A Dual Framework for Low-rank Tensor Completion
Authors: Madhav Nimishakavi, Pratik Kumar Jawanpuria, Bamdev Mishra
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The experiments illustrate the efficacy of the proposed algorithm on several real-world datasets across applications. |
| Researcher Affiliation | Collaboration | Indian Institute of Science, India Microsoft, India |
| Pseudocode | Yes | Algorithm 1 Proposed Riemannian trust-region algorithm for (7). Input: YΩ, rank (r1, . . . , r K), regularization parameter λ, and tolerance ϵ. Initialize : u M. repeat 1: Compute the gradient uℓfor (7) as given in Lemma 1. 2: Compute the search direction which minimizes the trust-region subproblem. It makes use of uℓand its directional derivative presented in Lemma 1 for (7). 3: Update x with the retraction step to maintain strict feasibility on M. Specifically for the spectrahedron manifold, Uk (Uk + Vk)/ Uk + Vk F , where Vk is the search direction. until uℓ F < ϵ. Output: u |
| Open Source Code | Yes | Our codes are available at https://pratikjawanpuria.com/. |
| Open Datasets | Yes | a) Ribeira is a hyperspectral image [16] of size 1017 1340 33, where each slice represents the image measured at a particular wavelength. We re-size it to 203 268 33 [37, 26, 24]; b) Tomato is a video sequence dataset [27, 8] of size 242 320 167; and c) Baboon is an RGB image [49], modeled as a 256 256 3 tensor. |
| Dataset Splits | Yes | We set λk = λnk k in (7). Hence, we tune only one hyper-parameter λ, from the set {10 3, 10 2, . . . , 103}, via five-fold cross-validation of the training data. |
| Hardware Specification | No | The paper mentions that the algorithm is implemented using Manopt in Matlab but does not specify any details about the hardware used for experiments (e.g., GPU/CPU models, memory). |
| Software Dependencies | No | Our algorithm is implemented using the Manopt toolbox [7] in Matlab, which has off-the-shelf generic TR implementation. The paper mentions software but does not provide version numbers for Manopt or Matlab. |
| Experiment Setup | Yes | We set λk = λnk k in (7). Hence, we tune only one hyper-parameter λ, from the set {10 3, 10 2, . . . , 103}, via five-fold cross-validation of the training data. |