Sérgio M. Dias

Knowledge reduction in formal contexts using non-negative matrix factorization

Formal Concept Analysis (FCA) is a mathematical framework that offers conceptual data analysis and knowledge discovery. One of the main issues of knowledge discovery is knowledge reduction. The objective of this paper is to investigate the knowledge reduction in FCA and propose a method based on Non-Negative Matrix Factorization (NMF) for addressing the issue. Experiments on real world and benchmark datasets offer the evidence for the performance of the proposed method.

Concept lattices reduction

Survey of the main existing techniques for concept lattices reduction.Classification of techniques in three classes based on seven dimensions.Analyzing reduction techniques with formal concept analysis.Considerations are carried out about computational complexity and feasibility. Formal concept analysis (FCA) is currently considered an important formalism for knowledge representation, extraction and analysis with applications in different areas. A problem identified in several applications is the computational cost due to the large number of formal concepts generated. Even when that number is not very large, the essential aspects, those effectively needed, can be immersed in a maze of irrelevant details. In fact, the problem of obtaining a concept lattice of appropriate complexity and size is one of the most important problems of FCA. In literature, several different approaches to control the complexity and size of a concept lattice have been described, but so far they have not been properly analyzed, compared and classified. We propose the classification of techniques for concept lattice reduction in three groups: redundant information removal, simplification, and selection. The main techniques to reduce concept lattice are analyzed and classified based on seven dimensions, each one composed of a set of characteristics. Considerations are made about the applicability and computational complexity of approaches of different classes.

Applying the JBOS reduction method for relevant knowledge extraction

This work presents results from an experiment used to assess the JBOS (junction based on objects similarity) reduction method. Two reductions were made of a formal context about patients having symptoms in a tuberculosis data base. The first reduction used the knowledge expressed in the original formal context and the second used the knowledge expressed in expert rules. The assessment was made, in the first case, by comparison of the performances of the sets of extracted rules (stem bases) before and after the reduction, and in the second case, by comparison of the performances of the set of extracted rules after reduction with that of the expert rules. The performance in the first case was exactly the same as before reduction. In the second case the performance even improved, showing that the weighting process, besides incorporating the expert knowledge, resulted in rules well adjusted to the knowledge expressed in the original formal context. So, both reductions resulted in rule sets absolutely consistent with the original ones. The expert rules, FCA rules and both set of rules obtained after reduction were used also to classify patients of a validation set. In this case, the results have shown that the performance was the same before and after reduction. Therefore, it was shown that by means of an appropriate attributes weight assignment it is possible, by the JBOS method, to achieve a suitable level of performance in a specific task after reduction.

A methodology for analysis of concept lattice reduction

Independent methodology for analysis of concept lattice reduction.We use sets of proper implications holding in the original and reduced structure.Highlight the kinds of changes propitiated by the different classes of techniques.Four reduction techniques were used to illustrate the proposed methodology. Formal concept analysis (FCA) is a mathematical theory of data analysis with applications in many areas. The problem of obtaining a concept lattice of an appropriate size was identified in several applications as one of the most important problems of FCA. In order to deal with this problem several techniques with different characteristics were proposed for concept lattice reduction. However, there are currently no adequate methods to assess what types of knowledge transformations can result from a reduction. A methodology for analysis of concept lattice reduction is presented here. It is based on the use of sets of proper implications holding in the original and reduced formal contexts or concept lattices. Working with both sets of implications, the methodology is able to show what is preserved, eliminated, inserted or transformed by a reduction technique. Three classes of reduction techniques are analyzed from the standpoint of the methodology in order to highlight techniques of each class have in common with respect to the transformations performed. Such analysis is followed by specific examples in each class.

Parallelization of the next Closure algorithm for generating the minimum set of implication rules

This paper addresses the problem of handling dense contexts of high dimensionality in the number of objects, which is still an open problem in formal concept analysis. The generation of minimal implication basis in contexts with such characteristics is investigated, where the \textit{NextClosure} algorithm is employed in obtaining the rules. Therefore, this work makes use of parallel computing as a means to reduce the prohibitive times observed in scenarios where the input context has high density and high dimensionality. The sequential and parallel versions of the \textit{NextClosure} algorithm applied to generating implications are employed. The experiments show a reduction of approximately 75\% in execution time in the contexts of greater size and density, which attests to the viability of the strategy presented in this work.

Extracting reducible knowledge from ANN with JBOS and FCANN approaches

Due to its ability to handle nonlinear problems, artificial neural networks are applied in several areas of science. However, the human elements are unable to assimilate the knowledge kept in those networks, since such knowledge is implicitly represented by their connections and the respective numerical weights. In recent formal concept analysis, through the FCANN method, it has demonstrated a powerful methodology for extracting knowledge from neural networks. However, depending on the settings used or the number of the neural network variables, the number of formal concepts and consequently of rules extracted from the network can make the process of knowledge and learning extraction impossible. Thus, this paper addresses the application of the JBOS approach to extracted reduced knowledge from the formal contexts extracted by FCANN from the neural network. Thus, providing a small number of formal concepts and rules for the final user, without losing the ability to understand the process learned by the network.

Formal Concept Analysis Applied to Professional Social Networks Analysis.

From the recent proliferation of online social networks, a set of specific type of social network is attracting more and more interest from people all around the world. It is professional social networks, where the users’ interest is oriented to business. The behavior analysis of this type of user can generate knowledge about competences that people have been developed in their professional career. In this scenario, and considering the available amount of information in professional social networks, it has been fundamental the adoption of effective computational methods to analyze these networks. The formal concept analysis (FCA) has been a effective technique tosocial network analysis (SNA) , because it allows identify conceptual structures in data sets, through conceptual lattice and implication rules. Particularly, a specific set of implications rules, know as proper implications, can represent the minimum set of conditions to reach a specific goal. In this work, we proposed a FCA-based approach to identify relations among professional competences through proper implications. The experimental results, with professional profiles from LinkedIn and proper implications extracted fromPropImalgorithm, shows the minimum sets of skills that is necessary to reach job positions.

Minimal Cover of Implication Rules to Represent Two Mode Networks

In a world full of connections between people and objects, new needs arise requiring multidisciplinary analysis of these new networks. This work presents a approach to analyze an Internet Service Provider (ISP) database using a minimal cover of implications extracted from formal concept analysis and complex network techniques. Our goal is to analyze access to the 25 most visited websites to find access patterns and its dependencies using a minimal cover of implications. 1,470,450 accesses carried out over a month were selected. The data were converted to a clarified formal context and the NextClosure algorithm was used to extract a minimal cover of implications. Implication rules were used to explore hidden substructures from the two mode networks. As a result, we found a set of 216 implications that explain every user access behavior. With a set of axioms we present the possibility of obtaining more specific rules by derivation. These implications represent access patterns that guarantee that whenever a set of websites are accessed, so is another set of websites. These results can aid in creating security policies and network configurations to help predict future accesses. Furthermore, with the implications we save a total of 99,90% of storage space needed to represent access behavior. Finally, we show that with the construction of the network based on implication rules, the relationships between the events (websites) of a two mode networks can be made.

Using Iceberg Concept Lattices and Implications Rules to Extract Knowledge from Ann

Nowadays, Artificial Neural Networks are being widely used in the representation of physical processes. Once trained, the networks are capable of solving unprecedented situations, keeping tolerable errors in their outputs. However, humans cannot assimilate the knowledge kept by these networks, since such knowledge is implicitly represented by their structure and connection weights. Recently, the FCANN method, based on Formal Concept Analysis, has been proposed as a new approach to extract, represent and understand the behavior of the processes based on rules. However, the extraction of those rules set is not an easy task. In this work, two main proposals to improve the FCANN method are presented and discussed: 1) the building of concept lattice using frequent item sets, which provides a threshold on the formal concepts number, and 2) the extraction of implications rules from the concept lattice, which provides clearer and more direct rules, thus facilitating the learning of the process by the user. As a c...

An Approach to Extract Proper Implications Set from High-dimension Formal Contexts using Binary Decision Diagram.

Formal concept analysis (FCA) is currently used in a large number of applications in different areas. However, in some applications the volume of information that needs to be processed may become infeasible. Thus, demand for new approaches and algorithms to enable the processing of large amounts of information is increasing substantially. This paper presents a new algorithm for extracting proper implications from highdimensional contexts. The proposed algorithm, ProperImplicBDD, was based on the PropIm algorithm. Using a data structure called binary decision diagram (BDD) it is possible to simplify the representation of the formal context and to improve the performance on extracting proper implications. In order to analyze the performance of the ProperImplicBDD algorithm, we performed tests using synthetic contexts varying the number of attributes and context density. The experiments shown that ProperImplicBDD has a better perfomance – up to 8 times faster – than the original one, regardless of the number of attributes, objetcts and densities.