Algorithms For Approximation Proc, Chester 2005 by Iske A , Levesley J (Eds)

By Iske A , Levesley J (Eds)

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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.

Wunsch II to some certain experimental conditions or cellular processes. A good survey paper on bi-clustering can be found in [55]. 3 Bioinformatics - DNA or Protein Sequences Clustering In recent decades, DNA and protein sequences grew explosively [23, 37]. 0) shows that there are 49,398,852,122 bases from 45,236,251 reported sequences in GenBank database [29]. The information hidden in the sequences offers a cue to identify functions of genes and proteins. In contrast to sequence comparison and search, cluster analysis provides a more effective way to discover complicated relations among these sequences.

Utilized an agglomerative hierarchical clustering paradigm to cluster all protein sequences in SWISSPROT [69]. In contrast with the proximity-based methods, Guralnik and Karypis transformed protein or DNA sequences into a new feature space, based on the detected sub-patterns working as the sequence features, and clustered with the K-means algorithm [36]. The method is immune from all-against-all expensive sequence comparison. However, it is largely dependent on the feature selection process, which may mislead the analysis.

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