zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Rough sets approach to symbolic value partition. (English) Zbl 1184.68518
Summary: In data mining, searching for simple representations of knowledge is a very important issue. Attribute reduction, continuous attribute discretization and symbolic value partition are three preprocessing techniques which are used in this regard. This paper investigates the symbolic value partition technique, which divides each attribute domain of a data table into a family for disjoint subsets, and constructs a new data table with fewer attributes and smaller attribute domains. Specifically, we investigates the optimal symbolic value partition (OSVP) problem of supervised data, where the optimal metric is defined by the cardinality sum of new attribute domains. We propose the concept of partition reducts for this problem. An optimal partition reduct is the solution to the OSVP-problem. We develop a greedy algorithm to search for a suboptimal partition reduct, and analyze major properties of the proposed algorithm. Empirical studies on various datasets from the UCI library show that our algorithm effectively reduces the size of attribute domains. Furthermore, it assists in computing smaller rule sets with better coverage compared with the attribute reduction approach.
MSC:
68T37Reasoning under uncertainty
68T05Learning and adaptive systems
References:
[1]Jensen, R.; Shen, Q.: Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches, IEEE transactions on knowledge and data engineering 16, No. 12, 1457-1471 (2004)
[2]Chan, C. C.; Grzymała-Busse, J. W.: On the two local inductive algorithms: PRISM and LEM2, Foundations of computing and deision sciences 19, 185-203 (1994) · Zbl 0939.68756
[3]Quinlan, J. R.: Induction of decision trees, Machine learning 1, 81-106 (1986)
[4], Intelligent decision support – handbook of applications and advances of the rough sets theory (1992)
[5]Pawlak, Z.: Rough sets, International journal of computer and information sciences 11, 341-356 (1982)
[6]J.G. Bazan, A. Skowron, P. Synak, Dynamic reducts as a tool for extracting laws from decision tables, in: Proceeding of the Symposium on Methodologies for Intelligent Systems, LNAI 869, 1994, pp. 346 – 355.
[7]Kryszkiewicz, M.: Comparative studies of alternative type of knowledge reduction in inconsistent systems, International journal of intelligent systems 16, No. 1, 105-120 (2001) · Zbl 0969.68146 · doi:10.1002/1098-111X(200101)16:1<105::AID-INT8>3.0.CO;2-S
[8]Liu, Q.; Chen, L.; Zhang, J.; Min, F.: Knowledge reduction in inconsistent decision tables, Adma, lncs 4093, 626-635 (2006)
[9]Xu, C.; Min, F.: Weighted reduction for decision tables, Proceedings of the third international conference on fuzzy systems and knowledge discovery (FSKD 2006), LNCS 4223, 246-255 (2006)
[10]J. Wróblewski, Finding minimal reducts using genetic algorithms, in: P.P. Wang (Ed.), JCIS’95, Wrightsville Beach, North Carolina, 1995, pp. 186 – 189.
[11]Wang, G.; Yu, H.; Yang, D.: Decision table reduction based on conditional information entropy, Chinese journal of computers 25, No. 7, 1-8 (2002)
[12]Yao, Y. Y.; Zhao, Y.; Wang, J.: On reduct construction algorithms, Lncs 4062, 297-304 (2006) · Zbl 1196.68275 · doi:10.1007/11795131_43
[13]F. Min, Q. Liu, C. Fang, J. Zhang, Reduction based symbolic value partition, in: ICHIT 2006 Electronic Proceeding, Soft Computing and Rough Sets, 2006, pp. 1 – 10.
[14]Ching, J. Y.; Wong, A. K. C.; Chan, K. C. C.: Class-dependent discretization for inductive learning from continuous and mixed-mode data, IEEE transactions on pattern analysis and machine intelligence 17, 641-651 (1995)
[15]H.S. Nguyen, Discretization of Real Value Attributes, Boolean Reasoning Approach, Ph.D. Thesis, Warsaw University, Warsaw, Poland, 1997.
[16]Kurgan, L. A.; Cios, K. J.: CAIM discretization algorithm, IEEE transactions on knowledge and data engineering 16, No. 2, 145-153 (2004)
[17], C4.5 programs for machine learning (1993)
[18]N.C. Berkman, Value Grouping for Binary Decision Trees, 1995.
[19]Ho, K. M.: Reducing decision tree fragmentation through attribute value grouping: a comparative study, Journal intelligent data analysis 4, No. 3 – 4, 255-274 (2000) · Zbl 1088.68784 · doi:http://iospress.metapress.com/link.asp?id=ctpt0payrx99rkvx
[20]Pawlak, Z.: Some issues on rough sets, Transactions on rough sets I, LNCS 3100, 1-58 (2004) · Zbl 1104.68108 · doi:10.1007/b98175
[21]S.H. Nguyen, Regularity Analysis and its Applications in Data Mining, Ph.D. Thesis, Warsaw University, Warsaw, Poland, 1999.
[22]Yao, Y. Y.: A partition model of granular computing, Transactions on rough sets I, 239-259 (2004)
[23]Min, F.; Liu, Q.; Tan, H.; Chen, L.: The M-relative reduct problem, Lncs 4062, 170-175 (2006) · Zbl 1196.68232 · doi:10.1007/11795131_25
[24], Formal concept analysis: mathematical foundations (1999)
[25]Skowron, A.; Rauszer, C.: The discernibility matrices and functions in information systems, Intelligent decision support – handbook of applications and advances of the rough sets theory, 331-362 (1992)
[26]C.L. Blake, C.J. Merz, UCI Repository of Machine Learning Databases, 1998, lt;http://www.ics.uci.edu/ mlearn/mlrepository.htmlgt;.