tSVD: Tensor Singular Value Decomposition Using Any Discrete...

In rTensor2: MultiLinear Algebra

Tensor Singular Value Decomposition Using Any Discrete Transform

Description

Performs a tensor singular value decomposition on any 3-mode tensor using any discrete transform.

Usage

tSVD(tnsr,tform)

Arguments

tnsr	: a 3-mode tensor
tform	: Any discrete transform. Supported transforms are: fft: Fast Fourier Transform dwt: Discrete Wavelet Transform (Haar Wavelet) dct: Discrete Cosine transform dst: Discrete Sine transform dht: Discrete Hadley transform dwht: Discrete Walsh-Hadamard transform

Value

a Tensor-class object

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)

Author(s)

Kyle Caudle [e-mail]

References

Kernfeld, E., Kilmer, M., & Aeron, S. (2015). Tensor-tensor products with invertible linear transforms. Linear Algebra and its Applications, 485, 545-570.

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

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

rTensor2 documentation built on Aug. 14, 2022, 9:05 a.m.