skeleton.decomp: Skeleton Decomposition

In rikenbit/ttTensor: Tensor-Train Decomposition

Skeleton Decomposition

Description

skeleton.decomp decomposes the input sparse matrix (n*m) and return the three matrices C (n*r), U (r*r), and R (r*m). Only sparse matrix defined by the Matrix package is acceptable as the input.

Usage

skeleton.decomp(A, r, thr=1E-10, num.iter=30)

Arguments

A	The input sparse matrix.
r	Rank parameter to specify the lower dimension (r <= min(A)).
thr	The threshold to determine the convergence (Default: 1E-10).
num.iter	The number of iteration (Default: 30).

Value

C : A[I, :] U : inverse(A[I, J]) R : A[:, J] rowidx :The indices of rows colidx : The indices of columns RecError : The reconstruction error between data matrix and reconstructed matrix from C, U, and R RelChange : The relative change of the error

Author(s)

Koki Tsuyuzaki

References

I. V. Oseledets, et. al., (2010). TT-cross approximation for multidimensional arrays. Linear Algebra and its Applications

See Also

maxvol

Examples

library("Matrix")
# Matrix data
X3 <- matrix(runif(10*20), nrow=10)
X3 <- as(X3, "sparseMatrix")
# Skeleton Decomposition
out.SKD <- skeleton.decomp(X3, r=3, num.iter=2, thr=1E-5)

rikenbit/ttTensor documentation built on Feb. 2, 2023, 4:32 a.m.