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Books > Computing & IT > Applications of computing > Signal processing
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From Algebraic Structures to Tensors (Hardcover)
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From Algebraic Structures to Tensors (Hardcover)
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Nowadays, tensors play a central role for the representation,
mining, analysis, and fusion of multidimensional, multimodal, and
heterogeneous big data in numerous fields. This set on Matrices and
Tensors in Signal Processing aims at giving a self-contained and
comprehensive presentation of various concepts and methods,
starting from fundamental algebraic structures to advanced
tensor-based applications, including recently developed tensor
models and efficient algorithms for dimensionality reduction and
parameter estimation. Although its title suggests an orientation
towards signal processing, the results presented in this set will
also be of use to readers interested in other disciplines. This
first book provides an introduction to matrices and tensors of
higher-order based on the structures of vector space and tensor
space. Some standard algebraic structures are first described, with
a focus on the hilbertian approach for signal representation, and
function approximation based on Fourier series and orthogonal
polynomial series. Matrices and hypermatrices associated with
linear, bilinear and multilinear maps are more particularly
studied. Some basic results are presented for block matrices. The
notions of decomposition, rank, eigenvalue, singular value, and
unfolding of a tensor are introduced, by emphasizing similarities
and differences between matrices and tensors of higher-order.
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