Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Higher-order_singular_value_decomposition> ?p ?o }
Showing triples 1 to 45 of
45
with 100 triples per page.
- Higher-order_singular_value_decomposition abstract "In multilinear algebra, there does not exist a general decomposition method for multi-way arrays (also known as N-arrays, higher-order arrays, or data-tensors) with all the properties of a matrix singular value decomposition (SVD). A matrix SVD simultaneously computes(a) a rank-R decomposition and(b) the orthonormal row/column matrices.These two properties can be captured separately by two different decompositions for multi-way arrays.Property (a) is extended to higher order by a class of closely related constructions known collectively as CP decomposition (named after the two most popular and general variants, CANDECOMP and PARAFAC). Such decompositions represent a tensor as the sum of the n-fold outer products of rank-1 tensors, where n is the dimension of the tensor indices.Property (b) is extended to higher order by a class of methods known variably as Tucker3, N-mode SVD, and N-mode principal component analysis (PCA). (This article will use the general term \"Tucker decomposition\".) These methods compute the orthonormal spaces associated with the different axes (or modes) of a tensor. The Tucker decomposition is also used in multilinear subspace learning as multilinear principal component analysis. This terminology was coined by P. Kroonenberg in the 1980s, but it was later called multilinear SVD and HOSVD (higher-order SVD) by L. De Lathauwer.Historically, much of the interest in higher-order SVDs was driven by the need to analyze empirical data, especially in psychometrics and chemometrics. As such, many of the methods have been independently invented several times, often with subtle variations, leading to a confusing literature. Abstract and general mathematical theorems are rare (though see Kruskal with regard to the CP decomposition); instead, the methods are often designed for analyzing specific data types. The 2008 review article by Kolda and Bader provides a compact summary of the history of these decompositions, and many references for further reading.The concept of HOSVD was carried over to functions by Baranyi and Yam via the TP model transformation . This extension led to the definition of the HOSVD based canonical form of tensor product functions and Linear Parameter Varying system models and to convex hull manipulation based control optimization theory, see TP model transformation in control theories.".
- Higher-order_singular_value_decomposition wikiPageID "20148816".
- Higher-order_singular_value_decomposition wikiPageLength "15031".
- Higher-order_singular_value_decomposition wikiPageOutDegree "29".
- Higher-order_singular_value_decomposition wikiPageRevisionID "697115941".
- Higher-order_singular_value_decomposition wikiPageWikiLink Category:Multilinear_algebra.
- Higher-order_singular_value_decomposition wikiPageWikiLink Chemometrics.
- Higher-order_singular_value_decomposition wikiPageWikiLink Conditional_independence.
- Higher-order_singular_value_decomposition wikiPageWikiLink Disease_surveillance.
- Higher-order_singular_value_decomposition wikiPageWikiLink Factor_analysis.
- Higher-order_singular_value_decomposition wikiPageWikiLink Higher-order_singular_value_decomposition.
- Higher-order_singular_value_decomposition wikiPageWikiLink Ledyard_Tucker.
- Higher-order_singular_value_decomposition wikiPageWikiLink Matrix_(mathematics).
- Higher-order_singular_value_decomposition wikiPageWikiLink Matrix_norm.
- Higher-order_singular_value_decomposition wikiPageWikiLink Multilinear_algebra.
- Higher-order_singular_value_decomposition wikiPageWikiLink Multilinear_principal_component_analysis.
- Higher-order_singular_value_decomposition wikiPageWikiLink Multilinear_subspace_learning.
- Higher-order_singular_value_decomposition wikiPageWikiLink Orthogonal_matrix.
- Higher-order_singular_value_decomposition wikiPageWikiLink Principal_component_analysis.
- Higher-order_singular_value_decomposition wikiPageWikiLink Psychometrics.
- Higher-order_singular_value_decomposition wikiPageWikiLink Quantum_mechanics.
- Higher-order_singular_value_decomposition wikiPageWikiLink Singular_value_decomposition.
- Higher-order_singular_value_decomposition wikiPageWikiLink TP_model_transformation_in_control_theory.
- Higher-order_singular_value_decomposition wikiPageWikiLink Tensor.
- Higher-order_singular_value_decomposition wikiPageWikiLink TensorFaces.
- Higher-order_singular_value_decomposition wikiPageWikiLink Tensor_product.
- Higher-order_singular_value_decomposition wikiPageWikiLink Tensor_product_model_transformation.
- Higher-order_singular_value_decomposition wikiPageWikiLink Tensor_rank_decomposition.
- Higher-order_singular_value_decomposition wikiPageWikiLink Topic_model.
- Higher-order_singular_value_decomposition wikiPageWikiLink Tucker_decomposition.
- Higher-order_singular_value_decomposition wikiPageWikiLinkText "Higher-order singular value decomposition".
- Higher-order_singular_value_decomposition wikiPageWikiLinkText "higher-order SVD".
- Higher-order_singular_value_decomposition wikiPageWikiLinkText "higher-order singular value decomposition".
- Higher-order_singular_value_decomposition wikiPageUsesTemplate Template:Main.
- Higher-order_singular_value_decomposition wikiPageUsesTemplate Template:Reflist.
- Higher-order_singular_value_decomposition wikiPageUsesTemplate Template:Very_long.
- Higher-order_singular_value_decomposition subject Category:Multilinear_algebra.
- Higher-order_singular_value_decomposition type Page.
- Higher-order_singular_value_decomposition comment "In multilinear algebra, there does not exist a general decomposition method for multi-way arrays (also known as N-arrays, higher-order arrays, or data-tensors) with all the properties of a matrix singular value decomposition (SVD).".
- Higher-order_singular_value_decomposition label "Higher-order singular value decomposition".
- Higher-order_singular_value_decomposition sameAs Q17097998.
- Higher-order_singular_value_decomposition sameAs m.04yc0hd.
- Higher-order_singular_value_decomposition sameAs Q17097998.
- Higher-order_singular_value_decomposition wasDerivedFrom Higher-order_singular_value_decomposition?oldid=697115941.
- Higher-order_singular_value_decomposition isPrimaryTopicOf Higher-order_singular_value_decomposition.