The focus of this paper is in Q-Lasso introduced in Alghamdi et al. (2013) which extended the Lasso by Tibshirani (1996). The closed convex subset Q belonging in a Euclidean m-space, for m is an element of IN, is the ...
详细信息
The focus of this paper is in Q-Lasso introduced in Alghamdi et al. (2013) which extended the Lasso by Tibshirani (1996). The closed convex subset Q belonging in a Euclidean m-space, for m is an element of IN, is the set of errors when linear measurements are taken to recover a signal/image via the Lasso. Based on a recent work by Wang (2013), we are interested in two new penalty methods for Q-Lasso relying on two types of difference of convex functions (DC for short) programming where the DC objective functions are the difference of l1 and l sigma q norms and the difference of l(1) and l(r) norms with r>1. By means of a generalized q-term shrinkage operator upon the special structure of l(sigma q) norm, we design a proximal gradient algorithm for handling the DC l(1)-l(sigma q) model. Then, based on the majorization scheme, we develop a majorized penalty algorithm for the DC l(1)-l(r) model. The convergence results of our new algorithms are presented as well. We would like to emphasize that extensive simulation results in the case Q={b} show that these two new algorithms offer improved signal recovery performance and require reduced computational effort relative to state-of-the-art l(1) and l(p) (p is an element of(0,1)) models, see Wang (2013). We also devise two DC algorithms on the spirit of a paper where exact DC representation of the cardinality constraint is investigated and which also used the largest-q norm of l(sigma q) and presented numerical results that show the efficiency of our DC algorithm in comparison with other methods using other penalty terms in the context of quadratic programing, see Jun-ya et al. (2017).
Classic multinomial logit model, commonly used in multiclass regression problem, is restricted to few predictors and does not take into account the relationship among variables. It has limited use for genomic data, wh...
详细信息
Classic multinomial logit model, commonly used in multiclass regression problem, is restricted to few predictors and does not take into account the relationship among variables. It has limited use for genomic data, where the number of genomic features far exceeds the sample size. Genomic features such as gene expressions are usually related by an underlying biological network. Efficient use of the network information is important to improve classification performance as well as the biological interpretability. We proposed a multinomial logit model that is capable of addressing both the high dimensionality of predictors and the underlying network information. Group lasso was used to induce model sparsity, and a network-constraint was imposed to induce the smoothness of the coefficients with respect to the underlying network structure. To deal with the non-smoothness of the objective function in optimization, we developed a proximal gradient algorithm for efficient computation. The proposed model was compared to models with no prior structure information in both simulations and a problem of cancer subtype prediction with real TCGA (the cancer genome atlas) gene expression data. The network-constrained mode outperformed the traditional ones in both cases.
Advancement in imaging technology has made hyperspectral images gathered from remote sensing much more common. The high-dimensional nature of these large scale data coupled with wavelength and spatial dependency neces...
详细信息
Advancement in imaging technology has made hyperspectral images gathered from remote sensing much more common. The high-dimensional nature of these large scale data coupled with wavelength and spatial dependency necessitates high-dimensional and efficient computation methods to address these issues while producing results that are concise and easy to understand. The thesis addresses these issues by examining high-dimensional methods in the context of hyperspectral image classification, unmixing and wavelength correlation estimation. Chapter 2 re-examines the sparse Bayesian learning (SBL) of linear models in a high-dimensional setting with sparse signal. The hard-thresholded version of the SBL estimator, under orthogonal design, achieves non-asymptotic error rate that is comparable to LASSO. We also establish in the chapter that with high-probability the estimator recovers the sparsity structure of the signal. The ability to recover sparsity structures in high dimensional settings is crucial for unmixing with high-dimensional libraries in the next chapter. In Chapter 3, the thesis investigates the application of SBL on the task of linear/bilinear unmixing and classification of hyperspectral images. The proposed model in this chapter uses latent Markov random fields to classify pixels and account for the spatial dependence between pixels. In the proposed model, the pixels belonging to the same group share the same mixture of pure endmembers. The task of unmixing and classification are performed simultaneously, but this method does not address wavelength dependence. Chapter 4 is a natural extension of the previous chapter that contains the framework to account for both spatial and wavelength dependence in the unmixing of hyperspectral images. The classification of the images are performed using approximate spectral clustering while the unmixing task is performed in tandem with sparse wavelength concentration matrix estimation.
For pixel-level image fusion, convolutional sparse representation model usually relies on the ADMM in the Fourier domain, generating many iterations and losing the sense of locality, which may result in fused images w...
详细信息
Low-rank minimization problems arise in numerous important applications such as recommendation systems, machine learning, network analysis, and so on. The problems however typically consist of minimizing a sum of a sm...
详细信息
Low-rank minimization problems arise in numerous important applications such as recommendation systems, machine learning, network analysis, and so on. The problems however typically consist of minimizing a sum of a smooth function and nonconvex nonsmooth composite functions, which solving them remains a big challenge. In this paper, we take inspiration from the Nesterov's acceleration technique to accelerate an iteratively reweighted nuclear norm algorithm for the considered problems ensuring that every limit point is a critical point. Our algorithm iteratively computes the proximal operator of a reweighted nuclear norm which has a closed-form solution by performing the SVD of a smaller matrix instead of the full SVD. This distinguishes our work from recent accelerated proximal gradient algorithms that require an expensive computation of the proximal operator of nonconvex nonsmooth composite functions. We also investigate the convergence rate with the Kurdyka-Lojasiewicz assumption. Numerical experiments are performed to demonstrate the efficiency of our algorithm and its superiority over well-known methods. (C) 2021 Elsevier B.V. All rights reserved.
Multispectral and hyperspectral image fusion (MS/HS fusion) aims to generate a high-resolution hyperspectral (HRHS) image by fusing a high-resolution multispectral (HRMS) and a low-resolution hyperspectral (LRHS) imag...
详细信息
Multispectral and hyperspectral image fusion (MS/HS fusion) aims to generate a high-resolution hyperspectral (HRHS) image by fusing a high-resolution multispectral (HRMS) and a low-resolution hyperspectral (LRHS) images. The deep unfolding-based MS/HS fusion method is a representative deep learning paradigm due to its excellent performance and sufficient interpretability. However, existing deep unfolding-based MS/HS fusion methods only rely on a fixed linear degradation model, which focuses on modeling the relationships between HRHS and HRMS, as well as HRHS and LRHS. In this paper, we break free from this observation model framework and propose a new observation model. Firstly, the proposed observation model is built based on the convolutional sparse coding (CSC) technique, and then a proximal gradient algorithm is designed to solve this model. Secondly, we unfold the iterative algorithm into a deep network, dubbed as MHF-CSCNet, where the proximal operators are learned using convolutional neural networks. Finally, all trainable parameters can be automatically learned end-to-end from the training pairs. Experimental evaluations conducted on various benchmark datasets demonstrate the superiority of our method both quantitatively and qualitatively compared to other state-of-the-art methods.
In the present work, we propose new methods for the problem of third-order tensor completion and tensor robust principal component analysis (TRPCA). The proposed approaches are based on finding a low-rank tensor by so...
详细信息
In the present work, we propose new methods for the problem of third-order tensor completion and tensor robust principal component analysis (TRPCA). The proposed approaches are based on finding a low-rank tensor by solving some optimization problems of tensor nuclear norm under some constraints and by using the discrete cosine transform. For the problem of completion, we add some regularization techniques by using the first order and a second-order total variation to enhance the results. Both the main optimization problems lead to some tensor problems that will be solved by using the Alternative Direction Method of Multipliers (ADMM), and also we use for the problem of TRPCA the proximal gradient algorithm to solve it and we will compare the results given by the two ways. We also present some numerical experiments of the proposed methods.
We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly...
详细信息
We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations' covariance matrix and the so-called graph shift operator (GSO-a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations' empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximalgradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.
暂无评论