24.04.2015 Views

A novel fuzzy clustering algorithm based on a fuzzy scatter matrix ...

A novel fuzzy clustering algorithm based on a fuzzy scatter matrix ...

A novel fuzzy clustering algorithm based on a fuzzy scatter matrix ...

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

652 K.-L. Wu et al. / Pattern Recogniti<strong>on</strong> Letters 26 (2005) 639–652<br />

and outliers than FCMwhen m is large. A theoretical<br />

analysis of FCS was also investigated. Overall,<br />

the proposed FCS is recommended as a good<br />

<str<strong>on</strong>g>clustering</str<strong>on</strong>g> <str<strong>on</strong>g>algorithm</str<strong>on</strong>g> when the most compact kernels<br />

are in the same cluster and most separated<br />

are in different clusters.<br />

Acknowledgement<br />

This work was supported in part by the Nati<strong>on</strong>al<br />

Science Council of Taiwan, ROC, under<br />

grant NSC-91-2118-M-033-001.<br />

References<br />

Bezdek, J.C., 1974. Cluster validity with <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g> sets. J. Cybernet.<br />

3, 58–73.<br />

Bezdek, J.C., 1981. Pattern Recogniti<strong>on</strong> with Fuzzy Objective<br />

Functi<strong>on</strong> Algorithms. Plenum Press, New York.<br />

Blake, C.L., Merz, C.J., 1998. UCI repository of machine<br />

learning databases, a huge collecti<strong>on</strong> of artificial and realworld<br />

data sets. Available from: .<br />

Dave, R.N., 1996. Validating <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g> partiti<strong>on</strong> obtained through<br />

c-shells <str<strong>on</strong>g>clustering</str<strong>on</strong>g>. Pattern Recogniti<strong>on</strong> Lett. 17, 613–623.<br />

Duda, R.O., Hart, P.E., 1973. Pattern Classificati<strong>on</strong> and Scene<br />

Analysis. Wiley, New York.<br />

Fukuyama, Y., Sugeno, M., 1989. A new method of choosing<br />

the number of clusters for <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g> c-means method. In:<br />

Proceedings of the 5th Fuzzy System Symposium (in<br />

Japanese), pp. 247–250.<br />

Gath, J., Geva, A.B., 1989. Unsupervised optimal <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g><br />

<str<strong>on</strong>g>clustering</str<strong>on</strong>g>. IEEE Trans. Pattern Anal. Mach. Intell. 11,<br />

773–781.<br />

Gunders<strong>on</strong>, M., 1978. Applicati<strong>on</strong> of <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g> ISODATA <str<strong>on</strong>g>algorithm</str<strong>on</strong>g>s<br />

to star tracker pointing systems. In: Proceedings of<br />

the 7th Triennial World IFCA C<strong>on</strong>g., Helsinki, Filind, pp.<br />

1319–1323.<br />

Gustafs<strong>on</strong>, D.E., Kessel, W.C., 1979. Fuzzy <str<strong>on</strong>g>clustering</str<strong>on</strong>g> with a<br />

<str<strong>on</strong>g>fuzzy</str<strong>on</strong>g> covariance <strong>matrix</strong>. In: Proceedings of the IEEE<br />

C<strong>on</strong>ference <strong>on</strong> Decisi<strong>on</strong> C<strong>on</strong>trol, San Diego, CA, pp.<br />

761–766.<br />

Huber, P.J., 1981. Robust Statistics. Wiley, New York.<br />

Jain, A.K., Dubes, R.C., 1988. In: Algorithm for Clustering<br />

Data. Prentice-Hall, Englewood Cliffs, NJ.<br />

Kaufman, L., Rousseeuw, P.J., 1990. Finding Groups in Data:<br />

An Introducti<strong>on</strong> to Cluster Analysis. Wiley, New York.<br />

Krishnapuram, R., Kim, J., 2000. Clustering <str<strong>on</strong>g>algorithm</str<strong>on</strong>g>s <str<strong>on</strong>g>based</str<strong>on</strong>g><br />

<strong>on</strong> volume criteria. IEEE Trans. Fuzzy Syst. 8, 228–236.<br />

Özdemir, D., Akarun, L., 2001. Fuzzy <str<strong>on</strong>g>algorithm</str<strong>on</strong>g>s for combined<br />

quantizati<strong>on</strong> and dithering. IEEE Trans. Image Processing<br />

10 (6), 923–931.<br />

Özdemir, D., Akarun, L., 2002. A <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g> <str<strong>on</strong>g>algorithm</str<strong>on</strong>g> for color<br />

quantizati<strong>on</strong> of images. Pattern Recogniti<strong>on</strong> 35, 1785–1791.<br />

Pal, N.R., Bezdek, J.C., 1995. On cluster validity for <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g><br />

c-means model. IEEE Trans. Fuzzy Syst., 370–379.<br />

Rouseeuw, P.J., Kaufman, L., Trauwaert, E., 1996. Fuzzy<br />

<str<strong>on</strong>g>clustering</str<strong>on</strong>g> using <strong>scatter</strong> matrices. Comput. Statist. Data<br />

Anal. 23, 135–151.<br />

Sugeno, M., Yasukawa, T., 1993. A <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g>-logic-<str<strong>on</strong>g>based</str<strong>on</strong>g> approach<br />

to qualitative modeling. IEEE Trans. Fuzzy Syst. 1, 7–31.<br />

Wu, K.L., Yang, M.S., 2002. Alternative c-means <str<strong>on</strong>g>clustering</str<strong>on</strong>g><br />

<str<strong>on</strong>g>algorithm</str<strong>on</strong>g>. Pattern Recogniti<strong>on</strong> 35, 2267–2278.<br />

Xie, X.L., Beni, G., 1991. A validity measure for <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g><br />

<str<strong>on</strong>g>clustering</str<strong>on</strong>g>. IEEE Trans. Pattern Anal. Mach. Intell. 13,<br />

841–847.<br />

Yang, M.S., 1993. A survey of <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g> <str<strong>on</strong>g>clustering</str<strong>on</strong>g>. Mathl Comput.<br />

Model. 18, 1–16.<br />

Yang, M.S., Hu, Y.J., Lin, K.C.R., Lin, C.C.L., 2002.<br />

Segmentati<strong>on</strong> techniques for tissue differentiati<strong>on</strong> in MRI<br />

of Ophthalmology using <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g> <str<strong>on</strong>g>clustering</str<strong>on</strong>g> <str<strong>on</strong>g>algorithm</str<strong>on</strong>g>s. Magn.<br />

Res<strong>on</strong>. Imaging 20, 173–179.<br />

Yang, M.S., Wu, K.L., Yu, J., 2003. A <str<strong>on</strong>g>novel</str<strong>on</strong>g> <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g> <str<strong>on</strong>g>clustering</str<strong>on</strong>g><br />

<str<strong>on</strong>g>algorithm</str<strong>on</strong>g>. In: Proceedings of the 2003 IEEE Internati<strong>on</strong>al<br />

Symposium <strong>on</strong> Computati<strong>on</strong>al Intelligence in Robotics and<br />

Automati<strong>on</strong> (CIRA2003), Kobe, Japan, pp. 647–652.<br />

Yu, J., Cheng, Q., Huang, H., 2004. Analysis of the weighting<br />

exp<strong>on</strong>ent in the FCM. IEEE Trans. Syst. Man Cybernet.<br />

Part B 34, 634–638.<br />

Zadeh, L.A., 1965. Fuzzy sets. Inform. C<strong>on</strong>tr. 8, 338–353.<br />

Zahid, N., Limouri, M., Essaid, A., 1999. A new cluster-validity<br />

for <str<strong>on</strong>g>fuzzy</str<strong>on</strong>g> <str<strong>on</strong>g>clustering</str<strong>on</strong>g>. Pattern Recogniti<strong>on</strong> 32, 1089–1097.

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!