Unsupervised matrix-factorization-based dimensionality reduction (DR) techniques are popularly used for feature engineering with the goal of improving the generalization performance of predictive models, especially with massive, sparse feature sets. Often DR is employed for the same purpose as supervised regularization and other forms of complexity control: exploiting a bias/variance tradeoff to mitigate overfitting. Contradicting this practice, there is consensus among existing expert guidelines that supervised regularization is a superior way to improve predictive performance. However, these guidelines are not always followed for this sort of data, and it is not unusual to find DR used with no comparison to modeling with the full feature set. Further, the existing literature does not take into account that DR and supervised regularization are often used in conjunction. We experimentally compare binary classification performance using DR features versus the original features under numerous conditions: using a total of 97 binary classification tasks, 6 classifiers, 3 DR techniques, and 4 evaluation metrics. Crucially, we also experiment using varied methodologies to tune and evaluate various key hyperparameters. We find a very clear, but nuanced result. Using state-of-the-art hyperparameter-selection methods, applying DR does not add value beyond supervised regularization, and can often diminish performance. However, if regularization is not done well (e.g., one just uses the default regularization parameter), DR does have relatively better performance—but these approaches result in lower performance overall. These latter results provide an explanation for why practitioners may be continuing to use DR without undertaking the necessary comparison to using the original features. However, this practice seems generally wrongheaded in light of the main results, if the goal is to maximize generalization performance.
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