Interpretable Dimensionality Reduction for Classification with Functional Data

Classification problems involving a categorical class label Y and a functional predictor X(t) are becoming increasingly common. Since X(t) is essentially infinite dimensional some form of dimensionality reduction is essential in these problems. Conventional data reduction techniques for functional data can be categorized into functional principal component analysis and filtering methods. However, they usually suffer from one or both of the following problems. First, they do not take the categorical response into consideration, and second, the resulting reduced data may be difficult to interpret. In this paper, we propose a dimensionality reduction method, “Functional Adaptive Classification” (FAC), specifically designed for functional classification problems. Based on a stochastic search procedure guided by the evaluation of model complexity, FAC makes use of the functional response and produces simple relationships between the reduced data, Z, and X(t). Hence, it can achieve both good classification accuracy and interpretability. Extensive simulation studies and an fMRI time course study show that FAC is extremely competitive in comparison to other potential approaches.