Sparse multivariate functional principal component analysis

Abstract

We introduce a sparse multivariate functional principal component analysis method by incorporating ideas from the group sparse maximum variance method to multivariate functional data. Our method can avoid the "curse of dimensionality" from a high-dimensional dataset and enjoy interpretability at the same time. In particular, our unsupervised method can capture important latent factors to explain variability of the dataset, which can induce a clear distinction between important variables in the principal components and unnecessary features based on the sparseness structure. Furthermore, our method can be applied to functional data from a multidimensional domain that hinges on different intervals. In the numerical experiment, we show that our method works well in both low- and high-dimensional multivariate functional data regardless of the number and the type of basis. We further apply our method to stock market data and electroencephalography data in an alcoholism study to demonstrate the theoretical result.