Global Identifiability of $\ell_1$-based Dictionary Learning via Matrix Volume Optimization

Authors: Jingzhou Hu, Kejun Huang

NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Finally, we propose algorithms to solve the new proposed formulation, specifically one based on the linearized-ADMM with efficient per-iteration updates. The proposed algorithms exhibit surprisingly effective performance in correctly and efficiently recovering the dictionary, as demonstrated in the numerical experiments.
Researcher Affiliation Academia Jingzhou Hu Kejun Huang Department of Computer and Information Science and Engineering University of Florida Gainesville, FL 32611 (jingzhouhu,kejun.huang)@ufl.edu
Pseudocode Yes Algorithm 1 Solving (7) with L-ADMM
Open Source Code No The paper does not provide explicit statements about releasing source code or links to a code repository.
Open Datasets No For π‘˜= 20 and 𝑛= 1000, we randomly generate the groundtruth sparse coefficient matrix 𝑺 according to the Bernoulli-Gaussian model with 𝑝= 0.5, and the groundtruth dictionary matrix 𝑨 completely random, and generate the data matrix 𝑿= 𝑨 𝑺 . For a given image, it is first divided into 8 8 non-overlapping patches, reshaped into a vector in Rπ‘˜with π‘˜= 64, and stacked as columns of the data matrix 𝑿.
Dataset Splits No The paper generates synthetic data and uses image patches from a natural image, but does not describe any train/validation/test dataset splits.
Hardware Specification No The paper states that experiments are conducted in MATLAB but does not provide specific details on the hardware used (e.g., CPU, GPU models, memory).
Software Dependencies No The paper mentions using MATLAB for experiments but does not provide specific version numbers for MATLAB or any other software dependencies.
Experiment Setup Yes For π‘˜= 20 and 𝑛= 1000, we randomly generate the groundtruth sparse coefficient matrix 𝑺 according to the Bernoulli-Gaussian model with 𝑝= 0.5, and the groundtruth dictionary matrix 𝑨 completely random, and generate the data matrix 𝑿= 𝑨 𝑺 . We empirically found that setting 𝜌= π‘›π‘˜works very well in practice.