Tucker Decomposition

Approximating A by a Tucker decomposition

\[\hat A = C \times_1 U \times_2 V \times_3 W\]

with multilinear rank mlrank can be computed as follows.

julia> mlrank = (5, 4, 3)
julia> tucker_res = tucker(A, mlrank)
TuckerResult{Float64, 3}
  Original size:    (20, 15, 10)
  Core size:        (5, 4, 3)
  Multilinear rank: (5, 4, 3)
  Compression:      12.0x

The core $C$ and the factor matrices $(U, V, W)$ of the decomposition can be accessed as follows.

core(tucker_res)
factors(tucker_res)

Tucker Docs

TensorKitchen.tucker — Function

tucker(A, ranks; method = :sthosvd, kwargs...) returns a TuckerResult

Computes a Tucker decomposition of A with multilinear rank ranks.

Main Options

method = :sthosvd: Sets the Tucker decomposition algorithm. Possible options are:
- :sthosvd (default): Sequentially Truncated HOSVD. A direct one-pass decomposition, mainly used as a fast standalone Tucker approximation or as the default initializer for :hooiFast, deterministic, and usually a good initial point.
- :hooi: High-Order Orthogonal Iteration. Iteratively refines the Tucker factors, initialized by ST-HOSVD by default.

Extended Options

For method = :hooi:

maxiter = 50: Maximum number of HOOI iterations.
tol = 1e-8: Convergence tolerance based on change in relative reconstruction error.
init = :sthosvd
- :sthosvd: Uses ST-HOSVD to initialize the Tucker factors.
- TuckerResult: Uses an existing Tucker decomposition as the initial point.

Example

julia> using Random
julia> Random.seed!(0)
julia> A = randn(20, 15, 10); ranks = (5, 4, 3)
julia> res = tucker(A, ranks; verbose = false)
TuckerResult{Float64, 3}
  Original size:    (20, 15, 10)
  Core size:        (5, 4, 3)
  Multilinear rank: (5, 4, 3)
  Compression:      12.0x

The core tensor and factor matrices can be accessed by

core(res)
factors(res)

A tensor approximation can be reconstructed by

reconstruct(res)

or equivalently

reconstruct_tucker(core(res), factors(res))

Notes

:sthosvd is not an iterative solver. It directly returns a TuckerResult and does not expose solver-style outputs such as iteration counts or convergence diagnostics.
:hooi is the iterative refinement method in the current Tucker implementation.
Important distinction: For the current Tucker implementation, do not use solver = :rgd, init = :auto, or manifold solvers like RGD, RCG, LBFGS, etc.

source

TensorKitchen.TuckerResult — Type