Abstract Sparse convex clustering is to group observations and conduct variable selection simultaneously in the framework of clustering. Although a weighted $$L_1$$ L 1 norm usually employed for regularization term sparse clustering, its use increases dependence on data...

In compressed sensing and statistical society, dozens of algorithms have been developed to solve `1 penalized least square regression, but constrained sparse quadratic optimization (SQO) is still an open problem. In this paper, we propose backward-forward least angle shrinkage (BF-LAS), which provides a scheme to solve general SQO including sparse eigenvalue minimization. BF-LAS starts from the...

We propose a unified modeling and algorithmic framework for audio restoration problem. It encompasses analysis sparse priors as well as more classical synthesis sparse priors, and regular sparsity as well as various forms of structured sparsity embodied by shrinkage operators (such as social shrinkage). The versatility of the framework is illustrated on two restoration scenarios: denoising, and...

We propose an accelerated path-following iterative shrinkage thresholding algorithm (APISTA) for solving high dimensional sparse nonconvex learning problems. The main difference between APISTA and the path-following iterative shrinkage thresholding algorithm (PISTA) is that APISTA exploits an additional coordinate descent subroutine to boost the computational performance. Such a modification, t...

In this paper, we propose to integrate sparse 3D depth information into pedestrian detection task, in order to achieve a fast boost in performance. Our proposed method uses a probabilistic way to integrate image-feature-based detection and sparse depth estimation together. The depth information is used as a cue, and provides additional discriminative ability for the detection. There are two con...

The reconstruction of a high resolution (HR) image from its low resolution (LR) counterpart is a challenging problem. The recently developed sparse representation (SR) techniques provide new solutions to this inverse problem by introducing the l1-norm sparsity prior into the super-resolution reconstruction process. In this paper, we present a new SR based image super-resolution by optimizing th...

We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a β-mixing time series, the model can be fitted by first approximating each unknown function with a linear combination of a set of B-spline bases, and then solving a group-lasso-t...

We present compiler technology for generating sparse matrix code from (i) dense matrix code and (ii) a description of the indexing structure of the sparse matrices. This technology embeds statement instances into a Cartesian product of statement iteration and data spaces, and produces efficient sparse code by identifying common enumerations for multiple references to sparse matrices. This appro...

The LDL software package is a set of short, concise routines for factorizing symmetric positive-definite sparse matrices, with some applicability to symmetric indefinite matrices. Its primary purpose is to illustrate much of the basic theory of sparse matrix algorithms in as concise a code as possible, including an elegant method of sparse symmetric factorization that computes the factorization...

We present compiler technology for generating sparse matrix code from (i) dense matrix code and (ii) a description of the indexing structure of the sparse matrices. This technology embeds statement instances into a Cartesian product of statement iteration and data spaces, and produces efficient sparse code by identifying common enumerations for multiple references to sparse matrices. This appro...