Predictive modelling of colossal ATR-FTIR spectral data using PLS-DA: empirical differences between PLS1-DA and PLS2-DA algorithms

Abstract

In response to our review paper [L. C. Lee et al., Analyst, 2018, 143, 3526–3539], we present a study that compares empirical differences between PLS1-DA and PLS2-DA algorithms in modelling a colossal ATR-FTIR spectral dataset. Over the past two decades, partial least squares-discriminant analysis (PLS-DA) has gained wide acceptance and huge popularity in the field of applied research, partly due to its dimensionality reduction capability and ability to handle multicollinear and correlated variables. To solve a K-class problem (K > 2) using PLS-DA and high-dimensional data like infrared spectra, one can construct either K one-versus-all PLS1-DA models or only one PLS2-DA model. The aim of this work is to explore empirical differences between the two PLS-DA algorithms in modeling a colossal ATR-FTIR spectral dataset. The practical task is to build a prediction model using the imbalanced, high dimensional, colossal and multi-class ATR-FTIR spectra of blue gel pen inks. Four different sub-datasets were prepared from the principal dataset by considering the raw and asymmetric least squares (AsLS) preprocessed forms: (a) Raw-global region; (b) Raw-local region; (c) AsLS-global region; and (d) AsLS-local region. A series of 50 models which includes the first 50 PLS components incrementally was constructed repeatedly using the four sub-datasets. Each model was evaluated using six different variants of v-fold cross validation, autoprediction and external testing methods. As a result, each PLS-DA algorithm was represented by a number of figures of merit. The differences between PLS1-DA and PLS2-DA algorithms were assessed using hypothesis tests with respect to model accuracy, stability and fitting. On the other hand, confusion matrices of the two PLS-DA algorithms were inspected carefully for assessment of model parsimony. Overall, both the algorithms presented satisfactory model accuracy and stability. Nonetheless, PLS1-DA models showed significantly higher accuracy rates than PLS2-DA models, whereas PLS2-DA models seem to be much more stable compared to PLS1-DA models. Eventually, PLS2-DA also proved to be less prone to overfitting and is more parsimonious than PLS1-DA. In conclusion, the relatively high accuracy of the PLS1-DA algorithm is achieved at the cost of rather low parsimony and stability, and with an increased risk of overfitting.