We consider the problem of learning an unknown (overcomplete) basis from data that are generated from unknown and sparse linear combinations. Introducing the Sparse Coding Neural Gas algorithm, we show how to employ a combination of the original Neural Gas algorithm and Oja’s rule in order to learn a simple sparse code that represents each training sample by only one scaled basis vector. We gen...

The Cimmino method is a row projection method in which the original linear system is divided into subsystems. At every iteration, it computes one projection per subsystem and uses these projections to construct an approximation to the solution of the linear system. The usual parallelization strategy in block algorithms is to distribute the different blocks on the available processors. In this p...

This paper studies estimation of covariance matrices with conditional sparse structure. We overcome the challenge estimating dense using a factor structure, large-dimensional by postulating sparsity on random noises, and varying allowing loadings to smoothly change. A kernel-weighted approach combined generalised shrinkage is proposed. Under some technical conditions, we derive uniform consiste...

Compressed sensing has shown to be promising to accelerate magnetic resonance imaging. In this new technology, magnetic resonance images are usually reconstructed by enforcing its sparsity in sparse image reconstruction models, including both synthesis and analysis models. The synthesis model assumes that an image is a sparse combination of atom signals while the analysis model assumes that an ...

Predicting stock exchange rates is receiving increasing attention and is a vital financial problem as it contributes to the development of effective strategies for stock exchange transactions. The forecasting of stock price movement in general is considered to be a thought-provoking and essential task for financial time series' exploration. In this paper, a Least Absolute Shrinkage and Selectio...

This paper proposes a new non-negative sparse coding (NNSC) model. And using this model, the features of natural image are extracted successfully. As a practical application, how to reduce noise added in a natural image is also discussed. Our assumptions are that the image is corrupted by additive and multiplicative white Gaussian noise and uniform distribution random noise. According to our ex...