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Sparse linear regression is closely related to sparse recovery and compressed sensing problems. The goal is to stably obtain and reconstruct the original high dimensional K -sparse signal X ECN from the noiseless finite-dimensional linear measurement Y E CM (K <; M <; N). In this paper, we propose a new design framework to effectively solve the parameter estimation problem in sparse linear regress...Show More
This paper demonstrates the feasibility of decoding neuronal population signals using a sparse linear regression model with an elastic net penalty. In offline analysis of real electrocorticographic (ECoG) neural data the elastic net achieved a timepoint decoding accuracy of 95% for classifying hand grasps vs. rest, and 82% for moving a cursor in 1-D space towards a target. These results were super...Show More
The linear model, in which a set of observations is assumed to be given by a linear combination of columns of a matrix (often termed a dictionary), has long been the mainstay of the statistics and signal processing literature. One particular challenge for inference under linear models is understanding the conditions on the dictionary under which reliable inference is possible. This challenge has a...Show More
We introduce a sparse multivariate regression algorithm which simultaneously performs dimensionality reduction and parameter estimation. We decompose the coefficient matrix into two sparse matrices: a long matrix mapping the predictors to a set of factors and a wide matrix estimating the responses from the factors. We impose an elastic net penalty on the former and an ℓ1 penalty on the latter. Our...Show More
In this paper, we develop algorithms for robust linear regression by leveraging the connection between the problems of robust regression and sparse signal recovery. We explicitly model the measurement noise as a combination of two terms; the first term accounts for regular measurement noise modeled as zero mean Gaussian noise, and the second term captures the impact of outliers. The fact that the ...Show More
In this paper the use of sparse linear regression algorithms in echo state networks (ESN) is presented for reducing the number of readouts and improving the robustness and generalization properties of ESNs. Three data sets with overall 80 tests are used to validate the use of sparse linear regression algorithms for echo state networks. It is shown that it is possible to increase accuracy on the te...Show More
A Bayesian approximation to finding the minimum ℓ0 norm solution for an underdetermined linear system is proposed that is based on the beta process prior. The beta process linear regression (BP-LR) model finds sparse solutions to the underdetermined model y = Φx + ɛ, by modeling the vector x as an element-wise product of a non-sparse weight vector, w, and a sparse binary vector, z, that is drawn f...Show More
In this paper, we propose a novel model selection method named multi-beta-test (MBT) for the sparse high-dimensional linear regression model. The estimation of the correct subset in the linear regression problem is formulated as a series of hypothesis tests where the test statistic is based on the relative least-squares cost of successive parameter models. The performance of MBT is compared to exi...Show More
Video-based crowd counting (VCC) is a high demanded technique in many video applications. Existing supervised VCC methods essentially learn an intrinsic mapping function between image features and corresponding crowd counts. However, imbalanced training dataset degrades the performance of VCC significantly. Encouraged by recent success in cost-sensitive learning for image classification with imbal...Show More
In this letter, we propose an approach for sparse linear regression in unions of bases inspired by Bayesian variable selection. Conditionally upon an indicator variable that is 0 or 1, one expansion coefficient of the signal corresponding to one atom of the dictionary is either set to zero or given a Student t prior. A Gibbs sampler (a standard Markov chain Monte Carlo technique) is used to sample...Show More
This paper addresses the problem of two-way sparse reduced-rank regression (TSRRR), which aims to estimate a coefficient matrix that is both low-rank and two-way sparse (sparse in both rows and columns) within a multiple response linear regression model. We formulate TSRRR as a nonconvex optimization problem and propose an efficient, scalable iterative algorithm called Scaled Gradient Descent with...Show More
Sparse matrix regression (SMR) is a two-dimensional supervised feature selection method that can directly select the features on matrix data. It uses several couples of left and right regression vectors for each classifier and integrates them in formulating the regression function. However, SMR does not consider the local geometry of image samples, and it assumes that the training samples should e...Show More
Spectral unmixing aims at finding the spectrally pure constituent materials (also called endmembers) and their respective fractional abundances in each pixel of a hyperspectral image scene. In recent years, sparse unmixing has been widely used as a reliable spectral unmixing methodology. In this approach, the observed spectral vectors are expressed as linear combinations of spectral signatures ass...Show More
In this paper, a novel multi-view facial expression recognition method is presented. Different from most of the facial expression methods that use one view of facial feature vectors in the expression recognition, we synthesize multi-view facial feature vectors and combine them to this goal. In the facial feature extraction, we use the grids with multi-scale sizes to partition each facial image int...Show More
Band selection is an important step towards effective and efficient object classification in hyperspectral imagery. In this paper, we propose a semi-supervised learning method for band selection based on a sparse linear regression model. This model uses a least absolute shrinkage and selection operator to compute the regression coefficients from both labeled and unlabeled samples. These coefficien...Show More
Localizing facial landmarks is a fundamental step in facial image analysis. However, the problem continues to be challenging due to the large variability in expression, illumination, pose, and the existence of occlusions in real-world face images. In this paper, we present a dual sparse constrained cascade regression model for robust face alignment. Instead of using the least-squares method during...Show More
Mixed pixels of hyperspectral image own very high sparsity if they are linearly represented by endmembers of aprior spectral library. Hence the sparse regression framework has been introduced to solve the linear spectral unmixing problem and produced sparse fractional abundances. But because of the high coherence of spectral library and noise disturbance, the solution could not be as sparse as rea...Show More
Locality preserving projections (LPP) has been widely studied and extended in recent years, because of its promising performance in feature extraction. In this paper, we propose a modified version of the LPP by constructing a novel regression model. To improve the performance of the model, we impose a low-rank constraint on the regression matrix to discover the latent relations between different n...Show More
Extended Bayesian information criterion (EBIC) and extended Fisher information criterion (EFIC) are two popular criteria for model selection in sparse high-dimensional linear regression models. However, EBIC is inconsistent in scenarios when the signal-to-noise-ratio (SNR) is high but the sample size is small, and EFIC is not invariant to data scaling, which affects its performance under different...Show More
Electroencephalogram (EEG) is physiological signal generated in the brain. Electroencephalography is a method to record the electrical activity of the brain in order to detect the abnormalities of the brain. However, EEG also detects the signals which are not originated from the brain called artifacts. This paper deals with the analysis and extraction of EEG signals in sparse representation using ...Show More
In this paper, a method called wavelet-based sparse reduced-rank regression (WSRRR) is proposed for hyperspectral image restoration. The method is based on minimizing a sparse regularization problem subject to an orthogonality constraint. A cyclic descent-type algorithm is derived for solving the minimization problem. For selecting the tuning parameters, we propose a method based on Stein's unbias...Show More
A novel superpixel-based discriminative sparse model (SBDSM) for spectral-spatial classification of hyperspectral images (HSIs) is proposed. Here, a superpixel in a HSI is considered as a small spatial region whose size and shape can be adaptively adjusted for different spatial structures. In the proposed approach, the SBDSM first clusters the HSI into many superpixels using an efficient oversegme...Show More
Statistical solutions find wide spread use in food and medicine quality control. We investigate the effect of different regression and sparse regression methods for a viscosity estimation problem using the spectro-temporal features from new Sub-Surface Laser Scattering (SLS) vision system. From this investigation, we propose the optimal solution for regression estimation in case of noisy and incon...Show More
Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise Regression. We present novel guarantees for the algorithm, propose an efficient, numerically stable implementation, and put forth Stepwise Regression with Replacemen...Show More
In this paper, a new classifier, called multiple linear regression coefficients (MLRC), is proposed for image recognition. Linear regression classification (LRC) uses the linear combination of the class-model for classification. Sparse representation based classification (SRC) utilizes the globalmodel for classification. Based on the global-concept of SRC, mean representation classification (MRC) ...Show More