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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.