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2009 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Inhibitory Rules in Data Analysis

A Rough Set Approach

verfasst von: Pawel Delimata, Mikhail Ju. Moshkov, Andrzej Skowron, Zbigniew Suraj

Verlag: Springer Berlin Heidelberg

Buchreihe : Studies in Computational Intelligence

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This monograph is devoted to theoretical and experimental study of inhibitory decision and association rules. Inhibitory rules contain on the right-hand side a relation of the kind “attribut = value”. The use of inhibitory rules instead of deterministic (standard) ones allows us to describe more completely infor- tion encoded in decision or information systems and to design classi?ers of high quality. The mostimportantfeatureofthis monographis thatit includesanadvanced mathematical analysis of problems on inhibitory rules. We consider algorithms for construction of inhibitory rules, bounds on minimal complexity of inhibitory rules, and algorithms for construction of the set of all minimal inhibitory rules. We also discuss results of experiments with standard and lazy classi?ers based on inhibitory rules. These results show that inhibitory decision and association rules can be used in data mining and knowledge discovery both for knowledge representation and for prediction. Inhibitory rules can be also used under the analysis and design of concurrent systems. The results obtained in the monograph can be useful for researchers in such areas as machine learning, data mining and knowledge discovery, especially for those who are working in rough set theory, test theory, and logical analysis of data (LAD). The monograph can be used under the creation of courses for graduate students and for Ph.D. studies. TheauthorsofthisbookextendanexpressionofgratitudetoProfessorJanusz Kacprzyk, to Dr. Thomas Ditzinger and to the Studies in Computational Int- ligence sta? at Springer for their support in making this book possible.

Inhaltsverzeichnis

Frontmatter
Introduction
Abstract
The monograph is devoted to the study of inhibitory rules. In contrast to deterministic (standard) rules which have the relation attribute = value on the right-hand side, inhibitory rules have on the right-hand side the relation attibute ≠ value. For information systems [60, 63, 72], we consider inhibitory association rules which on the right-hand side can have an arbitrary attribute. For decision systems (decision tables) [60], we consider inhibitory decision rules containing on the right-hand side the decision attribute. It is worthwhile mentioning that in the rough set approach the decision rules are used for extension of approximations of concepts from given samples of objects on the whole universe of objects (see, e.g., [5, 6, 75]).
Pawel Delimata, Mikhail Ju. Moshkov, Andrzej Skowron, Zbigniew Suraj
Maximal Consistent Extensions of Information Systems
Abstract
The idea of representation of concurrent system by information system is due to Z. Pawlak [61, 73, 74] In such a representation attributes are interpreted as local processes of a concurrent system, values of attributes – as states of local processes, and objects (tuples of values of attributes on objects) – as global states of the considered concurrent system.
The knowledge encoded in an information system can be represented by means of true rules which can be extracted from the information system. Besides “explicit” global states, corresponding to objects, the concurrent system generated by the considered information system can also have “hidden” global states, i.e., tuples of attribute values not belonging to a given information system but consistent with all the rules. Such “hidden” states can also be considered as realizable global states. This was a motivation for introducing in [73] maximal consistent extensions of information systems with both “explicit” and “hidden” global states. The maximal consistent extensions of information systems relative to the set of true and realizable deterministic rules were investigated in [70, 73, 85, 86].
Pawel Delimata, Mikhail Ju. Moshkov, Andrzej Skowron, Zbigniew Suraj
Minimal Inhibitory Association Rules for Almost All k-Valued Information Systems
Abstract
There are three approaches to use inhibitory rules in classifiers: (i) lazy algorithms based on an information about the set of all inhibitory rules, (ii) standard classifiers based on a subset of inhibitory rules constructed by a heuristic, and (iii) standard classifiers based on the set of all minimal (irreducible) inhibitory rules. The aim of this chapter is to show that the last approach is not feasible (from computational complexity point of view).
We restrict our considerations to the class of k-valued information systems, i.e., information systems with attributes having values from {0,...,k − 1}, where k ≥ 2. Note that the case k = 2 was considered earlier in [51].
Pawel Delimata, Mikhail Ju. Moshkov, Andrzej Skowron, Zbigniew Suraj
Partial Covers and Inhibitory Decision Rules
Abstract
In this chapter, we consider algorithms for construction of partial inhibitory decision rules and some bounds on the length such rules. These investigations are based on the use of known results for partial covers.
We show that:
  • Under some natural assumptions on the class NP, the greedy algorithm is close to the best polynomial approximate algorithms for the minimization of the length of partial inhibitory decision rules.
  • Based on an information received during the greedy algorithm work, it is possible to obtain nontrivial lower and upper bounds on the minimal length of partial inhibitory decision rules.
  • For the most part of randomly generated binary decision tables, greedy algorithm constructs simple partial inhibitory decision rules with relatively high accuracy. In particular, some theoretical results confirm the following 0.5-hypothesis for inhibitory decision rules: for the most part of decision tables for each row during each step the greedy algorithm chooses an attribute that separates from the considered row at least one-half of rows that should be separated.
Similar results can be obtained for partial inhibitory association rules over information systems. To this end, it is enough to fix an arbitrary attribute a i of the information system as the decision attribute and study inhibitory association rules with the right-hand side of the kind a i  ≠ c as inhibitory decision rules over the obtained decision system (decision table).
Pawel Delimata, Mikhail Ju. Moshkov, Andrzej Skowron, Zbigniew Suraj
Partial Covers and Inhibitory Decision Rules with Weights
Abstract
In this chapter, we consider the case, where each subset, used for covering, has its own weight, and we should minimize the total weight of subsets in partial cover. The same situation is with partial inhibitory decision rules: each conditional attribute has its own weight, and we should minimize the total weight of attributes occurring in partial inhibitory decision rule. If weights of attributes characterize time complexity of attribute value computation, then we try to minimize total time complexity of computation of attributes from partial inhibitory decision rule. If weights characterize a risk of attribute value computation (as in medical or technical diagnosis), then we try to minimize total risk, etc.
Pawel Delimata, Mikhail Ju. Moshkov, Andrzej Skowron, Zbigniew Suraj
Classifiers Based on Deterministic and Inhibitory Decision Rules
Abstract
In this chapter, we consider the following problem of classification (prediction): for a decision table T and a new object v, given by values of conditional attributes from T, it is required to generate a decision corresponding to v.
We compare qualities of classifiers based on exact deterministic and inhibitory decision rules.
The first type of classifiers is the following: for a given decision table we construct for each row an exact deterministic decision rule using the greedy algorithm. The obtained system of rules jointly with simple procedure of voting can be considered as a classifier. A deterministic rule, which is realizable for given object, is a vote “pro” the decision from the right-hand side of the rule.
Pawel Delimata, Mikhail Ju. Moshkov, Andrzej Skowron, Zbigniew Suraj
Lazy Classification Algorithms Based on Deterministic and Inhibitory Association Rules
Abstract
In this chapter, we consider the same classification problem as in Chap. 5: for a given decision table T and a new object v it is required to generate a value of the decision attribute on v using values of conditional attributes on v.
To this end, we divide the decision table T into a number of information systems S i , i ∈ Dec(T), where Dec(T) is the set of values of the decision attribute in T. For i ∈ Dec(T), the information system S i contains only objects (rows) of T with the value of the decision attribute equal to i.
Pawel Delimata, Mikhail Ju. Moshkov, Andrzej Skowron, Zbigniew Suraj
Lazy Classification Algorithms Based on Deterministic and Inhibitory Decision Rules
Abstract
In this chapter, we consider the same classification problem as in Chaps. 5 and 6: for a given decision table T and a new object v it is required to generate a value of the decision attribute on v using values of conditional attributes on v.
We compare two lazy [1] classification algorithms based on deterministic and inhibitory decision rules of the forms
$$ (a_1(x)=b_1)\wedge \ldots \wedge (a_t(x)=b_t)\rightarrow d(x)=b \; , $$
$$ (a_1(x)=b_1)\wedge \ldots \wedge (a_t(x)=b_t)\rightarrow d(x)\neq b $$
respectively, where a1,...,a t are conditional attributes, b1,...,b t are values of these attributes, d is the decision attribute and b is a value of d. By Dec(T) we denote the set of values of the decision attribute d.
Pawel Delimata, Mikhail Ju. Moshkov, Andrzej Skowron, Zbigniew Suraj
Final Remarks
Abstract
In this monograph, we studied inhibitory decision and association rules. We showed that using inhibitory rules one can describe more knowledge encoded in information and decision systems than in the case of deterministic (standard) rules.
Unfortunately, for almost all k-valued information systems with the polynomial number of objects in the number of attributes the number of minimal (irreducible) inhibitory association rules is not polynomial in the number of attributes. In some sense analogous situation is with minimal inhibitory decision rules.
In such a situation, we can either use some heuristics for generating of relatively small sets of “important” inhibitory rules, or use lazy classification algorithms which in polynomial time can find an information about the whole set of true and realizable inhibitory rules for a given information or decision system.
Pawel Delimata, Mikhail Ju. Moshkov, Andrzej Skowron, Zbigniew Suraj
Backmatter
Metadaten
Titel
Inhibitory Rules in Data Analysis
verfasst von
Pawel Delimata
Mikhail Ju. Moshkov
Andrzej Skowron
Zbigniew Suraj
Copyright-Jahr
2009
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-540-85638-2
Print ISBN
978-3-540-85637-5
DOI
https://doi.org/10.1007/978-3-540-85638-2

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