A comparison of two MLEM2 rule induction algorithms extended to probabilistic approximations

A probabilistic approximation is a generalization of the standard idea of lower and upper approximations, defined for equivalence relations. Recently probabilistic approximations were additionally generalized to an arbitrary binary relation so that probabilistic approximations may be applied for incomplete data. We discuss two ways to induce rules from incomplete data using probabilistic approximations, by applying true MLEM2 algorithm and an emulated MLEM2 algorithm. In this paper we report novel research on a comparison of both approaches: new results of experiments on incomplete data with three interpretations of missing attribute values. Our results show that both approaches do not differ much.     

Knowledge acquisition under uncertainty — a rough set approach

The paper describes knowledge acquisition under uncertainty using rough set theory, a concept introduced by Z. Pawlak in 1981. A collection of rules is acquired, on the basis of information stored in a data base-like system, called an information system. Uncertainty implies inconsistencies, which are taken into account, so that the produced rules are categorized into certain and possible with the help of rough set theory. The approach presented belongs to the class of methods of learning from examples. The taxonomy of all possible expert classifications, based on rough set theory, is also established. It is shown that some classifications are theoretically (and, therefore, in practice) forbidden.     

THE USEFULNESS OF A MACHINE LEARNING APPROACH TO KNOWLEDGE ACQUISITION

This paper presents results of experiments showing how machine learning methods arc useful for rule induction in the process of knowledge acquisition for expert systems. Four machine learning methods were used: ID3, ID3 with dropping conditions, and two options of the system LERS (Learning from Examples based on Rough Sets): LEM1 and LEM2. Two knowledge acquisition options of LERS were used as well. All six methods were used for rule induction from six real-life data sets. The main objective was to lest how an expert system, supplied with these rule sets, performs without information on a few attributes. Thus an expert system attempts to classify examples with all missing values of some attributes. As a result of experiments, it is clear that all machine learning methods performed much worse than knowledge acquisition options of LERS. Thus, machine learning methods used for knowledge acquisition should be replaced by other methods of rule induction that will generate complete sets of rules. Knowledge acquisition options of LERS are examples of such appropriate ways of inducing rules for building knowledge bases.     

Coping With Missing Attribute Values Based on Closest Fit in Preterm Birth Data: A Rough Set Approach

Data mining is frequently applied to data sets with missing attribute values. A new approach to missing attribute values, called closest fit, is introduced in this paper. In this approach, for a given case (example) with a missing attribute value we search for another case that is as similar as possible to the given case. Cases can be considered as vectors of attribute values. The search is for the case that has as many as possible identical attribute values for symbolic attributes, or as the smallest possible value differences for numerical attributes. There are two possible ways to conduct a search: within the same class (concept) as the case with the missing attribute values, or for the entire set of all cases. For comparison, we also experimented with another approach to missing attribute values, where the missing values are replaced by the most common value of the attribute for symbolic attributes or by the average value for numerical attributes. All algorithms were implemented in the system OOMIS. Our experiments were performed on the preterm birth data sets provided by the Duke University Medical Center.     

A Comparison of Three Strategies to Rule Induction from Data with Numerical Attributes

Our main objective was to compare two discretization techniques, both based on cluster analysis, with a new rule induction algorithm called MLEM2, in which discretization is performed simultaneously with rule induction. The MLEM2 algorithm is an extension of the existing LEM2 rule induction algorithm. The LEM2 algorithm works correctly only for symbolic attributes and is a part of the LERS data mining system. For the two strategies, based on cluster analysis, rules were induced by the LEM2 algorithm. Our results show that MLEM2 outperformed both strategies based on cluster analysis, in terms of complexity (size of rule sets) and, more importantly, error rates.     

Functional Behavioral Assessment Using the LERS Data Mining System—Strategies for Understanding Complex Physiological and Behavioral Patterns

Many individuals with mental retardation, autism, and other related disabilities lead lives that are significantly restricted because of problem behaviors such as self-injury and aggression. We processed two data sets, one describing heart rate patterns and the other describing the behavioral events of one subject diagnosed with severe mental retardation, visual impairments, and severe problem behavior. From these data sets the LERS data mining system induced certain and possible rule sets. In our research these rule sets were successfully used for interpretation, or, more specifically, to discover mechanisms of triggering specific physiological and behavioral patterns.     

On the endomorphisms of finite automata

The properties of endomorphisms and automorphisms of a finite, deterministic automatonA related to the smallest input-independent partition on the set of internal states ofA are investigated. The setH ^d of all thed-endomorphisms ofA defined here, as well as the setG ^d of all thed-automorphisms ofA, are studied in detail. It is proved thatH ^d forms a polyadic semigroup, whileG ^d forms a polyadic group. Connections betweenG ^d and the groupG(A) of all the automorphisms ofA are examined. The upper bound for the cardinality ofG ^d is given.Finally, by means of the theory ofd-automorphisms, some problems of the theory of strictly periodic automata are solved; in the first place, the necessary and sufficient condition for the reducibility of an arbitrary strictly periodic automation is given.