Low-rank matrix approximations are essential tools in the application of kernel methods to large-scale learning problems. Kernel methods (for instance...

In mathematics, low-rank approximation refers to the process of approximating a given matrix by a matrix of lower rank. More precisely, it is a minimization...

decomposition of the original matrix ⁠ M , {\displaystyle \mathbf {M} ,} ⁠ but rather provides the optimal low-rank matrix approximation ⁠ M ~ {\displaystyle {\tilde...

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...

or is low-rank. For example, one may assume the matrix has low-rank structure, and then seek to find the lowest rank matrix or, if the rank of the completed...

Analysis (PCA) exploit SVD: singular value decomposition yields low-rank approximations of data, effectively treating the data covariance as singular by...

of these approximation methods can be expressed in purely linear algebraic or functional analytic terms as matrix or function approximations. Others are...

matrices (H-matrices) are used as data-sparse approximations of non-sparse matrices. While a sparse matrix of dimension n {\displaystyle n} can be represented...

such norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication. Given a field...

In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a rectangular matrix in which each ascending skew-diagonal...

Locality-sensitive hashing Log-linear model Logistic model tree Low-rank approximation Low-rank matrix approximations MATLAB MIMIC (immunology) MXNet Mallet (software...

accelerates matrix multiplication by W {\displaystyle W} . Low-rank approximations can be found by singular value decomposition (SVD). The choice of rank for...

Kernel PCA L1-norm principal component analysis Low-rank approximation Matrix decomposition Non-negative matrix factorization Nonlinear dimensionality reduction...

Woodbury matrix identity – named after Max A. Woodbury – says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction...

except using approximations of the derivatives of the functions in place of exact derivatives. Newton's method requires the Jacobian matrix of all partial...

one wishes to compare p ( x , y ) {\displaystyle p(x,y)} to a low-rank matrix approximation in some unknown variable w {\displaystyle w} ; that is, to what...

eigenvalues is equal to the rank of the matrix A, and also the dimension of the image (or range) of the corresponding matrix transformation, as well as...

(singular-value decomposition) which computes the low-rank approximation of a single matrix (or a set of 1D vectors). Let matrix X = [ x 1 , … , x n ] {\displaystyle...

their rank: because of the rounding errors, a floating-point matrix has almost always a full rank, even when it is an approximation of a matrix of a much...

V.; Lim, L. (2008). "Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem". SIAM Journal on Matrix Analysis and Applications. 30...

occurrence matrix, LSA finds a low-rank approximation to the term-document matrix. There could be various reasons for these approximations: The original...

total number of pages. The PageRank values are the entries of the dominant right eigenvector of the modified adjacency matrix rescaled so that each column...

rank of a matrix equals the number of nonzero singular values, we find that rank ⁡ ( A ⊗ B ) = rank ⁡ A rank ⁡ B . {\displaystyle \operatorname {rank}...

includes a quality of data approximation and some penalty terms for the bending of the manifold. The popular initial approximations are generated by linear...

j]} element is incremented. The Spearman's rank correlation can then be computed, based on the count matrix M {\displaystyle M} , using linear algebra...

find a low rank approximation to an LU decomposition using a randomized algorithm. Given an input matrix A {\textstyle A} and a desired low rank k {\textstyle...

least squares approximation of the data is generically equivalent to the best, in the Frobenius norm, low-rank approximation of the data matrix. In the least...

In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space. For points x 1 , x 2 ,...

that retains all the defining properties of the matrix SVD. The matrix SVD simultaneously yields a rank-𝑅 decomposition and orthonormal subspaces for...

parameters, and so continuous approximations or bounds on evaluation measures have to be used. For example the SoftRank algorithm. LambdaMART is a pairwise...