scholarly journals A Novel Concept Acquisition Approach Based on Formal Contexts

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ting Qian ◽  
Ling Wei
Keyword(s):  
Data Analysis ◽  
Formal Concept Analysis ◽  
Real Life ◽  
Experimental Results ◽  
New Method ◽  
Concept Acquisition ◽  
Formal Concept ◽  
Knowledge Processing ◽  
Formal Concepts ◽  
Novel Concept

As an important tool for data analysis and knowledge processing, formal concept analysis (FCA) has been applied to many fields. In this paper, we introduce a new method to find all formal concepts based on formal contexts. The amount of intents calculation is reduced by the method. And the corresponding algorithm of our approach is proposed. The main theorems and the corresponding algorithm are examined by examples, respectively. At last, several real-life databases are analyzed to demonstrate the application of the proposed approach. Experimental results show that the proposed approach is simple and effective.

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 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.

scholarly journals Incremental Method of Generating Decision Implication Canonical Basis

2021 ◽  
Author(s):  
Shaoxia Zhang ◽  
Deyu Li ◽  
Yanhui Zhai
Keyword(s):  
Formal Concept Analysis ◽  
Canonical Basis ◽  
Concept Analysis ◽  
Experimental Results ◽  
Incremental Algorithm ◽  
Compact Representation ◽  
Formal Concept ◽  
Practical Applications ◽  
Incremental Method ◽  
Elementary Representation

Abstract Decision implication is an elementary representation of decision knowledge in formal concept analysis. Decision implication canonical basis (DICB), a set of decision implications with completeness and nonredundancy, is the most compact representation of decision implications. The method based on true premises (MBTP) for DICB generation is the most efficient one at present. In practical applications, however, data is always changing dynamically, and MBTP has to re-generate inefficiently the whole DICB. This paper proposes an incremental algorithm for DICB generation, which obtains a new DICB just by modifying and updating the existing one. Experimental results verify that when the samples in data are much more than condition attributes, which is actually a general case in practical applications, the incremental algorithm is significantly superior to MBTP. Furthermore, we conclude that, even for the data in which samples is less than condition attributes, when new samples are continually added into data, the incremental algorithm must be also more efficient than MBTP, because the incremental algorithm just needs to modify the existing DICB, which is only a part of work of MBTP.

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.

Formal Concept Analysis in knowledge processing: A survey on models and techniques

2013 ◽  
Vol 40 (16) ◽  
pp. 6601-6623 ◽  
Author(s):  
Jonas Poelmans ◽  
Sergei O. Kuznetsov ◽  
Dmitry I. Ignatov ◽  
Guido Dedene
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Formal Concept ◽  
Knowledge Processing

E-MsNFIS: Efficient Negative Frequent Itemsets Mining Based on Multiple Minimum Supports

2013 ◽  
Vol 411-414 ◽  
pp. 386-389 ◽  
Author(s):  
Tian Tian Xu ◽  
Xiang Jun Dong
Keyword(s):  
Association Rules ◽  
Real Life ◽  
Frequent Itemsets ◽  
Negative Association ◽  
Experimental Results ◽  
New Method ◽  
Minimum Support ◽  
Frequent Itemsets Mining ◽  
Negative Association Rules ◽  
Multiple Minimum Supports

Negative frequent itemsets (NFIS) like (a1a2¬a3a4) have played important roles in real applications because we can mine valued negative association rules from them. In one of our previous work, we proposed a method, namede-NFISto mine NFIS from positive frequent itemsets (PFIS). However,e-NFISonly uses single minimum support, which implicitly assumes that all items in the database are of the same nature or of similar frequencies in the database. This is often not the case in real-life applications. So a lot of methods to mine frequent itemsets with multiple minimum supports have been proposed. These methods allow users to assign different minimum supports to different items. But these methods only mine PFIS, doesn’t consider negative ones. So in this paper, we propose a new method, namede-msNFIS, to mine NFIS from PFIS based on multiple minimum supports. E-msNFIScontains three steps: 1) using existing methods to mine PFIS with multiple minimum supports; 2) using the same method ine-NFISto generate NCIS from PFIS got in step 1; 3) calculating the support of these NCIS only using the support of PFIS and then gettingNFIS. Experimental results show that thee-msNFISis efficient.

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