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

TL;DR

SparseEB-gMCR extends the generative MCR framework EB-gMCR to extreme sparsity by introducing a static EB-select gate that masks zero indices in the component set, with energy optimization adapted to stabilize sparse selection. The method preserves automatic component-number determination and decomposability while enabling accurate reconstruction of highly sparse chemical signals, and it enables unsupervised removal of unknown GC-MS contamination by leveraging a factorization of data-generating processes. Synthetic benchmarks show near-perfect reconstruction ( $R^2>0.99$ ) and exact zero enforcement, and real GC-MS data from coffee odors demonstrate removal of siloxane-related pollution and improved MassBank identifications. Overall, SparseEB-gMCR broadens the applicability of gMCR to sparse, irregular chemical data, offering a general mathematical tool for signal unmixing and contamination elimination in analytical chemistry.

Abstract

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.

Figures (4)

• Figure 1: EB-select module (a) Dynamic (refer from Chang2025EBgMCR) version; (b) Static version.
• Figure 2: Synthetic benchmarks. (a–d) SparseEB-gMCR checkpoints: estimated vs. true component number (dashed black line); mean (solid) and ±1 SD (shaded) over 5 replicates; colors denote $R^2$ checkpoint bands. Panels: (a) $4N$, $20$dB; (b) $4N$, $30$dB; (c) $8N$, $20$dB; (d) $8N$, $30$dB (e, g) EB-gMCR vs. baselines: estimated vs. true components at 4N under 20 dB and 30 dB. (f, h) Reconstruction $R^2$ at each method’s EC for the same settings.
• Figure 3: Reconstruction $R^2$ and estimated components (EC) of SparseEB-gMCR on 408 clean GC-MS chromatograms.
• Figure 4: Comparison of the polluted and reconstructed (cleaned) chromatogram of a Brazil coffee powder odor sample. (a) Total ion chromatogram (TIC); (b) Mass spectrum at RT = 15.65 min; (c) Mass spectrum at RT = 18.65 min.