Intelligent Data Analysis: An International Journal

The Iceberg-Cube problem is to identify the combinations of values for a set of attributes for which a specified aggregation function yields values over a specified aggregate threshold. We implemented bottom-up and top-down methods for this problem and performed extensive experiments featuring a variety of synthetic and real databases. The bottom-up method included pruning. Results show that in most cases the top-down method, with or without pruning, was slower than the bottom-up method, because of less effective pruning. However, below a crossover point, the top-down method is faster. This crossover point occurs at a relatively low minimum support threshold, such as 0.01% or 1.5%. The bottom-up method is recommended for cases when a minimum support threshold higher than the crossover point will be selected. The top-down method is recommended when a minimum support threshold lower than the crossover point will be used or when a large number of results is expected.

A rule-inducing learning algorithm may yield either an ordered or unordered set of decision rules. The latter seems to be more understandable by humans and directly applicable in most expert systems or decision-supporting ones. However, classification utilizing the unordered-mode decision rules may be accompanied by some conflict situations, particularly when several rules belonging to different classes match (‘fire’ for) an input to-be-classified (unseen) object. One of the possible solutions to this conflict is to associate each decision rule induced by a learning algorithm with a numerical factor which is commonly called the rule quality.

The paper first surveys empirical and statistical formulas of the rule quality and compares their characteristics. Statistical tools such as contingency tables, measures of association, measures of agreement are introduced as suitable vehicles for depicting a behaviour of a decision rule. The above formulas as well as schemes for their combinations are experimentally tested on several well-known AI databases and compared. The covering learning algorithm CN4, a large extension of CN2, is used as an inductive vehicle.

After that, theoretical methodology for defining rule qualities and schemes for their combination is acquainted. The general definitions of the notions of a Designer, Learner, and Classifier are presented in a formal matter, including parameters that are usually attached to these concepts such as rule consistency, completeness, quality, matching rate, etc. Hence, we provide the minimum-requirement definitions as necessary conditions for the above concepts. Any designer (decision-system builder) of a new multiple-rule system may start with these minimum requirements.

We conclude with a general flow chart for a decision-system builder. He/she can just pursue it and select parameters of a Learner and Classifier, following the minimum characteristics provided.

The paper addresses the question how learning class discriminations and learning characteristic class descriptions can be related in relational learning. We present the approach TRITOP/MATCHBOX combining the relational decision tree algorithm TRITOP with the connectionist approach MATCHBOX. TRITOP constructs efficiently a relational decision tree for the fast discrimination of classes of relational descriptions, while MatchBox is used for constructing class prototypes.

Although TRITOP's decision trees perform very well in the classification task, they are difficult to understand and to explain. In order to overcome this disadvantage of decision trees in general, in a second step the decision tree is supplemented by prototypes. Prototypes are generalized graph theoretic descriptions of common substructures of those subclasses of the training set that are defined by the leaves of the decision tree. Such prototypes give a comprehensive and understandable description of the subclasses. In the prototype construction, the connectionist approach MATCHBOX is used to perform fast graph matching and graph generalisation, which are originally NP-complete tasks. The constructed prototypes can be used for classification in a decision list framework, where the decision list is constructed from the decision tree.

Complex and extensive web sites are becoming more and more popular. Companies need to justify their investments. Web related data analysis is the way of providing this justification. It is usual that large amounts of data exist is the repositories and humans do not use. The reasons are simple. They don't know what to do with this data, how to prepare it and what kind of tasks should be performed to retrieve valuable knowledge. Commercial web mining packages do not answer all questions which maybe interesting to the data analyst. In this paper authors suggest several hypotheses what could help to improve web site's retention. The investigation proposes decision trees for web user behaviour analysis. This includes prediction of user future actions and the typical pages leading to browsing termination. Decision tree package C4.5 was used in this study. Decision trees showed reasonable computational performance and accuracy. Experiments showed that it is possible to predict future user actions with reasonable misclassification error as well as to find combinations of sequential pages resulting in browsing termination. In addition to this, decision trees generated human understandable rules which can be used to analyse further for web site improvement.

Intelligent data analysis faces the problem of the huge amounts of data. More and more, database management systems are required to deal with this large repositories. In this framework, multidimensional databases are particularly adapted. They have emerged to support the OLAP framework. OLAP, standing for On Line Analytical Processing, is devoted to the fast analysis of multidimensional data. This model has been recently extended to the treatment of imperfect data and flexible queries. In this paper, we propose a new architecture based on fuzzy multidimensional databases to generate fuzzy summaries. This approach offers two main advantages. First, it provides a scalable framework due to the use of a database management system. Second, the introduction of fuzziness provides a theoretical framework to handle data from the real world and flexible queries. The chosen data mining tool is the generation of linguistic summaries. This kind of rules is a more understandable knowledge for the user than classical association rules. A user-friendly system is provided. This approach is compared to existing frameworks devoted to data analysis with association rules or fuzzy summaries. We insist on the fact that this model generalizes the classical one. It provides a framework to handle all classical crisp cases, since fuzzy set theory provides means to handle imperfect and classical data. Thus this method may be applied on classical data to generate fuzzy summaries.