Concept Lattice Construction Research Articles

Individual entity induced label concept set for classification: An information fusion viewpoint

Formal concept analysis has seldom been employed for classification. This is mainly due to (1) the high time and space complexity of concept lattice construction, and (2) the difficulty of concept lattice based prediction. Inspired by information fusion, this paper introduces a new algorithm named CECS, which constructs a concept set instead of a lattice to ensure efficiency and enable direct classification. Regarding concept set construction, we define sub-formal context by grouping objects with the same label within the labeled formal context. Subsequently, we induce the label concept from the sub-formal context based on each individual entity (object or attribute). In this way, the information intrinsic to each label can be clearly expressed. At the same time, it reduces time consumption. Regarding classification, we define label confidence through fusing object and attribute induced concept sets. Respective calculation does not require additional prediction methods, thus becoming more efficient. Experiments are conducted on fifteen public datasets from UCI and KEEL in comparison with eight classical classification algorithms. Results validate the time complexity analysis, and show competitive classification performance of our algorithm. The source code is available at https://github.com/swpuzeng/cecs.

Survey on attribute and concept reduction methods in formal concept analysis

Formal concept analysis (FCA) is now widely recognized as a useful approach for extracting, representing, and analyzing knowledge in various domains. The high computational cost of knowledge processing and the difficulty of visualizing the lattice are two key challenges in practical FCA implementations. Moreover, assessing the finalized built-up lattice may be problematic due to the enormous number of formal concepts and the complexity of their connections. The challenge of constructing concept lattices of adequate size and structure to convey high-importance context features remains a significant FCA aim. In the literature, various strategies for concept lattice reduction have been presented. In this work, we suggest a categorization of reduction methods for concept lattice based on three main categories: context pre-processing, non-essential distinctions elimination, and concept filtration, whereby using FCA-based analysis, the most important methods in the literature are analyzed and compared based on six pillars: the preliminary step of the reduction process, domain expert, changing the original data structure, final concept lattice, quality of reduction, and category of reduction method.

Stability of three-way concepts and its application to natural language generation

• Three-way concept stability and its properties. • Algorithm for the computation of three-way concept stability. • A case study on natural language generation scenario. Three-way concept analysis (3WCA) has been an emerging and important methodology for knowledge discovery and data analysis. Particularly, 3WCA can efficiently characterize the information of “jointly possessed” and “jointly not possessed” compared to the classical formal concept only can describe common attributes owned by objects. This property, typical of 3WCA has a huge potential in the field of Natural Language Generation (NLG). However, the construction of a three-way concept lattice is proved as an NP-complete problem and even harder than the construction of conventional concept lattice. This could negatively affect the use of 3WCA for NLG in real contexts. Hence, it is necessary to prune the three-way concept lattice and extract more interesting three-way concepts for knowledge acquisition. To this end, this paper defines the stability of a three-way concept and analyzes the relevant properties. An efficient computational algorithm for calculating the stability of three-way concepts is developed and evaluated by an experiment. In addition, a case study on NLG is conducted for demonstrating the applicability of the proposed technique.

Incremental construction of three-way concept lattice for knowledge discovery in social networks

Three-way concept analysis (3WCA), a combination of three-way decision and formal concept analysis, is widely used in the field of knowledge discovery. Generally, constructing three-way concept lattices requires the original formal context and its complement context simultaneously. Additionally, the existing three-way concept lattice construction algorithms focus on the static formal context, and cannot cope with the dynamic formal context that is an essential representation in social networks. Toward this end, this paper pioneers a novel problem and method for the incremental construction of three-way concept lattice for knowledge discovery in social networks. Aiming to facilitate the construction efficiency, this paper firstly investigates the three-way concept lattice construction for attribute-incremental/object-incremental formal contexts, respectively. Then, the dynamic formal context of a social network can be viewed as a special formal context with both attribute-increment and object-increment. Further, we develop the AE/OE concept lattice incremental construction algorithms, called SNS-AE and SNS-OE. Extensive experiments are conducted on various formal contexts to evaluate the effectiveness of our incremental algorithms. The experimental results demonstrate that our proposed incremental algorithms can significantly decrease the construction time of three-way concept lattice compared to the non-incremental algorithm.

Triadic concept approximation

Formal Concept Analysis is a mathematical theory for knowledge representation as well as data analysis and visualization. It provides a mechanism for understanding and mining data through concept lattice construction and exploration. This theory assists in data processing by providing a framework for applying different analysis techniques. One of its potentials lies in its mathematical foundation that enables the generation, ordering, and visualization of knowledge in the form of formal concepts described in a hierarchy known as a concept lattice. However, as the input dataset grows, the search and especially the visualization and exploration of concepts becomes prohibitive. With the extension of the classical FCA approach to Triadic Concept Analysis, this problem becomes even more evident due to the complexity of the inherent structures in triadic concepts and relationships. In this work, we propose an approach to find triadic concepts when a query in the form of a triple is given, allowing the visualization and exploration of a Hasse diagram of triadic concepts.

Reduction of fuzzy-crisp concept lattice based on order-class matrix

Knowledge reduction is one of critical problems in data mining and information processing. It can simplify the structure of the lattice during the construction of fuzzy-crisp concept lattice. In terms of fuzzy-crisp concept, we develop an order-class matrix to represent extents and intents of concepts, respectively. In order to improve the computing efficiency, it is necessary to reduce the size of lattices as much as possible. Therefore the judgement theorem of meet-irreducible elements is proposed. To deal with attribute reductions, we develop a discernibility Boolean matrix in formal fuzzy contexts by preserving extents of meet-irreducible elements via order-class matrix. A heuristic attribute-reduction algorithm is proposed. Then we extend the proposed model to consistent formal fuzzy decision contexts. Our methods present a new framework for knowledge reduction in formal fuzzy contexts.

The construction of multi-granularity concept lattices

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.

Dependence space models to construct concept lattices

Concept lattice is a kind of efficient mathematical tools for data analysis and knowledge discovery. In this paper, dependence space models are constructed to obtain a concept lattice. For a formal context, a congruence relation is first defined based on a sufficiency operator on the power set of the attribute set. A dependence space is generated. By using the dependence space, we introduce a closure operator. Related properties of the operator are discussed. It is also proved that any closed element of the closure operator is the maximum element in the attribute granule generated by the element. Further, the closed element is just the intension of some formal concept. Similarly, we define a congruence relation on the basis of a sufficiency operator, and introduce a dependence space on the power set of the object set. A closure operator is proposed for the subset of objects. The corresponding closed element of the closure operator is the maximum element in each object granule. All maximum elements generate the set of all extensions of the concept lattice. An example is used to show the validity of the approach to obtain all intensions. Finally, we introduce a dominance congruence relation, which is used to produce a closure operator. The dependence of attributes is defined based on the closure operator. The related decision rules are discussed.

Constructing three-way concept lattice based on the composite of classical lattices

Three-way concept analysis provides a novel model for three-way decisions, and also extends the classical formal concept analysis, which has attracted many attentions in recent years. In order to construct three-way concept lattices, original formal context and its complement context need to be considered simultaneously. In this paper, a new method of constructing attribute-induced three-way (AE) and object-induced three-way (OE) concept lattices is proposed. Firstly, we introduce an AE-oriented composite operator and an OE-oriented composite operator that combine a pair of formal concepts coming from the concept lattices of original formal context and its complement context. Secondly, we define the candidate AE concepts and redundant AE concepts based on the AE-oriented composite operator, and define the candidate OE concepts and redundant OE concepts based on the OE-oriented composite operator, respectively. Finally, we propose an AE lattice construction algorithm and an OE lattice construction algorithm. Theoretical analysis and experimental results demonstrate that the proposed method is simple and effective, and it is a useful supplement to current three-way concept lattice construction methods.

Influences of Three-Way Concept Lattice Caused by Variations of Attribute Values

Three-way concept lattices have been widely used in various types of applications. As the construction of three-way concept lattices is rather time consuming, especially for large formal contexts, it is not applicable to construct the lattices from the beginning when changes are made to the contexts. Motivated by this problem, the influences of three-way concept lattices caused by variations of attribute values are explored in this study. Specifically, we discuss two types of changes. One is changing the value of a specific incidence relation from 0 to 1, and the other is from 1 to 0. Furthermore, two types of three-way concept lattices are investigated. One is the object-induced three-way concept lattice, and the other is the attribute-induced three-way concept lattice. Both the mathematical proofs and the examples show the effectiveness of our proposed methods.

The construction of fuzzy concept lattice based on weighted complete graph

The construction of fuzzy concept lattice based on weighted complete graph

The construction of attribute (object)-oriented multi-granularity concept lattices

How to reduce the complexity of lattice construction is an important research topic in formal concept analysis. Based on granularity tree, the relationship between the extent and the intent of the attribute (object)-oriented concept before and after granularity transformation are investigated. Then, zoom algorithms for attribute (object)-oriented concept lattices are proposed. Specifically, zoom-in algorithm is applied to change the attribute granularity from coarse-granularity to fine-granularity, and zoom-out algorithm achieves changing the attribute granularity from fine-granularity to coarse-granularity. Zoom algorithms deal with the problems of fast construction of the attribute (object)-oriented multi-granularity concept lattices. By using zoom algorithms, the attribute (object)-oriented concept lattice based on different attribute granularity can be directly generated through the existing attribute (object)-oriented concept lattice. The proposed algorithms not only reduce the computational complexity of concept lattice construction, but also facilitate further data mining and knowledge discovery in formal contexts. Furthermore, the transformation algorithms among three kinds of concept lattice are proposed.

Research on Two Main Construction Methods of Concept Lattices

Because of the completeness of concept lattices, the time complexity of constructing concept lattices has become the main factor affecting the application of formal concept analysis (FCA). The key problems in the research of concept lattices are how to improve the generation efficiency and how to reduce the space and time complexity of constructing concept lattices. So far, reviews on lattice construction algorithms have not been comprehensive. In view of this situation, we give a detailed review on two categories of construction algorithms: batch methods and incremental methods. The first category is a formal context that cannot be updated once the concept lattice has been constructed; the second category is a formal context that can be updated after a new object being added to the formal context. We briefly introduce classical and improved construction methods, illustrate the deficiencies of some algorithms and point out the improvements of the follow-up algorithms. Furthermore, we compare and discuss several key algorithms, and also pay attention to the application of concept lattices. Finally, two further research directions of concept lattices are proposed, including parallel construction methods of concept lattices and research of heterogeneous data concept lattices.

A fast algorithm on generating concept lattice for symmetry formal context constructed from social networks

Formal concept analysis has been witnessed to be an effective soft computing methodology for data analysis, rule extraction and clustering, but how to build a formal concept lattice efficiently is always a challenge issue. Recent years, several deformation formal contexts are emerging for addressing current important research problems, such as virtual machines scheduling in mobile cloud computing and topological structure analysis in social networks. In this paper, we focus on the symmetry formal context where the objects and attributes are identical, and its formal concept lattice construction. Firstly, we explore the properties of symmetry formal context and discover a symmetry line which must appear in the expected formal concept lattice. Further, a fast algorithm for building concept lattice for symmetry formal context is presented. Then, five social network datasets are utilized for evaluating our proposed algorithm. Experimental results show that our algorithm can speed up 1.2 times and 3.45 times compared to the concept-matrix based concepts generation algorithm and incremental algorithm, respectively.

A New Rapid Incremental Algorithm for Constructing Concept Lattices

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.

Granule description based on positive and negative attributes

Granule description is a fundamental problem in granular computing. The existing studies are mainly based on Wille’s concept lattice, and attribute reduction techniques, e.g., minimal generators of granules, are often adopted to compute the most concise description of a given granule. However, on one hand, as the construction of concept lattice has a relatively high time complexity especially for large formal contexts, it may bring difficulties in real applications. On the other hand, how to use positive and negative attributes for granule description is still an open problem. In this paper, to improve the description efficiency, we first consider attribute-induced atomic granules as the building blocks of more complicated granules. And then, we discuss granule description based on positive and negative attributes, respectively. Finally, granule description is also investigated by combining positive and negative attributes. The main contribution of this study is to find the most concise descriptions of definable granules from the perspectives of positive and negative attributes.

A parallel algorithm for constructing concept lattice based on hierarchical concept under MapReduce

A parallel algorithm for constructing concept lattice based on hierarchical concept under MapReduce

Efficiency analsyis of concept lattice construction algorithms

The theory of Formal Concept Analysis provides an efficient method for conceptualization of formal contexts. The methods for conceptualization are applied mainly in knowledge engineering and data mining areas. The key element in formal conceptualization applications is the concept set construction phase. The main goal of the research work is to analyse the different incremental methods and to optimize their efficiency. The proposed method is based on the novel combination of the Ferre and InClose methods providing an efficient update operation. Based on the performed comparison tests, the proposed method outperforms the main incremental methods and for some parameter ranges, its efficiency is comparable with the efficiency of the best batch methods.

Study on distributed generation algorithm of variable precision concept lattice based on ontology heterogeneous database

Integration of distributed heterogeneous data sources is the key issues under the big data applications. In this paper the strategy of variable precision is introduced to the concept lattice, and the one-to-one mapping mode of variable precision concept lattice and ontology concept lattice is constructed to produce the local ontology by constructing the variable precision concept lattice for each subsystem, and the distributed generation algorithm of variable precision concept lattice based on ontology heterogeneous database is proposed to draw support from the special relationship between concept lattice and ontology construction. Finally, based on the standard of main concept lattice of the existing heterogeneous database generated, a case study has been carried out in order to testify the feasibility and validity of this algorithm, and the differences between the main concept lattice and the standard concept lattice are compared. Analysis results show that this algorithm above-mentioned can automatically process the construction process of distributed concept lattice under the heterogeneous data sources.

Generalization of String Transformation Rules using Optimized Concept Lattice Construction Method

The sequences play an important role on many application areas. The strings as symbol sequences are investigated mainly in natural language processing and biological modeling. This paper investigates the transformation process of the strings and it proposes a method for induction of the string transformation rules. The presented method is based on the application of an FCA lattice for generalization of the transformation rules. The paper introduces an efficient construction algorithm for building the conceptualization lattice. Based on the performed comparison tests, the proposed method outperforms the main incremental methods and for some parameter ranges, its efficiency is comparable with the efficiency of the best batch methods.