Movatterモバイル変換


[0]ホーム

URL:


×

zbMATH Open — the first resource for mathematics

from until
Reset all

Examples

GeometrySearch for the termGeometry inany field. Queries arecase-independent.
Funct*Wildcard queries are specified by* (e .g.functions,functorial, etc.). Otherwise the search isexact.''Topological group'':Phrases (multi - words) should be set in''straight quotation marks''.
au: Bourbaki & ti: AlgebraSearch forauthorBourbaki andtitleAlgebra. Theand-operator & is default and can be omitted.
Chebyshev | TschebyscheffTheor-operator| allows to search forChebyshev orTschebyscheff.
Quasi* map* py: 1989The resulting documents havepublicationyear1989.
so:Eur* J* Mat* Soc* cc:14Search for publications in a particularsource with aMathematics SubjectClassificationcode in14.
cc:*35 ! any:ellipticSearch for documents about PDEs (prefix with * to search only primary MSC); the not-operator ! eliminates all results containing the wordelliptic.
dt: b & au: HilbertThedocumenttype is set tobooks; alternatively:j forjournal articles,a forbookarticles.
py: 2000 - 2015 cc:(94A | 11T)Numberranges when searching forpublicationyear are accepted . Terms can be grouped within( parentheses).
la: chineseFind documents in a givenlanguage .ISO 639 - 1 (opens in new tab) language codes can also be used.
st: c r sFind documents that arecited, havereferences and are from asingle author.

Fields

ab Text from the summary or review (for phrases use “. ..”)
an zbMATH ID, i.e.: preliminary ID, Zbl number, JFM number, ERAM number
any Includes ab, au, cc, en, rv, so, ti, ut
arxiv arXiv preprint number
au Name(s) of the contributor(s)
br Name of a person with biographic references (to find documents about the life or work)
cc Code from the Mathematics Subject Classification (prefix with* to search only primary MSC)
ci zbMATH ID of a document cited in summary or review
db Database: documents in Zentralblatt für Mathematik/zbMATH Open (db:Zbl), Jahrbuch über die Fortschritte der Mathematik (db:JFM), Crelle's Journal (db:eram), arXiv (db:arxiv)
dt Type of the document: journal article (dt:j), collection article (dt:a), book (dt:b)
doi Digital Object Identifier (DOI)
ed Name of the editor of a book or special issue
en External document ID: DOI, arXiv ID, ISBN, and others
in zbMATH ID of the corresponding issue
la Language (use name, e.g.,la:French, orISO 639-1, e.g.,la:FR)
li External link (URL)
na Number of authors of the document in question. Interval search with “-”
pt Reviewing state: Reviewed (pt:r), Title Only (pt:t), Pending (pt:p), Scanned Review (pt:s)
pu Name of the publisher
py Year of publication. Interval search with “-”
rft Text from the references of a document (for phrases use “...”)
rn Reviewer ID
rv Name or ID of the reviewer
se Serial ID
si swMATH ID of software referred to in a document
so Bibliographical source, e.g., serial title, volume/issue number, page range, year of publication, ISBN, etc.
st State: is cited (st:c), has references (st:r), has single author (st:s)
sw Name of software referred to in a document
ti Title of the document
ut Keywords

Operators

a & bLogical and (default)
a | bLogical or
!abLogical not
abc*Right wildcard
ab cPhrase
(ab c)Term grouping

See also ourGeneral Help.

Alternative c-means clustering algorithms.(English)Zbl 1006.68876

Summary: In this paper we propose a new metric to replace the Euclidean norm in c-means clustering procedures. On the basis of the robust statistic and the influence function, we claim that the proposed new metric is more robust than the Euclidean norm. We then create two new clustering methods called the alternative hard c-means (AHCM) and alternative fuzzy c-means (AFCM) clustering algorithms. These alternative types of c-means clustering have more robustness than c-means clustering. Numerical results show that AHCM has better performance than HCM and AFCM is better than FCM. We recommend AFCM for use in cluster analysis. Recently, this AFCM algorithm has successfully been used in segmenting the magnetic resonance image of Ophthalmology to differentiate the abnormal tissues from the normal tissues.

MSC:

68T10 Pattern recognition, speech recognition

Software:

clusfind

Cite

References:

[1]Duda, R. O.; Hart, P. E., Pattern Classification and Scene Analysis (1973), Wiley: Wiley New York ·Zbl 0277.68056
[2]Jain, A. K.; Bubes, R. C., Algorithm for Clustering Data (1988), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ ·Zbl 0665.62061
[3]Kaufman, L.; Rousseeuw, P. J., Finding Groups in Data: An Introduction to Cluster Analysis (1990), Wiley: Wiley New York ·Zbl 1345.62009
[4]Zadeh, L. A., Fuzzy sets, Inf. Control, 8, 338-353 (1965) ·Zbl 0139.24606
[5]Yang, M. S., A survey of fuzzy clustering, Math. Comput. Modelling, 18, 1-16 (1993) ·Zbl 0800.68728
[6]Bezdek, J. C., Pattern Recognition with Fuzzy Objective Function Algorithms (1981), Plenum: Plenum New York ·Zbl 0503.68069
[7]Dunn, J. C., A fuzzy relative of the ISODATA process and its use in detecting compact, well-separated clusters, J. Cybernet., 3, 32-57 (1974) ·Zbl 0291.68033
[8]Gath, I.; Geva, A. B., Unsupervised optimal fuzzy clustering, IEEE Trans. Pattern Anal. Mach. Intell., 11, 773-781 (1989) ·Zbl 0709.62592
[9]Dave, R. N., Fuzzy-shell clustering and applications to circle detection in digital images, Int. J. General Syst., 16, 343-355 (1990) ·Zbl 0701.62071
[10]Yang, M. S.; Ko, C. H., On cluster-wise fuzzy regression analysis, IEEE Trans. Systems, Man, Cybern., 27, 1-13 (1997)
[11]Rudin, W., Principles of Mathematical Analysis (1976), McGraw-Hill Book Company: McGraw-Hill Book Company New York ·Zbl 0148.02903
[12]Huber, P. J., Robust Statistics (1981), Wiley: Wiley New York ·Zbl 0536.62025
[13]Huber, P. J., Robust estimation of a location parameter, Ann. Math. Statist., 35, 73-101 (1964) ·Zbl 0136.39805
[14]M.S. Yang, Y.J. Hu, K.C.R. Lin, C.C.L. Lin, Segmentation techniques for tissue differentiation in MRI of Ophthalmology using fuzzy clustering algorithms, Magnetic Resonance Imaging (2001) (in the first revision).; M.S. Yang, Y.J. Hu, K.C.R. Lin, C.C.L. Lin, Segmentation techniques for tissue differentiation in MRI of Ophthalmology using fuzzy clustering algorithms, Magnetic Resonance Imaging (2001) (in the first revision).
[15]Krishnapuram, R.; Keller, J. M., A possibilistic approach to clustering, IEEE Trans. Fuzzy Systems, 1, 98-110 (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
© 2025FIZ Karlsruhe GmbHPrivacy PolicyLegal NoticesTerms & Conditions
  • Mastodon logo
 (opens in new tab)

[8]ページ先頭

©2009-2025 Movatter.jp