scholarly journals Deep First Formal Concept Search

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Tao Zhang ◽  
Hui Li ◽  
Wenxue Hong ◽  
Xiamei Yuan ◽  
Xinyu Wei
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
End Points ◽  
Depth First Search ◽  
Visualization Analysis ◽  
Main Challenge ◽  
Formal Concepts ◽  
Exponential Complexity

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.

The construction of multi-granularity concept lattices

2020 ◽  
Vol 39 (3) ◽  
pp. 2783-2790
Author(s):  
Qian Hu ◽  
Ke-Yun Qin
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Mutual Transformation ◽  
Concept Lattices ◽  
Construction Methods ◽  
Formal Concepts ◽  
Transformation Methods

The construction of concept lattices is an important research topic in formal concept analysis. Inspired by multi-granularity rough sets, multi-granularity formal concept analysis has become a new hot research issue. This paper mainly studies the construction methods of concept lattices in multi-granularity formal context. The relationships between concept forming operators under different granularity are discussed. The mutual transformation methods of formal concepts under different granularity are presented. In addition, the approaches of obtaining coarse-granularity concept lattice by fine-granularity concept lattice and fine-granularity concept lattice by coarse-granularity concept lattice are examined. The related algorithms for generating concept lattices are proposed. The practicability of the method is illustrated by an example.

scholarly journals Three-Way Concept Analysis for Incomplete Formal Contexts

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Huilai Zhi ◽  
Hao Chao
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Binary Relations ◽  
Formal Concepts ◽  
Target Set ◽  
The Relationship ◽  
Negative Attributes

Recently, incomplete formal contexts have received more and more attention from the communities of formal concept analysis. Different from a complete context where the binary relations between all the objects and attribute are known, an incomplete formal context has at least a pair of object and attribute with a completely unknown binary relation. Partially known formal concepts use interval sets to indicate the incompleteness. Three-way formal concept analysis is capable of characterizing a target set by combining positive and negative attributes. However, how to describe target set, by pointing out what attributes it has with certainty and what attributes it has with possibility and what attributes it does not has with certainty and what attributes it does not has with possibility, is still an open problem. This paper combines the ideas of three-way formal concept analysis and partially known formal concepts and presents a framework of approximate three-way concept analysis. At first, approximate object-induced and attribute-induced three-way concept lattices are introduced, respectively. And then, the relationship between approximate three-way concept lattice and classical three-way concept lattice are investigated. Finally, examples are presented to demonstrate and verify the obtained results.

Knowledge Representation Using Formal Concept Analysis

2014 ◽  
pp. 306-336 ◽  
Author(s):  
Ch. Aswani Kumar ◽  
Prem Kumar Singh
Keyword(s):  
Formal Concept Analysis ◽  
Lattice Structure ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Mathematical Framework ◽  
Formal Concepts ◽  
Conceptual Data ◽  
The Relationship

Introduced by Rudolf Wille in the mid-80s, Formal Concept Analysis (FCA) is a mathematical framework that offers conceptual data analysis and knowledge discovery. FCA analyzes the data, which is represented in the form of a formal context, that describe the relationship between a particular set of objects and a particular set of attributes. From the formal context, FCA produces hierarchically ordered clusters called formal concepts and the basis of attribute dependencies, called attribute implications. All the concepts of a formal context form a hierarchical complete lattice structure called concept lattice that reflects the relationship of generalization and specialization among concepts. Several algorithms are proposed in the literature to extract the formal concepts from a given context. The objective of this chapter is to analyze, demonstrate, and compare a few standard algorithms that extract the formal concepts. For each algorithm, the analysis considers the functionality, output, complexity, delay time, exploration type, and data structures involved.

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.

scholarly journals A Web Page Clustering Method Based on Formal Concept Analysis

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 228 ◽  
Author(s):  
Zuping Zhang ◽  
Jing Zhao ◽  
Xiping Yan
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Web Pages ◽  
Web Page ◽  
Data Links ◽  
Web Page Clustering ◽  
The Web

Web page clustering is an important technology for sorting network resources. By extraction and clustering based on the similarity of the Web page, a large amount of information on a Web page can be organized effectively. In this paper, after describing the extraction of Web feature words, calculation methods for the weighting of feature words are studied deeply. Taking Web pages as objects and Web feature words as attributes, a formal context is constructed for using formal concept analysis. An algorithm for constructing a concept lattice based on cross data links was proposed and was successfully applied. This method can be used to cluster the Web pages using the concept lattice hierarchy. Experimental results indicate that the proposed algorithm is better than previous competitors with regard to time consumption and the clustering effect.

scholarly journals Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2694
Author(s):  
Amira Mouakher ◽  
Axel Ragobert ◽  
Sébastien Gerin ◽  
Andrea Ko
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Order Structure ◽  
Formal Concept ◽  
Massive Datasets ◽  
Interestingness Measures ◽  
Galois Lattice ◽  
Formal Concepts ◽  
Representation Method

Formal concept analysis (FCA) is a mathematical theory that is typically used as a knowledge representation method. The approach starts with an input binary relation specifying a set of objects and attributes, finds the natural groupings (formal concepts) described in the data, and then organizes the concepts in a partial order structure or concept (Galois) lattice. Unfortunately, the total number of concepts in this structure tends to grow exponentially as the size of the data increases. Therefore, there are numerous approaches for selecting a subset of concepts to provide full or partial coverage. In this paper, we rely on the battery of mathematical models offered by FCA to introduce a new greedy algorithm, called Concise, to compute minimal and meaningful subsets of concepts. Thanks to its theoretical properties, the Concise algorithm is shown to avoid the sluggishness of its competitors while offering the ability to mine both partial and full conceptual coverage of formal contexts. Furthermore, experiments on massive datasets also underscore the preservation of the quality of the mined formal concepts through interestingness measures agreed upon by the community.

Representing and Processing Medical Knowledge Using Formal Concept Analysis

2002 ◽  
Vol 41 (02) ◽  
pp. 160-167 ◽  
Author(s):  
M. Schnabel
Keyword(s):  
Complete Lattice ◽  
Formal Concept Analysis ◽  
Medical Knowledge ◽  
Mathematical Structure ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Inference Process ◽  
Therapeutic Decisions ◽  
Analyze Data

Summary Objectives: The aim is to show the flexibility, adequateness, and generality of formal concept analysis (FCA) applied to expert systems in medicine. Methods: The basic idea of formal concept analysis is to look at a set of objects together with their attributes (formal context) under a definite mathematical view. This view leads to a mathematical structure, a complete lattice, which can be represented graphically. Results: Some examples show that this method is very general and can be used to describe diseases, relationships between diseases and findings, the inference process, and, among others, types of uncertainty. For many applications, the adequateness of this method, concerning the underlying semantics, can easily be made plausible. Conclusions: FCA can be used to analyze data that can be described by objects and attributes of any kind. The selected examples (diseases, patient cases, therapeutic decisions, rules) show the usefulness of this method. Although it is not difficult to transform the relevant semantics into a formal context in many cases, much more experience is necessary.

The Method of Discover the Attributes' Sequences of Objects in the Formal Context

2013 ◽  
Vol 427-429 ◽  
pp. 2536-2539
Author(s):  
Xue Song Dai ◽  
Yuan Ma ◽  
Wen Xue Hong
Keyword(s):  
Equivalence Relation ◽  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Analysis Method ◽  
Analysis Theory

Formal context is one of the research contents of formal concept analysis theory. In concept lattice, the attributes of the object are equivalent and there is no hierarchy. Facing to this problem, the equivalence relation which is on the attributes' set is defined and the corresponding σ operation is proposed. On this basis, the structure method of attribute hierarchical diagram is presented and attributes' sequences of associated objects are obtained. This conclusion enriches and extends the analysis method of the formal context.

scholarly journals Finding Music Formal Concepts Consistent with Acoustic Similarity

2020 ◽  
Author(s):  
Yoshiaki Okubo
Keyword(s):  
Efficient Algorithm ◽  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Point Of View ◽  
Experimental Results ◽  
Formal Concept ◽  
Acoustic Similarity ◽  
Formal Concepts

In this paper, we present a method of finding conceptual clusters of music objects based on Formal Concept Analysis. A formal concept (FC) is defined as a pair of extent and intent which are sets of objects and terminological attributes commonly associated with the objects, respectively. Thus, an FC can be regarded as a conceptual cluster of similar objects for which its similarity can clearly be stated in terms of the intent. We especially discuss FCs in case of music objects, called music FCs. Since a music FC is based solely on terminological information, we often find extracted FCs would not always be satisfiable from acoustic point of view. In order to improve their quality, we additionally require our FCs to be consistent with acoustic similarity. We design an efficient algorithm for extracting desirable music FCs. Our experimental results for The MagnaTagATune Dataset shows usefulness of the proposed method.

Critical Analysis on Open Source LMSs using FCA

2013 ◽  
Vol 11 (4) ◽  
pp. 97-111 ◽  
Author(s):  
K. Sumangali ◽  
Ch. Aswani Kumar
Keyword(s):  
Learning Environment ◽  
Open Source ◽  
Formal Concept Analysis ◽  
Critical Analysis ◽  
Management System ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Mathematical Framework ◽  
E Learning

The objective of this paper is to apply Formal Concept Analysis (FCA) to identify the best open source Learning Management System (LMS) for an E-learning environment. FCA is a mathematical framework that represents knowledge derived from a formal context. In constructing the formal context, LMSs are treated as objects and their features as attributes. This context is analysed and classified into concepts based on the rules of FCA. The knowledge derived from the concepts and our analyses reveal that Moodle is exceptional, with more features when compared with other LMSs.

Sign in / Sign up

Export Citation Format

Share Document