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Springer, 1997. 3. S. Dekel and D. Leviatan: The Bramble-Hilbert lemma for convex domains. SIAM J. Math. Anal. 35, 2004, 1203–1212. 4. S. Dekel and D. Leviatan: Whitney estimates for convex domains with applications to multivariate piecewise polynomial approximation. Found. Comput. Math. 4, 2004, 345–368. 5. R. Kazinnik: Image Compression using Geometric Piecewise Polynomials. D. thesis, School of Mathematics, Tel Aviv University, in preparation. 6. R. Kazinnik, S. Dekel, and N. Dyn: Low-bit rate image coding using adaptive geometric piecewise polynomial approximation.

HQ }(Q ≤ N ), such that Ci ∈ Hm , Cj ∈ Hl , and m > l imply Ci ⊂ Cj or Ci ∩ Cj = φ for all i, j = i, m, l = 1, . . , Q. Clustering consists of four basic steps: 1. Feature selection or extraction. As pointed out in [9] and [46], feature selection chooses distinguishing features from a set of candidates, while feature extraction utilizes some transformations to generate useful and novel features. 2. Clustering algorithm design or selection. The step is usually combined with the proximity measure selection and the criterion function construction.

The remainder of the paper is organized as follows. In Section 2, we briefly review major clustering techniques rooted in machine learning, computer science, and statistics. More discussions on computational intelligence technologies based clustering are given in Section 3 and 4. We illustrate five important applications of the clustering algorithms in Section 5. We conclude the paper and summarize the potential challenges in Section 6. 2 Clustering Algorithms Different objects and criteria usually lead to different taxonomies of clustering algorithms [28, 40, 45, 46].

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