t_svd

TSVD for a 3-Tensor. Constructs 3-Tensors <code>U, S, V</code> such that <code>tnsr = t_mult(t_mult(U,S),t(V))</code>. <code>U</code> and <code>V</code> are orthgonal 3-Tensors with orthogonality defined in Kilmer et al. (2013), and <code>S</code> is a 3-Tensor consists of facewise diagonal matrices. For more details on the TSVD, consult Kilmer et al. (2013).

A set of tools for creation, manipulation, and modeling
of tensors with arbitrary number of modes. A tensor in the context of data
analysis is a multidimensional array. rTensor does this by providing a S4
class 'Tensor' that wraps around the base 'array' class. rTensor
provides common tensor operations as methods, including matrix unfolding,
summing/averaging across modes, calculating the Frobenius norm, and taking
the inner product between two tensors. Familiar array operations are
overloaded, such as index subsetting via '[' and element-wise operations.
rTensor also implements various tensor decomposition, including CP, GLRAM,
MPCA, PVD, and Tucker. For tensors with 3 modes, rTensor also implements
transpose, t-product, and t-SVD, as defined in Kilmer et al. (2013). Some
auxiliary functions include the Khatri-Rao product, Kronecker product, and
the Hadamard product for a list of matrices.

Koki Tsuyuzaki

rTensor

Tools for Tensor Analysis and Decomposition

James Li

Jacob Bien

Martin Wells

t_svd function

<dl><dt>tnsr</dt>
<dd>3-Tensor to decompose via TSVD</dd></dl>

Arguments

Tensor Singular Value Decomposition — t_svd

<dl>

<dt>tnsr</dt>
<dd>3-Tensor to decompose via TSVD</dd>

</dl>

t_svd: Tensor Singular Value Decomposition

Description

Usage

Value

Arguments

References

See Also

Examples