EB-gMCR: Energy-Based Generative Modeling for Signal Unmixing and Multivariate Curve Resolution

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.