The Application of TOPSIS in the Selection of Statistical Prediction Model: A Forensic Ink Analysis Case Study

Forensic ink analysis is aiming to determine source of an unknown ink entry found on a questioned document. A forgery indicator is established if the source of a questioned ink entry is different from the other ink entries on the same document. A statistical predictive model built from a chemical data of pen ink is useful in accomplishing the goal. Multiple statistical prediction model could be constructed from a chemical data after it was preprocessed via multiple data preprocessing techniques. Commonly, hypothesis test is employed to choose the best prediction model. However, when the number of models and model performance metric are overwhelming, this can be a laborious task. This work aims to explore the feasibility of Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) for selecting the best predictive model. A total of 40 models have been constructed using an attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectral data of blue gel pen inks via Partial Least Squares-Discriminant Analysis (PLS-DA) technique. The ATR- FTIR spectral data was preprocessed using nine different data preprocessing techniques by considering the global and three different sub-spectral regions. The results showed that TOPSIS produced similar ranking model performances to that derived via conventional approach, i.e. univariate hypothesis test. The advantages of TOPSIS method in this context are no statistical assumptions compliance, e.g. normality; and numerical score presenting together with a rank allows inference of relative difference between the models.