Sparse-smooth regularized singular value decomposition

We consider penalized singular value decomposition (SVD) for a (noisy) data matrix when the left singular vector has a sparse structure and the right singular vector is a discretized function. Such situations typically arise from spatio-temporal data where only some small spatial regions are “activated” as in fMRI data. We use two penalties that impose sparsity and smoothness. However, it is shown, somewhat surprisingly, that the value of only one parameter has to be chosen. This is in stark contrast to the penalized SVD models proposed by Huang et al. (2009) [12] and by Lee et al. (2010) [14]. We carry out some simulation studies and use an artificial fMRI data set and a real data set to illustrate the proposed approach.