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)
Symbolic classification, clustering and fuzzy radial basis function network. (English) Zbl 1101.68775
Summary: Symbolic fuzzy classification is proposed using fuzzy radial basis function network, with fuzzy $c$-medoids clustering at the hidden layer. Symbolic objects include linguistic, nominal, boolean and interval-type of features, along with quantitative attributes. Classification and clustering in this domain involve the use of symbolic dissimilarity between the objects. Fuzzy memberships are used for appropriately handling uncertainty inherent in real-life decisions. The fuzzy radial basis function network here comprises an integration of the principles of radial basis function network and fuzzy c-medoids clustering, for handling non-numeric data. The optimal number of hidden nodes is determined by using clustering validity indices, like normalized modified Hubert’s statistic and Davies-Bouldin index, in the symbolic framework. The effectiveness of the symbolic fuzzy classification is demonstrated on real-life benchmark data sets. Comparison is provided with the performance of a decision tree.

MSC:
68T05Learning and adaptive systems
68T10Pattern recognition, speech recognition
Software:
UCI-ml
WorldCat.org
Full Text: DOI
References:
[1] Bezdek, J. C.: Pattern recognition with fuzzy objective function algorithms. (1981) · Zbl 0503.68069
[2] Bezdek, J. C.; Pal, N. R.: Some new indexes for cluster validity. IEEE trans. Systems man cybernet. Part-B 28, 301-315 (1998)
[3] C.L. Blake, C.J. Merz, UCI repository of machine learning databases, Department of Information and Computer Sciences, University of California, Irvine, 1998. http://www.ics.uci.edu/ mlearn/MLRepository.html.
[4] Gowda, K. Chidananda; Diday, E.: Symbolic clustering using a new dissimilarity measure. Pattern recognition 24, No. 6, 567-578 (1991)
[5] Gowda, K. Chidananda; Ravi, T. V.: Divisive clustering of symbolic objects using the concepts of both similarity and dissimilarity. Pattern recognition 28, No. 8, 1277-1282 (1995)
[6] Jain, A. K.; Dubes, R. C.: Algorithms for clustering data. (1988) · Zbl 0665.62061
[7] Krishnapuram, R.; Joshi, A.; Nasraoui, O.; Yi, L.: Low complexity fuzzy relational clustering algorithms for web mining. IEEE trans. Fuzzy systems 9, 595-607 (2001)
[8] Mali, K.; Mitra, S.: Clustering and its validation in a symbolic framework. Pattern recognition lett. 24, 2367-2376 (2003) · Zbl 1047.68132
[9] Mitra, S.; Acharya, T.: Data miningmultimedia, soft computing, and bioinformatics. (2003)
[10] Mitra, S.; Basak, J.: FRBFA fuzzy radial basis function network. Neural comput. Appl. 10, 244-252 (2001) · Zbl 0989.68113
[11] Moody, J.; Darken, C. J.: Fast learning in networks of locally-tuned processing units. Neural comput. 1, 281-294 (1989)
[12] Pal, S. K.; Mitra, S.: Neuro-fuzzy pattern recognitionmethods in soft computing. (1999)
[13] Pao, Y. H.: Adaptive pattern recognition and neural networks. (1989) · Zbl 0748.68061
[14] Zadeh, L. A.: Fuzzy logic, neural networks, and soft computing. Comm. ACM 37, 77-84 (1994)