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...

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...

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

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

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

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...

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...

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...

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...

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...

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...

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

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

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

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

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...

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

(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...

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

involves a low-rank representation for the direct and/or inverse Hessian. This represents the Hessian as a sum of a diagonal matrix and a low-rank update...

line by moving along the line Low-rank approximation — find best approximation, constraint is that rank of some matrix is smaller than a given number...

covariance matrix amounts to learning a second order model of the underlying objective function similar to the approximation of the inverse Hessian matrix in...

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...

correlation of 1) rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc.) between the two variables, and low when observations...

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...

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 ,...

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...