Module tensor_decomp 

Tensor decomposition algorithms: CP, Tucker, and Tensor-Train (TT).

This module provides CPU-side implementations of the three most widely used tensor decomposition methods, which can be used to generate PTX kernels for GPU execution.

Decompositions

• CP (CANDECOMP/PARAFAC) — decomposes a tensor into a sum of rank-one tensors via Alternating Least Squares (ALS).
• Tucker — decomposes a tensor into a core tensor multiplied by factor matrices along each mode, via HOSVD or HOOI.
• Tensor-Train (TT) — decomposes a tensor into a chain of 3D cores via sequential SVDs.

References

• Kolda & Bader, “Tensor Decompositions and Applications”, SIAM Review 2009
• Oseledets, “Tensor-Train Decomposition”, SIAM J. Sci. Comput. 2011

Structs

CpAlsConfig

Configuration for CP-ALS algorithm.

CpDecomposition

CP (CANDECOMP/PARAFAC) decomposition result.

Matrix

A dense row-major matrix.

Tensor

A dense multi-dimensional tensor.

TtConfig

Configuration for TT-SVD algorithm.

TtDecomposition

Tensor-Train (TT) decomposition result.

TuckerConfig

Configuration for Tucker decomposition.

TuckerDecomposition

Tucker decomposition result.

Functions

cp_als

CP decomposition via Alternating Least Squares (ALS).

hadamard_product

Element-wise (Hadamard) product of two matrices.

khatri_rao_product

Khatri-Rao product (column-wise Kronecker product).

mode_n_product

Mode-n product: multiplies a tensor by a matrix along mode n.

tt_svd

TT-SVD decomposition.

tucker_hooi

Higher-Order Orthogonal Iteration (HOOI) for Tucker decomposition.

tucker_hosvd

Higher-Order SVD (HOSVD) for Tucker decomposition.