zbMATH — the first resource for mathematics

L\({}_ 1\)-norm based fuzzy clustering. (English) Zbl 0714.62052
The presented fuzzy clustering problem uses the distance between observations and location parameter vectors, which is based on the \(L_ 1\)-norm, instead of the inner product induced norm used in classical fuzzy ISODATA. Two alternative methods to solve the \(L_ 1\) fuzzy clustering problem are derived.

62H30 Classification and discrimination; cluster analysis (statistical aspects)
Full Text: DOI
[1] Ball, G.H.; Hall, D.J., A clustering technique for summarizing multivariate data, Behavioral sci., 12, 153-165, (1967)
[2] Bezdek, J.C., Numerical taxonomy with fuzzy sets, J. math. biology, 1, 57-71, (1974) · Zbl 0403.62039
[3] Bloomfield, P.; Steiger, W.L., Least absolute deviations, (1983), Birkhäuser Boston, MA · Zbl 0536.62049
[4] Dunn, J.C., A fuzzy relative of the ISODATA process and its use in detecting compact, well-separated clusters, J. of cybernet., 3, 32-57, (1973) · Zbl 0291.68033
[5] Fisher, R.A., The use of multiple measurements in taxonomic problems, Ann. eugenics, 7, 179-188, (1936)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.