Ink source prediction and assessment based on direct analysis in real-time mass spectrometry via the likelihood ratio

Ink classification is the ability to distinguish unknown inks into different groups, and ink source prediction is the ability to predict the manufacturer or model of an unknown ink. These are regular tasks in forensic analysis. The latter is more challenging than the former, as ink source prediction has expanded beyond ink classification. In this work, we reported on an approach to predict the source of black inks based on direct analysis in real time mass spectrometry and assess the strength of black ink source prediction conclusion via the likelihood ratio, using a dataset that included 39 inks from three manufacturers with a high market share. Most of these inks contain similar or identical chemical components. Dimensionality reduction based on the principal component analysis and unified manifold approximation and projection algorithms was implemented, and subsequently, the distribution plots illustrated the variations between and within the inks. Unified manifold approximation and projection showed significant priority in avoiding overcrowding of cluster representation versus principal component analysis, with results as high as 99.83% for the prediction of the ink source using 41,432 spectra data (70% data for training and 30% data for testing) after dimensionality reduction. A likelihood ratio was used to evaluate the strength of ink evidence, and the pool-adjacent-violators algorithm and logistic algorithms were used to calibrate the likelihood ratio. The results showed that the pool-adjacent-violators algorithm and logistic algorithms both had an excellent equal error rate of 0.004 but slightly different results in the rates of misleading evidence in favor of the prosecutor's hypothesis, rates of misleading evidence in favor of the defense's hypothesis, log likelihood ratio costs after calibration ( $C_{\mathrm{llr}}^{\mathrm{cal}}$), and minimum log likelihood ratio costs ( $C_{\mathrm{llr}}^{\min }$). A blind test validated the robustness of the methods.