We consider the problem of recovering clustered sparse signals with no prior knowledge of the sparsity pattern. Beyond simple sparsity, signals of interest often exhibits an underlying sparsity pattern which, if leveraged, can improve the reconstruction performance. However, the sparsity pattern is usually unknown a priori. Inspired by the idea of k-nearest neighbor (k-NN) algorithm, we propose...

In traditional sparse modeling, it is assumed that a signal/feature/image can be either accurately or approximately represented by a sparse linear combination of atoms from a learned dictionary. Structured sparsity, which is beyond traditional sparse modeling, addresses collaborative structured sparsity to add stability and prior information to the representation. Specifically, in structured sp...

For spline regressions, it is well known that the choice of knots is crucial for the performance of the estimator. As a general learning framework covering the smoothing splines, learning in a Reproducing Kernel Hilbert Space (RKHS) has a similar issue. However, the selection of training data points for kernel functions in the RKHS representation has not been carefully studied in the literature...

Non-negative matrix factorization (NMF) is an appealing technique for many audio applications, such as automatic music transcription, source separation and speech enhancement. Sparsity constraints are commonly used on the NMF model to discover a small number of dominant patterns. Recently, group sparsity has been proposed for NMF based methods, in which basis vectors belonging to a same group a...

One of the major issues in signed networks is to use network structure to predict the missing sign of an edge. In this paper, we introduce a novel probabilistic approach for the sign prediction problem. The main characteristic of the proposed models is their ability to adapt to the sparsity level of an input network. The sparsity of networks is one of the major reasons for the poor performance ...