Latent Sparse Modeling of Longitudinal Multi-Dimensional Data

We propose a tensor-based approach to analyze multi-dimensional data describing sample subjects. It simultaneously discovers patterns in features and reveals past temporal points that have impact on current outcomes. The model coefficient, a k-mode tensor, is decomposed into a summation of k tensors of the same dimension. To accomplish feature selection, we introduce the tensor '"atent L F,1 norm" as a grouped penalty in our formulation. Furthermore, the proposed model takes into account within-subject correlations by developing a tensor-based quadratic inference function. We provide an asymptotic analysis of our model when the sample size approaches to infinity. To solve the corresponding optimization problem, we develop a linearized block coordinate descent algorithm and prove its convergence for a fixed sample size. Computational results on synthetic datasets and real-file fMRI and EEG problems demonstrate the superior performance of the proposed approach over existing techniques.