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- CUR_matrix_approximation abstract "A CUR matrix approximation is a set of three matrices that, when multiplied together, closely approximate a given matrix. A CUR approximation can be used in the same way as the low-rank approximation of the Singular value decomposition (SVD). CUR approximations are less accurate than the SVD, but since the rows and columns come from the original matrix (rather than left and right singular vectors), the CUR approximation is often easy for users to comprehend.Formally, a CUR matrix approximation of a matrix A is three matrices C, U, and R such that C is made from columns of A, R is made from rows of A, and that the product CUR closely approximates A. Usually the CUR is selected to be a rank-k approximation, which means that C contains k columns of A, R contains k rows of A, and U is a k-by-k matrix. There are many possible CUR matrix approximations, and many CUR matrix approximations for a given rank.The CUR matrix approximation is often used in place of the low-rank approximation of the SVD in Principal components analysis. The CUR is less accurate, but the columns of the matrix C are taken from A and the rows of R are taken from A. In PCA, each column of A contains a data sample; thus, the matrix C is made of a subset of data samples. This is much easier to interpret than the SVD's left singular vectors, which represent the data in a rotated space. Similarly, the matrix R is made of a subset of variables measured for each data sample. This is easier to comprehend than the SVD's right singular vectors, which are another rotations of the data in space.".
- CUR_matrix_approximation wikiPageID "36254198".
- CUR_matrix_approximation wikiPageLength "2221".
- CUR_matrix_approximation wikiPageOutDegree "6".
- CUR_matrix_approximation wikiPageRevisionID "635082451".
- CUR_matrix_approximation wikiPageWikiLink Category:Matrices.
- CUR_matrix_approximation wikiPageWikiLink Low-rank_approximation.
- CUR_matrix_approximation wikiPageWikiLink Matrix_(mathematics).
- CUR_matrix_approximation wikiPageWikiLink Principal_component_analysis.
- CUR_matrix_approximation wikiPageWikiLink Principal_components_analysis.
- CUR_matrix_approximation wikiPageWikiLink Rank_(linear_algebra).
- CUR_matrix_approximation wikiPageWikiLink Singular_value_decomposition.
- CUR_matrix_approximation wikiPageWikiLinkText "CUR matrix approximation".
- CUR_matrix_approximation hasPhotoCollection CUR_matrix_approximation.
- CUR_matrix_approximation wikiPageUsesTemplate Template:Cn.
- CUR_matrix_approximation subject Category:Matrices.
- CUR_matrix_approximation hypernym Set.
- CUR_matrix_approximation type Article.
- CUR_matrix_approximation type Article.
- CUR_matrix_approximation type Matrix.
- CUR_matrix_approximation comment "A CUR matrix approximation is a set of three matrices that, when multiplied together, closely approximate a given matrix. A CUR approximation can be used in the same way as the low-rank approximation of the Singular value decomposition (SVD).".
- CUR_matrix_approximation label "CUR matrix approximation".
- CUR_matrix_approximation sameAs m.0k2g2kp.
- CUR_matrix_approximation sameAs Q5014719.
- CUR_matrix_approximation sameAs Q5014719.
- CUR_matrix_approximation wasDerivedFrom CUR_matrix_approximation?oldid=635082451.
- CUR_matrix_approximation isPrimaryTopicOf CUR_matrix_approximation.