SparseEB-gMCR: A Generative Solver for Extreme Sparse Components with Application to Contamination Removal in GC-MS

Analytical chemistry instruments provide physically meaningful signals for elucidating analyte composition and play important roles in material, biological, and food analysis. These instruments are valued for strong alignment with physical principles, enabling compound identification through pattern matching with chemical libraries. More reliable instruments generate sufficiently sparse signals for direct interpretation. Generative multivariate curve resolution (gMCR) and its energy-based solver (EB-gMCR) offer powerful tools for decomposing mixed signals suitable for chemical data analysis. However, extreme signal sparsity from instruments such as GC-MS or 1H-NMR can impair EB-gMCR decomposability. To address this, a fixed EB-select module inheriting EB-gMCR's design was introduced for handling extreme sparse components. Combined with minor adjustments to energy optimization, this led to SparseEB-gMCR. In synthetic datasets, SparseEB-gMCR exhibited comparable decomposability and graceful scalability to dense-component EB-gMCR. The sparse variant was applied to real GC-MS chromatograms for unsupervised contamination removal. Analysis showed siloxane-related pollution signals were effectively eliminated, improving compound identification reliability. Results demonstrate that SparseEB-gMCR preserves the decomposability and self-determining component capability of EB-gMCR while extending adaptability to sparse and irregular chemical data. With this sparse extension, the EB-gMCR family becomes applicable to wider ranges of real-world chemical datasets, providing a general mathematical framework for signal unmixing and contamination elimination in analytical chemistry.