Hung Son Nguyen

Rough set algorithms in classification problem

We we present some algorithms, based on rough set theory, that can be used for the problem of new cases classification. Most of the algorithms were implemented and included in Rosetta system [43]. We present several methods for computation of decision rules based on reducts. We discuss the problem of real value attribute discretization for increasing the performance of algorithms and quality of decision rules. Finally we deal with a problem of resolving conflicts between decision rules classifying a new case to different categories (classes). Keywords: knowledge discovery, rough sets, classification algorithms, reducts, decision rules, real value attribute discretization

Approximate boolean reasoning: foundations and applications in data mining

Since its introduction by George Boole during the mid-1800s, Boolean algebra has become an important part of the lingua franca of mathematics, science, engineering, and research in artificial intelligence, machine learning and data mining. The Boolean reasoning approach has manifestly become a powerful tool for designing effective and accurate solutions for many problems in decision-making and approximate reasoning optimization. In recent years, Boolean reasoning has become a recognized technique for developing many interesting concept approximation methods in rough set theory. The problem considered in this paper is the creation of a general framework for concept approximation. The need for such a general framework arises in machine learning and data mining. This paper presents a solution to this problem by introducing a general framework for concept approximation which combines rough set theory, Boolean reasoning methodology and data mining. This general framework for approximate reasoning is called Rough Sets and Approximate Boolean Reasoning (RSABR). The contribution of this paper is the presentation of the theoretical foundation of RSABR as well as its application in solving many data mining problems and knowledge discovery in databases (KDD) such as feature selection, feature extraction, data preprocessing, classification of decision rules and decision trees, association analysis.

Layered learning for concept synthesis

We present a hierarchical scheme for synthesis of concept approximations based on given data and domain knowledge. We also propose a solution, founded on rough set theory, to the problem of constructing the approximation of higher level concepts by composing the approximation of lower level concepts. We examine the effectiveness of the layered learning approach by comparing it with the standard learning approach. Experiments are carried out on artificial data sets generated by a road traffic simulator.

Discretization Problem for Rough Sets Methods

We study the relationship between reduct problem in Rough Sets theory and the problem of real value attribute discretization. We consider the problem of searching for a minimal set of cuts on attribute domains that preserves discernibility of objects with respect to any chosen attributes subset of cardinality s (where s is a parameter given by a user). Such a discretization procedure assures that one can keep all reducts consisting of at least s attributes. We show that this optimization problem is NP-hard and it is interesting to find efficient heuristics for solving this problem.

Pattern Extraction from Data

Searching for patterns is one of the main goals in data mining. Patterns have important applications in many KDD domains like rule extraction or classification. In this paper we present some methods of rule extraction by generalizing the existing approaches for the pattern problem. These methods, called partition of attribute values or grouping of attribute values, can be applied to decision tables with symbolic value attributes. If data tables contain symbolic and numeric attributes, some of the proposed methods can be used jointly with discretization methods. Moreover, these methods are applicable for incomplete data. The optimization problems for grouping of attribute values are either NP-complete or NP-hard. Hence we propose some heuristics returning approximate solutions for such problems.

Boolean Reasoning for Feature Extraction Problems

We recall several applications of Boolean reasoning for feature extraction and we propose an approach based on Boolean reasoning for new feature extraction from data tables with symbolic (nominal, qualitative) attributes. New features are of the form a E V, where V ⊆ V a and V a is the set of values of attribute a. We emphasize that Boolean reasoning is also a good framework for complexity analysis of the approximate solutions of the discussed problems.

From Optimal Hyperplanes to Optimal Decision Trees

We present an optimal hyperplane searching method for decision tables using Genetic Algorithms. This method can be used to construct a decision tree for a given decision table. We also present some properties of the set of hyperplanes determined by our methods and evaluate an upper bound on the depth of the constructed decision tree.

Boolean Reasoning Scheme with Some Applications in Data Mining

We present a general encoding scheme for a wide class of problems (including among others such problems like data reduction, feature selection, feature extraction, decision rules generation, pattern extraction from data or conflict resolution in multi-agent systems) and we show how to combine it with a propositional (Boolean) reasoning to develop efficient heuristics searching for (approximate) solutions of these problems. We illustrate our approach by examples, we show some experimental results and compare them with those reported in literature. We also show that association rule generation is strongly related with reduct approximation.

Approximate Reducts and Association Rules

We consider approximate versions of fundamental notions of theories of rough sets and association rules. We analyze the complexity of searching for α-reducts, understood as subsets discerning “α-almost” objects from different decision classes, in decision tables. We present how optimal approximate association rules can be derived from data by using heuristics for searching for minimal α-reducts. NP-hardness of the problem of finding optimal approximate association rules is shown as well. It makes the results enabling the usage of rough sets algorithms to the search of association rules extremely important in view of applications.

Rough Set Methods in Approximation of Hierarchical Concepts

Many learning methods ignore domain knowledge in synthesis of concept approximation. We propose to use hierarchical schemes for learning approximations of complex concepts from experimental data using inference diagrams based on domain knowledge. Our solution is based on the rough set and rough mereological approaches. The effectiveness of the proposed approach is performed and evaluated on artificial data sets generated by a traffic road simulator.