scholarly journals ImplicPBDD: A New Approach to Extract Proper Implications Set from High-Dimension Formal Contexts Using a Binary Decision Diagram †

Information ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 266
Author(s):  
Phillip Santos ◽  
Pedro Ruas ◽  
Julio Neves ◽  
Paula Silva ◽  
Sérgio Dias ◽  
...  
Keyword(s):  
Data Structure ◽  
High Dimension ◽  
Formal Concept Analysis ◽  
Binary Decision Diagram ◽  
High Dimensional ◽  
Formal Context ◽  
Formal Concept ◽  
Binary Decision ◽  
New Approach ◽  
Original Algorithm

Formal concept analysis (FCA) is largely applied in different areas. However, in some FCA applications the volume of information that needs to be processed can become unfeasible. Thus, the demand for new approaches and algorithms that enable processing large amounts of information is increasing substantially. This article presents a new algorithm for extracting proper implications from high-dimensional contexts. The proposed algorithm, called ImplicPBDD, was based on the PropIm algorithm, and uses a data structure called binary decision diagram (BDD) to simplify the representation of the formal context and enhance the extraction of proper implications. In order to analyze the performance of the ImplicPBDD algorithm, we performed tests using synthetic contexts varying the number of objects, attributes and context density. The experiments show that ImplicPBDD has a better performance—up to 80% faster—than its original algorithm, regardless of the number of attributes, objects and densities.

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.

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 A New Rapid Incremental Algorithm for Constructing Concept Lattices

Information ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 78 ◽  
Author(s):  
Jingpu Zhang ◽  
Ronghui Liu ◽  
Ligeng Zou ◽  
Licheng Zeng
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Incremental Algorithm ◽  
Formal Context ◽  
Formal Concept ◽  
Concept Lattices ◽  
Covering Relation ◽  
Canonical Generator ◽  
Lattice Construction ◽  
Time And Space Complexity

Formal concept analysis has proven to be a very effective method for data analysis and rule extraction, but how to build formal concept lattices is a difficult and hot topic. In this paper, an efficient and rapid incremental concept lattice construction algorithm is proposed. The algorithm, named FastAddExtent, is seen as a modification of AddIntent in which we improve two fundamental procedures, including fixing the covering relation and searching the canonical generator. The proposed algorithm can locate the desired concept quickly by adding data fields to every concept. The algorithm is depicted in detail, using a formal context to show how the new algorithm works and discussing time and space complexity issues. We also present an experimental evaluation of its performance and comparison with AddExtent. Experimental results show that the FastAddExtent algorithm can improve efficiency compared with the primitive AddExtent algorithm.

A new approach for textual feature selection based on N-composite isolated labels

2019 ◽  
Vol 26 (2) ◽  
pp. 221-243
Author(s):  
Samir Elloumi
Keyword(s):  
Feature Selection ◽  
Formal Context ◽  
Formal Concept ◽  
Processing Efficiency ◽  
New Approach ◽  
Textual Data ◽  
Isolated Points ◽  
Document Categorization ◽  
Textual Features ◽  
Textual Feature

AbstractTextual Feature Selection (TFS) aims to extract relevant parts or segments from text as being the most relevant ones w.r.t. the information it expresses. The selected features are useful for automatic indexing, summarization, document categorization, knowledge discovery, so on. Regarding the huge amount of electronic textual data daily published, many challenges related to the semantic aspect as well as the processing efficiency are addressed. In this paper, we propose a new approach for TFS based on Formal Concept Analysis background. Mainly, we propose to extract textual features by exploring the regularities in a formal context where isolated points exist. We introduce the notion ofN-composite isolated points as a set ofNwords to be considered as a unique textual feature. We show that a reduced value ofN(between 1 and 3) allows extracting significant textual features compared with existing approaches even for non-completely covering an initial formal context.

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.

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 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 Détection des préoccupations transversales par l'analyse formelle de concepts des diagrammes de séquence

2014 ◽  
Vol Volume 18, 2014 ◽  
Author(s):  
Fairouz Dahi ◽  
Nora Bounour
Keyword(s):  
Formal Concept Analysis ◽  
Source Code ◽  
Object Oriented ◽  
Formal Concept ◽  
Conceptual Level ◽  
Sequence Diagrams ◽  
New Approach ◽  
Crosscutting Concerns ◽  
International Audience ◽  
Industrial Adoption

International audience The existence of crosscutting concerns tangled or scattered, complicates the understanding and evolution of object oriented source code. The industrial adoption of aspect-oriented paradigm has led to research new approaches supporting aspect oriented migration. This migration requires the identification of crosscutting concerns, in order to encapsulate them into aspects. We propose in this paper a new approach for the identification of crosscutting concerns at the conceptual level. We materialize this latter by the UML class and sequence diagrams. We use the formal concept analysis to group scattered functionalities in sequence diagrams, and we analyze the order of method calls to detect the tangled ones. Then, we filter all obtained candidate aspects, in order to avoid the mistakes.

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