About: Low-rank matrix approximations

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Low-rank matrix approximations are essential tools in the application of kernel methods to large-scale learning problems. Kernel methods (for instance, support vector machines or Gaussian processes) project data points into a high-dimensional or infinite-dimensional feature space and find the optimal splitting hyperplane. In the kernel method the data is represented in a kernel matrix (or, Gram matrix). Many algorithms can solve machine learning problems using the kernel matrix. The main problem of kernel method is its high computational cost associated with kernel matrices. The cost is at least quadratic in the number of training data points, but most kernel methods include computation of matrix inversion or eigenvalue decomposition and the cost becomes cubic in the number of training dat

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rdfs:label	Low-rank matrix approximations (en)
rdfs:comment	Low-rank matrix approximations are essential tools in the application of kernel methods to large-scale learning problems. Kernel methods (for instance, support vector machines or Gaussian processes) project data points into a high-dimensional or infinite-dimensional feature space and find the optimal splitting hyperplane. In the kernel method the data is represented in a kernel matrix (or, Gram matrix). Many algorithms can solve machine learning problems using the kernel matrix. The main problem of kernel method is its high computational cost associated with kernel matrices. The cost is at least quadratic in the number of training data points, but most kernel methods include computation of matrix inversion or eigenvalue decomposition and the cost becomes cubic in the number of training dat (en)
dcterms:subject	Kernel methods for machine learning
Wikipage page ID	48832912 (xsd:integer)
Wikipage revision ID	1107120420 (xsd:integer)
Link from a Wikipage to another Wikipage	Kernel methods for machine learning Algorithmic efficiency Regularized least squares Nyström method Matrix multiplication Eigendecomposition of a matrix Gaussian process Gramian matrix Monte Carlo method Machine learning Cholesky decomposition Kernel method Feature vector Singular value Fourier transform Diagonal matrix Random variable Rank (linear algebra) Invertible matrix Support vector machine Woodbury matrix identity Orthogonal matrix Radial basis function kernel L1 distance Singular-value decomposition dbr:Feature_map
Link from a Wikipage to an external page	http://peekaboo-vision.blogspot.de/2012/12/kernel-approximations-for-efficient.html
sameAs	Low-rank matrix approximations Low-rank matrix approximations
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Use_dmy_dates
has abstract	Low-rank matrix approximations are essential tools in the application of kernel methods to large-scale learning problems. Kernel methods (for instance, support vector machines or Gaussian processes) project data points into a high-dimensional or infinite-dimensional feature space and find the optimal splitting hyperplane. In the kernel method the data is represented in a kernel matrix (or, Gram matrix). Many algorithms can solve machine learning problems using the kernel matrix. The main problem of kernel method is its high computational cost associated with kernel matrices. The cost is at least quadratic in the number of training data points, but most kernel methods include computation of matrix inversion or eigenvalue decomposition and the cost becomes cubic in the number of training data. Large training sets cause large storage and computational costs. Despite low rank decomposition methods (Cholesky decomposition) reduce this cost, they continue to require computing the kernel matrix. One of the approaches to deal with this problem is low-rank matrix approximations. The most popular examples of them are Nyström method and the random features. Both of them have been successfully applied to efficient kernel learning. (en)
prov:wasDerivedFrom	wikipedia-en:Low-rank_matrix_approximations?oldid=1107120420&ns=0
page length (characters) of wiki page	14706 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Low-rank_matrix_approximations
is Link from a Wikipage to another Wikipage of	Low Rank Matrix Approximations Ewin Tang Outline of machine learning
is Wikipage redirect of	Low Rank Matrix Approximations
is foaf:primaryTopic of	wikipedia-en:Low-rank_matrix_approximations

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