Related papers: Sparse PCA via $l_{2,p}$-Norm Regularization for U…

In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…

It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications…

For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done…

Spectral unmixing (SU) is a technique to characterize mixed pixels in hyperspectral images measured by remote sensors. Most of the spectral unmixing algorithms are developed using the linear mixing models. To estimate endmembers and…

The problem of joint feature selection across a group of related tasks has applications in many areas including biomedical informatics and computer vision. We consider the l2,1-norm regularized regression model for joint feature selection…

Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…

Accurate land cover segmentation of spectral images is challenging and has drawn widespread attention in remote sensing due to its inherent complexity. Although significant efforts have been made for developing a variety of methods, most of…

Sparse regression methods have been proven effective in a wide range of signal processing problems such as image compression, speech coding, channel equalization, linear regression and classification. In this paper a new convex method of…

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit…

A wide range of systems exhibit high dimensional incomplete data. Accurate estimation of the missing data is often desired, and is crucial for many downstream analyses. Many state-of-the-art recovery methods involve supervised learning…

An efficient spatial regularization method using superpixel segmentation and graph Laplacian regularization is proposed for sparse hyperspectral unmixing method. Since it is likely to find spectrally similar pixels in a homogeneous region,…

Identifying co-varying causal elements in very high dimensional feature space with internal structures, e.g., a space with as many as millions of linearly ordered features, as one typically encounters in problems such as whole genome…

Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…

We present a novel feature selection technique, Sparse Linear Centroid-Encoder (SLCE). The algorithm uses a linear transformation to reconstruct a point as its class centroid and, at the same time, uses the $\ell_1$-norm penalty to filter…

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

Feature selection is a prevalent data preprocessing paradigm for various learning tasks. Due to the expensive cost of acquiring supervision information, unsupervised feature selection sparks great interests recently. However, existing…

For very large datasets, random projections (RP) have become the tool of choice for dimensionality reduction. This is due to the computational complexity of principal component analysis. However, the recent development of randomized…

In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…