{"ID":2888410,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.23600","arxiv_id":"2507.23600","title":"EB-gMCR: Energy-Based Generative Modeling for Signal Unmixing and Multivariate Curve Resolution","abstract":"Signal unmixing analysis decomposes data into basic patterns and is widely applied in chemical and biological research. Multivariate curve resolution (MCR), a branch of signal unmixing, separates mixed signals into components (base patterns) and their concentrations (intensity), playing a key role in understanding composition. Classical MCR is typically framed as matrix factorization (MF) and requires a user-specified number of components, usually unknown in real data. Once data or component number increases, the scalability of these MCR approaches face significant challenges. This study reformulates MCR as a data generative process (gMCR), and introduces an Energy-Based solver, EB-gMCR, that automatically discovers the smallest component set and their concentrations for reconstructing the mixed signals faithfully. On synthetic benchmarks with up to 256 components, EB-gMCR attains high reconstruction fidelity and recovers the component count within 5% at 20dB noise and near-exact at 30dB. On two public spectral datasets, it identifies the correct component count and improves component separation over MF-based MCR approaches (NMF variants, ICA, MCR-ALS). EB-gMCR is a general solver for fixed-pattern signal unmixing (components remain invariant across mixtures). Domain priors (non-negativity, nonlinear mixing) enter as plug-in modules, enabling adaptation to new instruments or domains without altering the core selection learning step. The source code is available at https://github.com/b05611038/ebgmcr_solver.","short_abstract":"Signal unmixing analysis decomposes data into basic patterns and is widely applied in chemical and biological research. Multivariate curve resolution (MCR), a branch of signal unmixing, separates mixed signals into components (base patterns) and their concentrations (intensity), playing a key role in understanding comp...","url_abs":"https://arxiv.org/abs/2507.23600","url_pdf":"https://arxiv.org/pdf/2507.23600v4","authors":"[\"Yu-Tang Chang\",\"Shih-Fang Chen\"]","published":"2025-07-31T14:40:33Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CE\"]","methods":"[]","has_code":false,"code_links":[{"ID":611538,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2888410,"paper_url":"https://arxiv.org/abs/2507.23600","paper_title":"EB-gMCR: Energy-Based Generative Modeling for Signal Unmixing and Multivariate Curve Resolution","repo_url":"https://github.com/b05611038/ebgmcr_solver","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}