Spectral-Correlation and Random Matrix Theory- Analysis of Raman Spectra for Detection of Milk Adulterants

Detection of adulterants in milk remains a critical challenge for food safety and quality assurance. In this work, spectral-correlation diagnostics and random matrix theory (RMT) are demonstrated as sensitive mathematical tools for the analysis of Raman spectra of pure milk and milk adulterated with hydrogen peroxide H ₂ O ₂ , urea CH ₄ N ₂ O, and formalin CH ₂ O. A total of 124 Raman spectra were acquired across 31 pure and 93 adulterated samples, , and 700 × 700 spectral correlation matrices were computed separately for pure and adulterated groups. Eigenvalue decomposition and eigenvector analysis were performed on each correlation matrix, and unfolded eigenvalue-spacing distributions were compared against the Wigner Surmise to quantify spectral randomness and eigenvalue fluctuations. Pure milk exhibited broad, strongly correlated spectral domains consistent with its biochemical uniformity. Among the adulterants, urea produced the strongest localized deviation near its characteristic Raman signature at 1006 cm ⁻¹ , with structured eigenvector distortions, while H ₂ O ₂ introduced a narrow correlation break at 878 cm ⁻¹ . Formalin induced a global weakening of spectral correlations and showed the closest agreement with the Wigner distribution, indicating the highest degree of spectral randomization among the three adulterants. Difference-correlation eigenvectors sharply isolated additive-specific Raman shifts, while high-rank eigenvalues identified chemically dominant sources of variance. To quantitatively corroborate these trends, the Brody parameter was fitted to each class’s eigenvalue-spacing distribution, yielding a systematic increase from pure milk (β = 0.749) to formalin-adulterated milk (β = 0.970), with urea (β = 0.801) and H ₂ O ₂ (β = 0.841) occupying intermediate positions — providing a single, continuous, statistically grounded measure of adulterant-induced spectral randomization. These results establish RMT-based spectral correlation analysis, quantitatively grounded by the Brody parameter, as a robust, adulterant-specific diagnostic framework, offering a pathway toward real-time, multi-adulterant food authentication systems.