We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pair-wise symmetric tensors.

N k=1 α k y k = 0 0 ≤ α k ≤ c, k = 1, ..., N. Note: w and ϕ(x k) are not calculated. • Mercer condition: K(x k , x l) = ϕ(x k) T ϕ(x l) • Obtained classifier: y(x) = sign[ N k=1 α k y k K(x, x k) + b] with α k positive real constants, b real constant, that follow as solution to the QP problem. Non-zero α k are called support values and the corresponding data points are called support vectors. The bias term b follows from KKT conditions. • Some possible kernels K(•, •): K(x, x k) = x T k x (linear SVM) K(x, x k) = (x T k x + 1) d (polynomial SVM of degree d) K(x, x k) = exp{− x − x k 2 2 /σ 2 } (RBF SVM) K(x, x k) = tanh(κ x T k x + θ) (MLP SVM) • In the case of RBF and MLP kernel, the number of hidden units corresponds to the number of support vectors.

biomaRt is a new Bioconductor package that integrates BioMart data resources with data analysis software in Bioconductor. It can annotate a wide range of gene or gene product identifiers (e.g. Entrez-Gene and Affymetrix probe identifiers) with information such as gene symbol, chromosomal coordinates, Gene Ontology and OMIM annotation. Furthermore biomaRt enables retrieval of genomic sequences and single nucleotide polymorphism information, which can be used in data analysis. Fast and up-to-date data retrieval is possible as the package executes direct SQL queries to the BioMart databases (e.g. Ensembl). The biomaRt package provides a tight integration of large, public or locally installed BioMart databases with data analysis in Bioconductor creating a powerful environment for biological data mining.

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