| Title:
|
Detecting a data set structure through the use of nonlinear projections search and optimization (English) |
| Author:
|
Brailovsky, Victor L. |
| Author:
|
Har-Even, Michael |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
[375]-380 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Detecting a cluster structure is considered. This means solving either the problem of discovering a natural decomposition of data points into groups (clusters) or the problem of detecting clouds of data points of a specific form. In this paper both these problems are considered. To discover a cluster structure of a specific arrangement or a cloud of data of a specific form a class of nonlinear projections is introduced. Fitness functions that estimate to what extent a given subset of data points (in the form of the corresponding projection) represents a good solution for the first or the second problem are presented. To find a good solution one uses a search and optimization procedure in the form of Evolutionary Programming. The problems of cluster validity and robustness of algorithms are considered. Examples of applications are discussed. (English) |
| Keyword:
|
cluster structure |
| Keyword:
|
nonlinear projection |
| MSC:
|
62H30 |
| MSC:
|
68T10 |
| idZBL:
|
Zbl 1274.68376 |
| . |
| Date available:
|
2009-09-24T19:17:23Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135218 |
| . |
| Reference:
|
[1] Ballard D. H., Brown C. H.: Computer Vision.Prentice–Hall, 1982 |
| Reference:
|
[2] Brailovsky V. L., Har-even M.: Detecting a data set structure through the use of nonlinear projections and stochastic optimization.In: Proc. 1st IARP TC1 Workshop on Statistical Techniques in Pattern Recognition, Prague 1997, pp. 7–12 |
| Reference:
|
[3] Everitt B. S.: Cluster Analysis.Wiley, New York 1974 MR 0455213 |
| Reference:
|
[4] Har–even M., Brailovsky V. L.: Probabilistic validation approach for clustering.Pattern Recognition Lett. 16 (1995), 1189–1196 10.1016/0167-8655(95)00073-P |
| Reference:
|
[5] Jain A. K., Dubes R. C.: Algorithms for Clustering Data.Prentice Hall, 1988 Zbl 0665.62061, MR 0999135 |
| Reference:
|
[6] Jain A. K., Moreau J. V.: Bootstrap technique in cluster analysis.Pattern Recognition 20 (1987), 547–568 10.1016/0031-3203(87)90081-1 |
| Reference:
|
[7] Porto V. W., Fogel D. B., Fogel L. J.: Alternative neural network training methods.IEEE Expert 10 (1995), 3, 16–22 10.1109/64.393138 |
| Reference:
|
[8] (ed.) S. C. Shapiro: Encyclopedia of Artificial Intelligence, Vol.1, ‘Clustering’. Wiley, New York 1990, pp. 103–111 MR 1059716 |
| Reference:
|
[9] Vapnik V. N.: The Nature of Statistical Learning Theory.Springer Verlag, Berlin 1995 Zbl 0934.62009, MR 1367965 |
| . |
