierarchies from a text corpus. The approach is based on Formal Concept Analysis (FCA), a method mainly used for the analysis of data, i.e. for investigating and processing explicitly given information. We follow Harris' distributional hypothesis and model the context of a certain term as a vector representing syntactic dependencies which are automatically acquired from the text corpus with a linguistic parser. On the basis of this context information, FCA produces a lattice that we convert into a special kind of partial order constituting a concept hierarchy. The approach is evaluated by comparing the resulting concept hierarchies with hand-crafted taxonomies for two domains: tourism and finance. We also directly compare our approach with hierarchical agglomerative clustering as well as with Bi-Section-KMeans as an instance of a divisive clustering algorithm. Furthermore, we investigate the impact of using different measures weighting the contribution of each attribute as well as of applying a particular smoothing technique to cope with data sparseness.

An Approach Using Concept Lattice Structure for Data Mining and Information Retrieval

2015 ◽  
Vol 1 ◽  
pp. 1
Author(s):  
Tran Lam Quan ◽  
Vu Tat Thang
Keyword(s):  
Data Mining ◽  
Information Retrieval ◽  
Text Mining ◽  
Formal Concept Analysis ◽  
Mathematical Theory ◽  
Lattice Structure ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Frequent Itemset ◽  
Formal Concept

Since the 1980s, the concept lattice was studied and applied to the problems of text mining, frequent itemset, classification, etc. The formal concept analysis - FCA is one of the main techniques applied in the concept lattice. FCA is a mathematical theory which is applied to the data mining by setting a table with rows describing objects and columns describing attributes, with relationships between them, and then sets up the concept lattice structure. In the area of information retrieval, FCA considers the correlation of objects-attributes the same as those of documents-terms. In the process of setting up the lattice, FCA defines each node in the lattice as a concept. The algorithm for the construction of concept lattice will install a couple on each node, including a set of documents with common terms, and a set of terms which co-occurs in documents. In a larger scale, each concept in the lattice could be recognized as a couple of questions - answers. In the lattice, the action of browsing up or down of nodes will allow approaching more general concepts or more detail concepts, respectively.

scholarly journals Continuous Domains in Formal Concept Analysis*

2021 ◽  
Vol 179 (3) ◽  
pp. 295-319
Author(s):  
Longchun Wang ◽  
Lankun Guo ◽  
Qingguo Li
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Continuous Functions ◽  
Formal Context ◽  
Formal Concept ◽  
Contractive Mappings ◽  
Continuous Domains ◽  
Algebraic Domains ◽  
Scott Continuous ◽  
Continuous Domain

Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion of contractive mappings over formal contexts is proposed, which can be viewed as a generalization of interior operators on sets into the framework of FCA. Then, by considering subset-selections consistent with contractive mappings, the notions of attribute continuous formal contexts and continuous concepts are introduced. It is shown that the set of continuous concepts of an attribute continuous formal context forms a continuous domain, and every continuous domain can be restructured in this way. Moreover, the notion of F-morphisms is identified to produce a category equivalent to that of continuous domains with Scott continuous functions. The paper also investigates the representations of various subclasses of continuous domains including algebraic domains and stably continuous semilattices.

The Research of Semantic Web Service Matching Algorithm Based on the Formal Concept Analysis

2013 ◽  
Vol 760-762 ◽  
pp. 1708-1712
Author(s):  
Ying Fang Li ◽  
Ying Jiang Li ◽  
Yan Li ◽  
Yang Bo
Keyword(s):  
Semantic Web ◽  
Web Service ◽  
Formal Concept Analysis ◽  
Service Discovery ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Concept ◽  
Semantic Web Service ◽  
Matching Algorithm ◽  
Service Matching

At present, as the number of web services resources on the network drastically increased, how to quickly and efficiently find the needed services from publishing services has become a problem to resolve. Aiming at the problems of low efficiency in service discovery of traditional web service, the formal concept analysis ( FCA) is introduced into the semantic Web service matching, and a Matching Algorithm based semantic web service is proposed. With considering the concept of limited inheritance,this method introduces the concept of limited inheritance to the semantic similarity calculation based on the concept lattice. It is significant in enhancing the service function matching in practical applications through adjust the calculation.

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