So you think you can PLS-DA?

Partial Least-Squares Discriminant Analysis (PLS-DA) is a popular machine learning tool that is gaining increasing attention as a useful feature selector and classifier. In an effort to understand its strengths and weaknesses, we performed a series of experiments with synthetic data and compared its performance to its close relative from which it was initially invented, namely Principal Component Analysis (PCA). We demonstrate that even though PCA ignores the information regarding the class labels of the samples, this unsupervised tool can be remarkably effective as a feature selector. In some cases, it outperforms PLS-DA, which is made aware of the class labels in its input.Our experiments range from looking at the signal-to-noise ratio in the feature selection task, to considering many practical distributions and models encountered when analyzing bioinformatics and clinical data. Other methods were also evaluated.Our work sheds light on the kind of relationships and data models with which PLS-DA can be effective both as a feature selector as well as a classifier. In particular, we claim that when classes are determined by linear or non-linear relationships, PLS-DA provides almost no insight into the data. But it is effective when the classes have a clustered distribution on the signal features, even when these features are hidden among a large number of noise. PLS-DA retains a strong performance even when the classes are contained in n-orthotopes (i.e., rectangular boxes in the subspace of the signal features).Finally, we analyzed an interesting data set from 396 vaginal microbiome samples where the ground truth for the feature selection was available. Again, the results highlighted the strengths and weaknesses of PLS-DA in comparison with PCA.