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.

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 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.

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.

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.

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.

An Algorithm for Recomputing Concepts in Microarray Data Analysis by Biological Lattice

2013 ◽  
Vol 17 (5) ◽  
pp. 761-771 ◽  
Author(s):  
Hidenobu Hashikami ◽  
◽  
Takanari Tanabata ◽  
Fumiaki Hirose ◽  
Nur Hasanah ◽  
...  
Keyword(s):  
Gene Expression ◽  
Microarray Data ◽  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Microarray Gene Expression Data ◽  
Microarray Data Analysis ◽  
Formal Concept ◽  
Two Phase ◽  
Microarray Gene Expression ◽  
Formal Concepts

A data-analytic system is proposed for microarray gene expression data based on Formal Concept Analysis (FCA). The purpose of the system is to systematically organize data and to build a complete lattice that analyzes complex relations among genes and give biological interpretation of microarray data. In the system, formal concept analysis handles complex relations, so the microarray data is binarized by setting up a threshold. When change occurs in a conventional algorithm, formal concepts that are nodes of the lattice were calculated from the beginning, but the calculation is inefficient. This paper proposes a new algorithm that has two phase of matrix detection and updating concepts to efficiently update only altered concepts from previously generated concepts. Experiments on run time show that the algorithm takes an average of 0.94 seconds to process real microarray data containing of 43,734 genes and 6 gene expression values.

Web Pages Mining Based on Terms and Formal Concept Analysis

2014 ◽  
Vol 981 ◽  
pp. 187-191
Author(s):  
Bo Yu ◽  
Deng Ju Yao ◽  
Guang Yi Tang
Keyword(s):  
Formal Concept Analysis ◽  
Research Work ◽  
Concept Analysis ◽  
Difficult Problem ◽  
Formal Concept ◽  
Web Pages ◽  
Mining System ◽  
Main Research ◽  
Galois Lattice ◽  
The Web

In the face of immense Web pages of WWW, how to extract valuable knowledge from the Internet is a difficult problem. The main research work of this paper was to apply FCA (Formal concept analysis) and Web terms on the Web representing the relationship between Web pages and web terms. We deeply studied how to apply Galois to Web page mining, and used the Java language to design the Web pages mining system. The system uses the constructed Galois lattice to extract potential knowledge of WWW. The results prove that the use of Galois Lattices and Web terms for Web pages mining is feasible.

scholarly journals Formalių konceptų analizė, kuriant taikomosios srities ontologijas

2008 ◽  
Vol 46 ◽  
pp. 115-126
Author(s):  
Darius Jurkevičius ◽  
Olegas Vasilecas ◽  
Algirdas Laukaitis
Keyword(s):  
Formal Concept Analysis ◽  
Main Idea ◽  
Concept Analysis ◽  
Formal Concept ◽  
Analysis Method ◽  
Specific Domain ◽  
Hierarchical Tree ◽  
Formal Concepts

Straipsnyje pristatomas naujas metodas, kuris padeda sukurti dalykinės srities ontologiją. Pagrindinis metodo bruožas pasireiškia tuo, kad ontologijos kūrimo metu dalykinės srities objektai, konceptai, bei konceptų atributai analizuojami atliekant formalių konceptų analizės algoritmus. Be to, šio metodo ontologijos kūrimo rezultatai gali būti taikomi dalykinės srities dokumentų semantiniam indeksavimui, kas ypač svarbu plėtojant semantinio interneto technologijas. Be šio metodo pristatymo, šiame straipsnyje yra aprašytas eksperimentinis tyrimas susijęs su nekilnojamojo turto dalykine sritimi. Eksperimento metu buvo sukurtas sistemos prototipas, kuris realizuoja straipsnyje pateiktą ontologijos kūrimo metodą. Manome, kad sukurto prototipo architektūra taip pat bus naudinga kitiems tyrėjams ontologijų kūrimo srityje.Pagrindiniai žodžiai: ontologija, formalių konceptų analizė, formalus konceptas, duomenų analizė.Ontology building using formal conceptDarius Jurkevičius, Olegas Vasilecas, Algirdas Laukaitis SummaryIn this article the method how to make ontology using formal concepts is described. This method is used to collect terms of specific domain. This method allows to represent the hierarchical tree of concepts without analysing terms of specific domain. The main idea of proposed method is to select terms (objects) from collected data using templates. Later collected terms are analysed using formal concept analysis method. This allows to simplify the steps of terms analysis and ontology representing in ontology creating process. In this article the experiment and it‘s results and conclusions are described. The realty domain is select for the experiment.Keywords. Ontology, formal concept analysis, formal concept, programme agent.x;">

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.

HaLoop Approach for Concept Generation in Formal Concept Analysis

2018 ◽  
Vol 17 (03) ◽  
pp. 1850029 ◽  
Author(s):  
Raghavendra K. Chunduri ◽  
Aswani Kumar Cherukuri
Keyword(s):  
Formal Concept Analysis ◽  
Iterative Algorithms ◽  
Concept Analysis ◽  
Formal Concept ◽  
Concept Generation ◽  
Mapreduce Framework ◽  
Theoretical Concepts ◽  
Hadoop Mapreduce ◽  
Runtime Environment ◽  
Formal Concepts

This paper describes an efficient algorithm for formal concepts generation in large formal contexts. While many algorithms exist for concept generation, they are not suitable for generating concepts efficiently on larger contexts. We propose an algorithm named as HaLoopUNCG algorithm based on MapReduce framework that uses a lightweight runtime environment called HaLoop. HaLoop, a modified version of Hadoop MapReduce, suits better for iterative algorithms over large datasets. Our approach uses the features of HaLoop efficiently to generate concepts in an iterative manner. First, we describe the theoretical concepts of formal concept analysis and HaLoop. Second, we provide a detailed representation of our work based on Lindig’s fast concept analysis algorithm using HaLoop and MapReduce framework. The experimental evaluations demonstrate that HaLoopUNCG algorithm is performing better than Hadoop version of upper neighbour concept generation (MRUNCG) algorithm, MapReduce implementation of Ganter’s next closure algorithm and other distributed implementations of concept generation algorithms.

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