This paper combines linear sparse coding and nonnegative matrix factorization into sparse non-negative matrix factorization. In contrast to non-negative matrix factorization, the new model can leam much sparser representation via imposing sparseness constraints explicitly; in contrast to a close model non-negative sparse coding, the new model can learn parts-based representation via fully multi...

Estimation of a high dimensional precision matrix is critical problem to many areas statistics including Gaussian graphical models and inference on data. Working under the structural assumption sparsity, we propose novel methodology for estimating such matrices while controlling false positive rate, percentage entries incorrectly chosen be non-zero. We specifically focus rates tending towards z...

We propose an image classification framework by leveraging the non-negative sparse coding, correlation constrained low rank and sparse matrix decomposition technique (CCLR-ScSPM). First, we propose a new non-negative sparse coding along with max pooling and spatial pyramid matching method (ScSPM) to extract local feature’s information in order to represent images, where non-negative sparse codi...

We consider designing a sparse sensing matrix which contains few non-zero entries per row for compressive sensing (CS) systems. By unifying the previous approaches for optimizing sensing matrices based on minimizing the mutual coherence, we propose a general framework for designing a sparse sensing matrix that minimizes the mutual coherence of the equivalent dictionary and is robust to sparse r...

Sparse representations are widely used tools in image super-resolution (SR) tasks. In the sparsity-based SR methods, linear sparse representations are often used for image description. However, the non-linear data distributions in images might not be well represented by linear sparse models. Moreover, many sparsity-based SR methods require the image patch self-similarity assumption; however, th...

Several estimation problems in vision involve the minimization of cumulative geometric error using non-linear least-squares fitting. Typically, this error is characterized by the lack of interdependence among certain subgroups of the parameters to be estimated, which leads to minimization problems possessing a sparse structure. Taking advantage of this sparseness during minimization is known to...

Sparse signals (i.e., vectors with a small number of non-zero entries) build the foundation of most kernel (or nullspace) results, uncertainty relations, and recovery guarantees in the sparse signal-processing and compressive-sensing literature. In this paper, we introduce a novel signal-density measure that extends the common notion of sparsity to non-sparse signals whose entries’ magnitudes d...