Multilayer Perceptron for Sparse Functional Data

In this paper, we propose a novel algorithm for generalizing Multilayer Perceptron (MLP) to handle sparse functional data, wherein for a given subject there are multiple observations available over time and these observations are sparsely and irregularly distributed within the considered time range. The algorithm uses pooled observations across all the subjects to estimate a set of basis functions for the underlying correlation between time steps and then use these basis functions to build a sparse functional neuron that extracts features for each subject. We justify the validity of our algorithm through theoretical arguments. We also demonstrate the use of the proposed algorithm in solving three data challenges: the classification of synthetic curves, the prediction of patient's long-term survival, and the estimation of the remaining time to critical failures for turbofan engines. To show the superiority of our algorithm under sparse functional data scenarios, we compare the performance of our model with two alternative common practices, and demonstrate that our method outperforms the baseline methods in all numerical studies.