Sr isotopes and REEs fingerprints coupled with machine learning for the traceability of cereal vinegars

The geographical origin of vinegar is becoming increasingly important for food authenticity, yet effective traceability tools remain underdeveloped. This study evaluates the potential of strontium isotopes (⁸⁷Sr/⁸⁶Sr) and rare earth elements (REEs) as multi-element geochemical fingerprints to differentiate four representative Chinese cereal vinegars. The ⁸⁷Sr/⁸⁶Sr ratios of vinegar were determined as 0.71064 ± 0.00054, 0.71156 ± 0.00040, 0.71206 ± 0.00065, and 0.70910 ± 0.00014 for Shanxi, Sichuan, Jiangsu, and Fujian, respectively. These signatures largely reflected the bioavailable Sr from local geological backgrounds, with the exception of Fujian vinegar, which showed an isotopic shift associated with some non-local raw materials used in liquid-state brewing. REE contents exhibited strong internal coherence and significant correlations with both Sr content and ⁸⁷Sr/⁸⁶Sr ratios, indicating their shared provenance-related controls. Multivariate chemometric analyses demonstrated the high discriminatory capability of combined elemental and isotopic markers. Principal component analysis (PCA) provided a preliminary separation, whereas linear discriminant analysis (LDA) and random forest (RF) models achieved markedly higher classification accuracy, with LDA attaining 100% recognition accuracy and RF achieving 88.89% on the test set. This study confirms that the integrated application of ⁸⁷Sr/⁸⁶Sr, REEs, and machine learning models offers a reliable and highly discriminative strategy for verifying the geographical origin of vinegars.