eig_svd(A, [k]; [kwargs...])

Perform singular value decomposition of a matrix A by estimating svd(A' * A). If k is provided, Krylov iterative solver is used to return only k largest singular values and corresponding singular vectors.

Designed to work with sparse matrices. Keyword arguments are forwarded to KrylovKit.svdsolve.

Examples

using SparseArrays
eig_svd(sprand(100, 100, 0.2), 10)

pca(A, k; [q=10], [exact_svd=false], [s=5])

Perform fast randomized PCA of a matrix A to return k first components.

Designed to work with sparse matrices.

Keyword arguments

• exact_svd - if true, use exact SVD on random projections, otherwise use eig_svd approximation. Setting it to true would improve precision of the algorithm on small eigenvalues, but would drastically decrease performance on large matrices (>1M rows).
• q is the number of pass over A, q should larger than 1 and q times pass eqauls to (q-2)/2 times power iteration
• s is the excess dimension for the random matrix. This parameter is not supposed to be changed normally.

Examples

using SparseArrays
pca(sprand(100, 100, 0.2), 10; q=3)