Mikhail Ju. Moshkov

On partial covers, reducts and decision rules

In the paper, the accuracy of greedy algorithms for construction of partial covers, reducts and decision rules is considered. Bounds on the minimal complexity of partial covers, reducts and decision rules based on an information about greedy algorithm work are studied. The results of experiments with greedy algorithms are described.

Maximal consistent extensions of information systems relative to their theories

Knowledge encoded in information systems can be represented by different sets of rules generated by these systems. One can consider sets of deterministic, nondeterministic or probabilistic rules. Such sets of rules can be treated as theories of information systems. Any such a theory generated from a given information system corresponds to a subjective view on knowledge encoded in this information system. Such theories can be used for solving different problems. For example, the maximal consistent extensions of information systems were studied for synthesis of concurrent processes specified by information systems. In this approach, the maximal consistent extension of a given information system consists of all objects perceived by means of attributes which are consistent with the theory including all the so called true and realizable deterministic rules extracted from the original information system. In this paper, we report results on the maximal consistent extensions of information systems relative to some other theories of information systems, e.g., theories consisting of rules such as true and realizable inhibitory rules, true inhibitory rules, and true deterministic rules. We also discuss algorithmic problems related to the maximal consistent extensions. In particular, from the obtained results it follows that solutions based on these new sets of rules, e.g., on inhibitory rules can be of higher quality than in the case of deterministic rules.

On partial covers, reducts and decision rules with weights

In the paper the accuracy of greedy algorithms with weights for construction of partial covers, reducts and decision rules is considered. Bounds on minimal weight of partial covers, reducts and decision rules based on an information on greedy algorithm work are studied. Results of experiments with software implementation of greedy algorithms are described.

On Covering Attribute Sets by Reducts

For any fixed natural k, there exists a polynomial in time algorithm which for a given decision table Tand given kconditional attributes recognizes if there exist a decision reduct of Tcontaining these kattributes.

On testing membership to maximal consistent extensions of information systems

This paper provides a new algorithm for testing membership to maximal consistent extensions of information systems. A maximal consistent extension of a given information system includes all objects corresponding to known attribute values which are consistent with all true and realizable rules extracted from the original information system. An algorithm presented here does not involve computing any rules, and has polynomial time complexity. This algorithm is based on a simpler criterion for membership testing than the algorithm described in [4]. The criterion under consideration is convenient for theoretical analysis of maximal consistent extensions of information systems.

On optimization of decision trees

In the paper algorithms are considered which allow to consecutively optimize decision trees for decision tables with many-valued decisions relatively different complexity measures such as number of nodes, weighted depth, average weighted depth, etc. For decision tables over an arbitrary infinite restricted information system [5] these algorithms have (at least for the three mentioned measures) polynomial time complexity depending on the length of table description. For decision tables over one of such information systems experimental results of decision tree optimization are described.

Two Families of Classification Algorithms

In the paper, two families of lazy classification algorithms of polynomial time complexity are considered. These algorithms are based on ordinary and inhibitory rules, but the direct generation of rules is not required. Instead of this, the considered algorithms extract efficiently for a new object some information on the set of rules which is next used by a decision-making procedure.

Comparison of lazy classification algorithms based on deterministic and inhibitory decision rules

In the paper, two lazy classification algorithms of polynomial time complexity are considered. These algorithms are based on deterministic and inhibitory decision rules, but the direct generation of rules is not required. Instead of this, for any new object the considered algorithms extract from a given decision table efficiently some information about the set of rules. Next, this information is used by a decision-making procedure. The reported results of experiments show that the algorithms based on inhibitory decision rules are often better than those based on deterministic decision rules.

Extracting Relevant Information about Reduct Sets from Data Tables

The direct searching for relevant reducts in the set of all reducts of a given data table can be often computationally infeasible, especially for large data tables. Hence, there is a need for developing efficient methods for extracting relevant information about reducts from data tables which could help us to perform efficiently the inducing process of the high quality data models such as rule based classifiers. Such relevant information could help, e.g., to reduce the dimensionality of the attribute set. We discuss methods for generating relevant information about reduct sets from information systems or decision tables. In particular, we consider a binary relation on attributes satisfied for two given attributes if and only if there is no reduct consisting them both. Moreover, we prove that for any fixed natural k , there exists a polynomial in time algorithm which for a given decision table T and given k conditional attributes recognizes if there exists a decision reduct of T covering these k attributes. We also present a list of problems related to the discussed issues. The reported results create a step toward construction of a software library reducing the searching costs for relevant reducts.

On the class of restricted linear information systems

In the paper the class of restricted linear information systems is described completely. For decision tables over each such information system there exist low upper bounds on minimal complexity of decision trees and polynomial algorithms of decision tree optimization for various complexity measures. A corollary connected with combinatorial geometry is considered.