TensorTools (version 1.0.0)

tSVD: Singular value decomposition (SVD)

Description

Performs a Singular Value Decomposition of 3 mode tensor T using any discrete transform. The result is a left singular value tensor object U, a right singular value tensor object V, and a diagonal tensor S so that T = USV^t

Usage

tSVD(tnsr, tform)

Value

If the SVD is performed on a \(m\) x \(n\) x \(k\) tensor, the components in the returned value are:

U, the left singular value tensor object (\(m\) x \(m\) x \(k\))

V, The right singular value tensor object (\(n\) x \(n\) x \(k\))

S: A diagonal tensor (\(m\) x \(n\) x \(k\))#' @examples

Arguments

tnsr,

a 3-mode tensor S3 class object

tform,

Any discrete transform.

fft: Fast Fourier Transorm

dwt: Discrete Wavelet Transform (Haar Wavelet)

dct: Discrete Cosine transform

dst: Discrete Sine transform

dht: Discrete Hadley transform

dwht: Discrete Walsh-Hadamard transform

Author

Kyle Caudle

Randy Hoover

Jackson Cates

Everett Sandbo

References

M. E. Kilmer, C. D. Martin, and L. Perrone, “A third-order generalization of the matrix svd as a product of third-order tensors,” Tufts University, Department of Computer Science, Tech. Rep. TR-2008-4, 2008

K. Braman, "Third-order tensors as linear operators on a space of matrices", Linear Algebra and its Applications, vol. 433, no. 7, pp. 1241-1253, 2010.

Examples

T <- t_rand(modes=c(2,3,4))
print(tSVD(T,"dst"))