Weighted Group Sparsity-Constrained Tensor Factorization for Hyperspectral Unmixing

Recently, unmixing methods based on nonnegative tensor factorization have played an important role in the decomposition of hyperspectral mixed pixels. According to the spatial prior knowledge, there are many regularizations designed to improve the performance of unmixing algorithms, such as the total variation (TV) regularization. However, these methods mostly ignore the similar characteristics among different spectral bands. To solve this problem, this paper proposes a group sparse regularization that uses the weighted constraint of the L2,1 norm, which can not only explore the similar characteristics of the hyperspectral image in the spectral dimension, but also keep the data smooth characteristics in the spatial dimension. In summary, a non-negative tensor factorization framework based on weighted group sparsity constraint is proposed for hyperspectral images. In addition, an effective alternating direction method of multipliers (ADMM) algorithm is used to solve the algorithm proposed in this paper. Compared with the existing popular methods, experiments conducted on three real datasets fully demonstrate the effectiveness and advancement of the proposed method.

COVID-19 Spread Prediction Using Prophet and Data Fusion Algorithm

Today, technology plays a vital role in the healthcare industry. In the traditional way, physicians' minds were predicting the unknown disease based on their expertise and experience. Use of new technology like predictive analytics is transforming the healthcare industry. Predictive analytics in healthcare uses historical data (demographic information, person's past medical history and behaviors) to make predictions about the future. In this chapter, a predictive model is proposed to predict COVID-19 using prophet algorithm. A novel approach based on longitudinal data fusion approach will maintain temporal data from time to time. Sparse regularization regression uses data source and feature level to predict the spread of virus. The proposed model designed using longitudinal data fusion offers better clinical insights. Predictions will be very beneficial to government and healthcare groups to provoke suitable measures in controlling coronavirus. It is also beneficial to pharmaceutical companies to fabricate pills at a quicker rate.

A Novel Downward-Looking Linear Array SAR Imaging Method Based on Multiple Measurement Vector Model with L 2 , 1 -Norm

Downward-looking linear array synthetic aperture radar (DLLA SAR) is a kind of three-dimensional (3-D) radar imaging system. To obtain the superresolution along the crosstrack direction of DLLA SAR, the sparse regularization models with single measurement vector (SMV) have been widely applied. However, the robustness of the sparse regularization models with SMV is unsatisfactory, especially in the low signal-to-noise rate (SNR) environment. To solve this problem, we proposed a novel imaging method for DLLA SAR based on the multiple measurement vector (MMV) model with L 2 , 1 -norm. At first, we exchange the processing order between the along-track (AT) domain and the crosstrack (CT) domain to keep the same sparse structure of the signal in the crosstrack domain so that we can establish the imaging problem as a sparse regularization model based on the MMV model. Moreover, the mixed L 2 , 1 -norm is introduced into the regularization term of the MMV model. Finally, the modified orthogonal matching pursuit (OMP) algorithm is designed for the MMV model with the L 2 , 1 -norm. The simulations verify that the proposed method has better performance in the lower SNR environment and requires lower computation compared with the conventional methods.

Nonconvex Sparse Regularization for Deep Neural Networks and Its Optimality

Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However, the sparsity constraint requires knowing certain properties of the true model, which are not available in practice. Moreover, computation is difficult due to the discrete nature of the sparsity constraint. In this letter, we propose a novel penalized estimation method for sparse DNNs that resolves the problems existing in the sparsity constraint. We establish an oracle inequality for the excess risk of the proposed sparse-penalized DNN estimator and derive convergence rates for several learning tasks. In particular, we prove that the sparse-penalized estimator can adaptively attain minimax convergence rates for various nonparametric regression problems. For computation, we develop an efficient gradient-based optimization algorithm that guarantees the monotonic reduction of the objective function.

Towards Compact Broad Learning System by Combined Sparse Regularization

Broad Learning System (BLS) has been proven to be one of the most important techniques for classification and regression in machine learning and data mining. BLS directly collects all the features from feature and enhancement nodes as input of the output layer, which neglects vast amounts of redundant information. It usually leads to be inefficient and overfitting. To resolve this issue, we propose sparse regularization-based compact broad learning system (CBLS) framework, which can simultaneously remove redundant nodes and weights. To be more specific, we use group sparse regularization based on [Formula: see text] norm to promote the competition between different nodes and then remove redundant nodes, and a class of nonconvex sparsity regularization to promote the competition between different weights and then remove redundant weights. To optimize the resulting problem of the proposed CBLS, we exploit an efficient alternative optimization algorithm based on proximal gradient method together with computational complexity. Finally, extensive experiments on the classification task are conducted on public benchmark datasets to verify the effectiveness and superiority of the proposed CBLS.