http://repub.eur.nl/res/aut/390/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/1201/ 2004-04-01T00:00:00Z The monotonicity property is ubiquitous in our lives and it appears in different roles: as domain knowledge, as a requirement, as a property that reduces the complexity of the problem, and so on. It is present in various domains: economics, mathematics, languages, operations research and many others. This thesis is focused on the monotonicity property in knowledge discovery and more specifically in classification, attribute reduction, function decomposition, frequent patterns generation and missing values handling. Four specific problems are addressed within four different methodologies, namely, rough sets theory, monotone decision trees, function decomposition and frequent patterns generation. In the first three parts, the monotonicity is domain knowledge and a requirement for the outcome of the classification process. The three methodologies are extended for dealing with monotone data in order to be able to guarantee that the outcome will also satisfy the monotonicity requirement. In the last part, monotonicity is a property that helps reduce the computation of the process of frequent patterns generation. Here the focus is on two of the best algorithms and their comparison both theoretically and experimentally. About the Author: Viara Popova was born in Bourgas, Bulgaria in 1972. She followed her secondary education at Mathematics High School "Nikola Obreshkov" in Bourgas. In 1996 she finished her higher education at Sofia University, Faculty of Mathematics and Informatics where she graduated with major in Informatics and specialization in Information Technologies in Education. She then joined the Department of Information Technologies, First as an associated member and from 1997 as an assistant professor. In 1999 she became a PhD student at Erasmus University Rotterdam, Faculty of Economics, Department of Computer Science. In 2004 she joined the Artificial Intelligence Group within the Department of Computer Science, Faculty of Sciences at Vrije Universiteit Amsterdam as a PostDoc researcher. http://repub.eur.nl/res/pub/271/ 2003-02-10T00:00:00Z This paper focuses on the problem of monotone decision trees from the point of view of the multicriteria decision aid methodology (MCDA). By taking into account the preferences of the decision maker, an attempt is made to bring closer similar research within machine learning and MCDA. The paper addresses the question how to label the leaves of a tree in a way that guarantees the monotonicity of the resulting tree. Two approaches are proposed for that purpose - dynamic and static labeling which are also compared experimentally. The paper further considers the problem of splitting criteria in the con- text of monotone decision trees. Two criteria from the literature are com- pared experimentally - the entropy criterion and the number of con criterion - in an attempt to find out which one fits better the specifics of the monotone problems and which one better handles monotonicity noise. http://repub.eur.nl/res/pub/207/ 2002-06-17T00:00:00Z The decision tree algorithm for monotone classification presented in [4, 10] requires strictly monotone data sets. This paper addresses the problem of noise due to violation of the monotonicity constraints and proposes a modification of the algorithm to handle noisy data. It also presents methods for controlling the size of the resulting trees while keeping the monotonicity property whether the data set is monotone or not. http://repub.eur.nl/res/pub/76/ 2001-02-22T00:00:00Z The bankruptcy prediction problem can be considered an or dinal classification problem. The classical theory of Rough Sets describes objects by discrete attributes, and does not take into account the order- ing of the attributes values. This paper proposes a modification of the Rough Set approach applicable to monotone datasets. We introduce re- spectively the concepts of monotone discernibility matrix and monotone (object) reduct. Furthermore, we use the theory of monotone discrete functions developed earlier by the first author to represent and to com- pute decision rules. In particular we use monotone extensions, decision lists and dualization to compute classification rules that cover the whole input space. The theory is applied to the bankruptcy prediction problem.