Globally Convergent Block Coordinate Descent Algorithms for Semi-Nonnegative Independent Component Analysis
Abstract
We propose a subgradient-based block coordinate descent (BCD-SubG) framework for nonconvex optimization over products of probability simplices and a closed feasible set, motivated by semi-nonnegative independent component analysis (Semi-NNICA). Elementary column transformations are used to preserve simplex feasibility, while first-order information guides block and pair selection. We establish the global convergence of BCD-SubG using a constrained Lojasiewicz inequality; additional eventual-interiority conditions yield stationary limits and convergence rates. We then specialize BCD-SubG to the direct-fit and indirect-fit Semi-NNICA models and derive explicit updates that ensure global convergence without further assumptions. For both models, eventual interiority also yields stationary limits and convergence-rate estimates. Experiments on synthetic mixtures and simulated magnetic resonance spectroscopy data show generally lower recovery errors and shorter wall-clock times than the tested Semi-NNICA baselines. Joint diagonalization experiments further demonstrate lower final objective values.
Related
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BibTeX
@misc{cai2026globally,
title = {{Globally Convergent Block Coordinate Descent Algorithms for Semi-Nonnegative Independent Component Analysis}},
author = {Zhenyu Cai and Wentao Ding and Jianze Li and Wen Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16765},
eprint = {2610.16765},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16765},
}
RIS
TY - UNPB
TI - Globally Convergent Block Coordinate Descent Algorithms for Semi-Nonnegative Independent Component Analysis
AU - Zhenyu Cai
AU - Wentao Ding
AU - Jianze Li
AU - Wen Huang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16765
UR - https://arxiv.org/abs/2610.16765
AB - We propose a subgradient-based block coordinate descent (BCD-SubG) framework for nonconvex optimization over products of probability simplices and a closed feasible set, motivated by semi-nonnegative independent component analysis (Semi-NNICA). Elementary column transformations are used to preserve simplex feasibility, while first-order information guides block and pair selection. We establish the global convergence of BCD-SubG using a constrained Lojasiewicz inequality; additional eventual-interiority conditions yield stationary limits and convergence rates. We then specialize BCD-SubG to the direct-fit and indirect-fit Semi-NNICA models and derive explicit updates that ensure global convergence without further assumptions. For both models, eventual interiority also yields stationary limits and convergence-rate estimates. Experiments on synthetic mixtures and simulated magnetic resonance spectroscopy data show generally lower recovery errors and shorter wall-clock times than the tested Semi-NNICA baselines. Joint diagonalization experiments further demonstrate lower final objective values.
ER -