Fundamenta Informaticae

We present results of extensive experiments performed on nine data sets with numerical attributes using six promising discretization methods. For every method and every data set 30 experiments of ten-fold cross validation were conducted and then means and sample standard deviations were computed. Our results show that for a specific data set it is essential to choose an appropriate discretization method since performance of discretization methods differ significantly. However, in general, among all of these discretization methods there is no statistically significant worst or best method. Thus, in practice, for a given data set the best discretization method should be selected individually.

Dominance-based rough set introduced by Greco et al. is an extension of Pawlak¡¯s classical rough set theory by using dominance relations in place of equivalence relations for approximating sets of preference ordered decision classes satisfying upward and downward union properties. This paper introduces the concept of indexed blocks for representing dominance-based approximation spaces. Indexed blocks are sets of objects indexed by pairs of decision values. In our study, inconsistent information is represented by exclusive neighborhoods of indexed blocks. They are used to define approximations of decision classes. It turns out that a set of indexed blocks with exclusive neighborhoods forms a partition on the universe of objects. Sequential rules for updating indexed blocks incrementally are considered and illustrated with examples.

Generalized approximation algebras and approximation algebras are defined as a theoretical counterpart of all the situations where a "lower" and an "upper" mapping are used. Some models of these structures are discusse, among them rough sets, fuzzy rough sets and possibility theory. Generalized approximation framework and approximation framework are also introduced as an abstraction of all those cases where several approximations are possibile on the same element. Also in this case some examples are given.

Ordinal classification problems with monotonicity constraints (also referred to as multicriteria classification problems) often appear in real-life applications, however, they are considered relatively less frequently in theoretical studies than regular classification problems. We introduce a rule induction algorithm based on the statistical learning approach that is tailored for this type of problems. The algorithm first monotonizes the dataset (excludes strongly inconsistent objects), using Stochastic Dominance-based Rough Set Approach, and then uses forward stagewise additive modeling framework for generating a monotone rule ensemble. Experimental results indicate that taking into account knowledge about order andmonotonicity constraints in the classifier can improve the prediction accuracy.

Human beings are born with a natural capacity of recovering shape from merely one image. However, it is still a challenging mission for current techniques to make a computer have such an ability. To simulate the modeling procedure of human visual system, a Ternary Deformation Framework (TDF) is proposed to reconstruct a realistic 3D face from one 2D frontal facial image, with prior knowledge regarding facial shape learnt from a 3D face data set. Based upon the reconstructed 3D face, a novelmethod via linear regression is then proposed to estimate that person's pose on another image with pose variations. Simulation results show that TDF outperforms the conventional methods with respect to the modeling precision and that reconstructions on real photographs have achieved favorable visual effects. Moreover, the comparison results validated the effectiveness of using the 3D face in the proposed pose estimation method.

A systematic procedure for deriving weakly ordered non-numerical rankings from given sets of data is proposed and analysed. The data are assumed to be collected using the Pairwise Comparisons paradigm. The concept of a partially ordered approximation of an arbitrary binary relation is formally defined and some solutions are proposed. The problem of testing and the importance of indifference and the power of weak order extensions are also discussed.

A two-phase learning strategy for rule induction from incomplete data is proposed, and a new form of rules is introduced so that a user can easily identify attributes with or without missing values in a rule. Two levels of measurement are assigned to a rule. An algorithm for two-phase rule induction is presented. Instead of filling in missing attribute values before or during the process of rule induction, we divide rule induction into two phases. In the first phase, rules and partial rules are induced based on non-missing values. In the second phase, partial rules are modified and refined by the imputation of some missing values. Such rules truthfully reflect the knowledge embedded in the incomplete data. The study not only presents a new view of rule induction from incomplete data, but also provides a practical solution. Experiments validate the effectiveness of the proposed method.

Most of the business decisions are based on cost and benefit considerations. Data mining techniques that make it possible for the businesses to incorporate financial considerations will be moremeaningful to the decisionmakers. Decision theoretic framework has been helpful in providing a better understanding of classification models. This study describes a semi-supervised decision theoretic rough set model. The model is based on an extension of decision theoretic model proposed by Yao. The proposal is used to model financial cost/benefit scenarios for a promotional campaign in a real-world retail store.

Knowledge in an information system evolves with its dynamical environment. A new concept of interesting knowledge based on both accuracy and coverage is defined in this paper for dynamic information systems. An incremental model and approach as well as its algorithm for inducing interesting knowledge are proposed when the object set varies over time. A case study validates the feasibility of the proposed method.

Decision trees are one of the most popular data-mining techniques for knowledge discovery. Many approaches for induction of decision trees often deal with the continuous data and missing values in information systems. However, they do not perform well in real situations. This paper presents a new algorithm, decision tree construction based on the Cloud transform and Rough set theory under the characteristic relation (CR), for mining classification knowledge from a given data set. The continuous data is transformed into discrete qualitative concepts via the cloud transformation and then the attribute with the smallest weighted mean roughness under the characteristic relation is selected as the current splitting node. Experimental evaluation shows the decision trees constructed by the CR algorithm tend to have a simpler structure, much higher classification accuracy and more understandable rules than those by C5.0 in most cases.