Newton José Vieira

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.

Language emulator, a helpful toolkit in the learning process of computer theory

Language Emulator, written in Java, is a toolkit to help undergraduate students to understand the concepts of Automata Theory. The software allows the manipulation of regular expressions, regular grammars, deterministic finite automata, nondeterministic finite automata with and without lambda transitions, and Moore and Mealy machines. Language Emulator introduces error-detecting and internationalization functionalities into automata tools. It has been accepted by 95% of students in a recent survey, indicating that it is a helpful toolkit in learning Automata Theory.

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.

Explicit-Symbolic Modelling for Formal Verification

We propose a model that combines explicit and symbolic representations in an explicit-symbolic formal verification model. Both explicit and symbolic models have been successfully used in the verification of finite state concurrent systems, such as complex sequential circuits and communication protocols. The proposed model aims to use explicit and symbolic techniques simultaneously to verify the same model and to make it possible to employ the most efficient technique to each aspect of the model. First, we formalize the explicit-symbolic model and show how it can be generated from a labeled state-transition system. Then, we apply those ideas to systems described in the Verimag Intermediate Format and present the main algorithms for integrating the underlying models.

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.

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...

A Classification Algorithm based on Concept Similarity

Due to its mathematical foundation and intuitive diagrams (concept lattices), formal concept analysis (FCA) is an attractive alternative for data mining. This work proposes a FCA-based classification algorithm called “Similar Concepts”. Unlike previous proposals, the algorithm searches the concept lattice for similar formal concepts, which classify unseen objects. Despite its complexity limitations (inherent to FCA algorithms), “Similar Concepts” usually presents better accuracy than previous FCA-based classification algorithms.