Jan Rauch

Logic of Association Rules

Association rules corresponding to general relation of two Boolean attributes are introduced. Association rules based on statistical hypotheses test are also included. Several classes of association rules are defined e.g. classes of implicational and of equivalence rules. Special logical calculi such that their formulae correspond to association rules are defined and studied. Practically important deduction rules of these calculi are introduced. It is shown that the question if the given association rule logically follows from an other given association rule can be converted into the question if suitable formulae of propositional calculus are tautologies. Several further theoretical results and research directions are mentioned.

The GUHA method and its meaning for data mining

The paper presents the history and present state of the GUHA method, its theoretical foundations and its relation and meaning for data mining.

Logical Calculi for Knowledge Discovery in Databases

Observational calculi were defined in relation to GUHA method of mechanising hypotheses formation. Formulae of observational calculi correspond to statistical hypothesis tests and various further assertions verificated in the process of data analysis. An example of application of the GUHA procedure PC-ASSOC is described in the paper. Logical relation among formulae of observational calculi are discussed and some important results concerning deduction rules are shown. Possibilities of applications of logical properties of formulae corresponding to hypotheses tests in the field of KDD are suggested.

Classes of Four-Fold Table Quantifiers

Four-fold table logical calculi are defined. Formulae of these calculi correspond to patterns based on four-fold contingency tables of two Boolean attributes. An FFT quantifier is a part of the formula, it corresponds to an assertion concerning frequencies from four-fold table. Several classes of FFT quantifiers are defined and studied. It is shown that each particular class has interesting properties from the point of view of KDD. Deduction rules concerning formulae of four-fold tables calculi are demonstrated. It is shown that complex computation of statistical tests can be avoided by using tables of critical frequencies.

Ontology-Enhanced association mining

The roles of ontologies in KDD are potentially manifold. We track them through different phases of the KDD process, from data understanding through task setting to mining result interpretation and sharing over the semantic web. The underlying KDD paradigm is association mining tailored to our 4ft-Miner tool. Experience from two different application domains-medicine and sociology-is presented throughout the paper. Envisaged software support for prior knowledge exploitation via customisation of an existing user-oriented KDD tool is also discussed.

Mining for 4ft Association Rules

An association rule [1] is an expression of the form X → Y where X and Y are sets of items. The intuitive meaning is that transactions (e.g. supermarket baskets) containing set X of items tend to contain set Y of items. Two measures of intensity of association rule are used, confidence C and support S.

Observational Calculi and Association Rules

Observational calculi were introduced in the 1960s as a tool of logic of discovery. Formulas of observational calculi correspond to assertions on analysed data. Truthfulness of suitable assertions can lead to acceptance of new scientific hypotheses. The general goal was to automate the process of discovery of scientific knowledge using mathematical logic and statistics. The GUHA method for producing true formulas of observational calculi relevant to the given problem of scientific discovery was developed. Theoretically interesting and practically important results on observational calculi were achieved. Special attention was paid to formulas - couples of Boolean attributes derived from columns of the analysed data matrix. Association rules introduced in the 1990s can be seen as a special case of such formulas. New results on logical calculi and association rules were achieved. They can be seen as a logic of association rules. This can contribute to solving contemporary challenging problems of data mining research and practice. The book covers thoroughly the logic of association rules and puts it into the context of current research in data mining. Examples of applications of theoretical results to real problems are presented. New open problems and challenges are listed. Overall, the book is a valuable source of information for researchers as well as for teachers and students interested in data mining.

Considerations on Logical Calculi for Dealing with Knowledge in Data Mining

An attempt to develop and apply logical calculi in exploratory data analysis was made 30 years ago. It resulted in a definition and study of observational logical calculi based on modifications of classical predicate calculi and on mathematical statistics. Additional results followed the definition and first implementations of the GUHA method of mechanizing hypothesis formation. The GUHA method can be seen as one of the first data mining methods. Applications of modern and enhanced implementation of the GUHA method confirmed the generally accepted need to use domain knowledge in the process of data mining. Moreover it inspired considerations on the application of logical calculi for dealing with domain knowledge in data mining. This paper presents these considerations.

Data Mining and Medical Knowledge Management: Cases and Applications

The healthcare industry produces a constant flow of data, creating a need for deep analysis of databases through data mining tools and techniques resulting in expanded medical research, diagnosis, and treatment. Data Mining and Medical Knowledge Management: Cases and Applications presents case studies on applications of various modern data mining methods in several important areas of medicine, covering classical data mining methods, elaborated approaches related to mining in electroencephalogram and electrocardiogram data, and methods related to mining in genetic data. A premier resource for those involved in data mining and medical knowledge management, this book tackles ethical issues related to cost-sensitive learning in medicine and produces theoretical contributions concerning general problems of data, information, knowledge, and ontologies.

Dealing with Background Knowledge in the SEWEBAR Project

SEWEBAR is a research project the goal of which is to study possibilities of dissemination of analytical reports through Semantic Web. We are interested in analytical reports presenting results of data mining. Each analytical report gives answer to one analytical question. Lot of interesting analytical questions can be answered by GUHA procedures implemented in the LISp-Miner system. The SEWEBAR project deals with these analytical questions. However the process of formulating and answering such analytical questions requires various background knowledge. The paper presents first steps in storing and application of several forms of background knowledge in the SEWEBAR project. Examples concerning dealing with medical knowledge are presented.