Co-sparse Non-negative Matrix Factorization

Non-negative matrix factorization, which decomposes the input non-negative matrix into product of two non-negative matrices, has been widely used in the neuroimaging field due to its flexible interpretability with non-negativity property. Nowadays, especially in the neuroimaging field, it is common to have at least thousands of voxels while the sample size is only hundreds. The non-negative matrix factorization encounters both computational and theoretical challenge with such high-dimensional data, i.e., there is no guarantee for a sparse and part-based representation of data. To this end, we introduce a co-sparse non-negative matrix factorization method to high-dimensional data by simultaneously imposing sparsity in both two decomposed matrices. Instead of adding some sparsity induced penalty such as l1 norm, the proposed method directly controls the number of non-zero elements, which can avoid the bias issues and thus yield more accurate results. We developed an alternative primal-dual active set algorithm to derive the co-sparse estimator in a computationally efficient way. The simulation studies showed that our method achieved better performance than the state-of-art methods in detecting the basis matrix and recovering signals, especially under the high-dimensional scenario. In empirical experiments with two neuroimaging data, the proposed method successfully detected difference between Alzheimer's patients and normal person in several brain regions, which suggests that our method may be a valuable toolbox for neuroimaging studies.

Adaptive event-triggered distributed recursive filtering with stochastic parameters and faults

This paper investigates the distributed recursive filtering issue of a class of stochastic parameter systems with randomly occurring faults. An event-triggered scheme with an adaptive threshold is designed to better reduce the communication load by considering dynamic changes of measurement sequences. In the framework of Kalman filtering, a distributed filter is constructed to simultaneously estimate both system states and faults. Then, the upper bound of filtering error covariance is derived with the help of stochastic analysis combined with basis matrix inequalities. The obtained condition with a recursive feature is dependent on the statistical characteristic of stochastic parameter matrices as well as the time-varying threshold. Furthermore, the desired filter gain is derived by minimizing the trace of the obtained upper bound. Finally, two simulation examples are conducted to demonstrate the effectiveness and feasibility of the proposed filtering method.

Spectral-Smoothness and Non-Local Self-Similarity Regularized Subspace Low-Rank Learning Method for Hyperspectral Mixed Denoising

During the imaging process, hyperspectral image (HSI) is inevitably affected by various noises, such as Gaussian noise, impulse noise, stripes or deadlines. As one of the pre-processing steps, the removal of mixed noise for HSI has a vital impact on subsequent applications, and it is also one of the most challenging tasks. In this paper, a novel spectral-smoothness and non-local self-similarity regularized subspace low-rank learning (termed SNSSLrL) method was proposed for the mixed noise removal of HSI. First, under the subspace decomposition framework, the original HSI is decomposed into the linear representation of two low-dimensional matrices, namely the subspace basis matrix and the coefficient matrix. To further exploit the essential characteristics of HSI, on the one hand, the basis matrix is modeled as spectral smoothing, which constrains each column vector of the basis matrix to be a locally continuous spectrum, so that the subspace formed by its column vectors has continuous properties. On the other hand, the coefficient matrix is divided into several non-local block matrices according to the pixel coordinates of the original HSI data, and block-matching and 4D filtering (BM4D) is employed to reconstruct these self-similar non-local block matrices. Finally, the formulated model with all convex items is solved efficiently by the alternating direction method of multipliers (ADMM). Extensive experiments on two simulated datasets and one real dataset verify that the proposed SNSSLrL method has greater advantages than the latest state-of-the-art methods.

Two-Dimensional ISAR Fusion Imaging of Block Structure Targets

The range resolution and azimuth resolution are restricted by the limited transmitting bandwidth and observation angle in a monostatic radar system. To improve the two-dimensional resolution of inverse synthetic aperture radar (ISAR) imaging, a fast linearized Bregman iteration for unconstrained block sparsity (FLBIUB) algorithm is proposed to achieve multiradar ISAR fusion imaging of block structure targets. First, the ISAR imaging echo data of block structure targets is established based on the geometrical theory of the diffraction model. The multiradar ISAR fusion imaging is transformed into a signal sparse representation problem by vectorization operation. Then, considering the block sparsity of the echo data of block structure targets, the FLBIUB algorithm is utilized to achieve the block sparse signal reconstruction and obtain the fusion image. The algorithm further accelerates the iterative convergence speed and improves the imaging efficiency by combining the weighted back-adding residual and condition number optimization of the basis matrix. Finally, simulation experiments show that the proposed method can effectively achieve block sparse signal reconstruction and two-dimensional multiradar ISAR fusion imaging of block structure targets.

Transition Matrices Between Young's Natural and Seminormal Representations

We derive a formula for the entries in the change-of-basis matrix between Young's seminormal and natural representations of the symmetric group. These entries are determined as sums over weighted paths in the weak Bruhat graph on standard tableaux, and we show that they can be computed recursively as the weighted sum of at most two previously-computed entries in the matrix. We generalize our results to work for affine Hecke algebras, Ariki-Koike algebras, Iwahori-Hecke algebras, and complex reflection groups given by the wreath product of a finite cyclic group with the symmetric group.

Adaptive-Weighted Multiview Deep Basis Matrix Factorization for Multimedia Data Analysis

Feature representation learning is a key issue in artificial intelligence research. Multiview multimedia data can provide rich information, which makes feature representation become one of the current research hotspots in data analysis. Recently, a large number of multiview data feature representation methods have been proposed, among which matrix factorization shows the excellent performance. Therefore, we propose an adaptive-weighted multiview deep basis matrix factorization (AMDBMF) method that integrates matrix factorization, deep learning, and view fusion together. Specifically, we first perform deep basis matrix factorization on data of each view. Then, all views are integrated to complete the procedure of multiview feature learning. Finally, we propose an adaptive weighting strategy to fuse the low-dimensional features of each view so that a unified feature representation can be obtained for multiview multimedia data. We also design an iterative update algorithm to optimize the objective function and justify the convergence of the optimization algorithm through numerical experiments. We conducted clustering experiments on five multiview multimedia datasets and compare the proposed method with several excellent current methods. The experimental results demonstrate that the clustering performance of the proposed method is better than those of the other comparison methods.

SPAER: Sparse Deep Convolutional Autoencoder Model to Extract Low Dimensional Imaging Biomarkers for Early Detection of Breast Cancer Using Dynamic Thermography

Early diagnosis of breast cancer unequivocally improves the survival rate of patients and is crucial for disease treatment. With the current developments in infrared imaging, breast screening using dynamic thermography seems to be a great complementary method for clinical breast examination (CBE) prior to mammography. In this study, we propose a sparse deep convolutional autoencoder model named SPAER to extract low-dimensional deep thermomics to aid breast cancer diagnosis. The model receives multichannel, low-rank, approximated thermal bases as input images. SPAER provides a solution for high-dimensional deep learning features and selects the predominant basis matrix using matrix factorization techniques. The model has been evaluated using five state-of-the-art matrix factorization methods and 208 thermal breast cancer screening cases. The best accuracy was for non-negative matrix factorization (NMF)-SPAER + Clinical and NMF-SPAER for maintaining thermal heterogeneity, leading to finding symptomatic cases with accuracies of 78.2% (74.3–82.5%) and 77.7% (70.9–82.1%), respectively. SPAER showed significant robustness when tested for additive Gaussian noise cases (3–20% noise), evaluated by the signal-to-noise ratio (SNR). The results suggest high performance of SPAER for preserveing thermal heterogeneity, and it can be used as a noninvasive in vivo tool aiding CBE in the early detection of breast cancer.

Physics Based Compressive Sensing to Enable Digital Twins of Additive Manufacturing Processes

Sensors play an important role in monitoring manufacturing processes and update their digital twins. However, the data transmission bandwidth and sensor placement limitations in the physical systems may not allow us to collect the amount or the type of data that we wish. Recently, a physics based compressive sensing (PBCS) approach was proposed to monitor manufacturing processes and obtain high-fidelity information with the reduced number of sensors by incorporating physical models of processes in compressed sensing. It can recover and reconstruct complete three-dimensional temperature distributions based on some limited measurements. In this paper, a constrained orthogonal matching pursuit algorithm is developed for PBCS, where coherence exists between the measurement matrix and basis matrix. The efficiency of recovery is improved by introducing a boundary-domain reduction approach, which reduces the size of PBCS model matrices during the inverse operations. The improved PBCS method is demonstrated with the measurement of temperature distributions in the cooling and real-time printing processes of fused filament fabrication.

Multi-lead ECG Compression Based on Compressive Sensing

Compressed Sensing (CS) has been considered a very effective means of reducing energy consumption at the energy-constrained wireless body sensor networks for monitoring the multi-lead Electrocardiogram (MECG) signals. This paper develops the compressed sensing theory for sparse modeling and effective multi-channel ECG compression. A basis matrix with Gaussian kernels is proposed to obtain the sparse representation of each channel, which showed the closest similarity to the ECG signals. Thereafter, the greedy orthogonal matching pursuit (OMP) method is used to obtain the sparse representation of the signals. After obtaining the sparse representation of each ECG signal, the compressed sensing theory could be used to compress the signals as much as possible. Following the compression, the compressed signal is reconstructed utilizing the greedy orthogonal matching pursuit (OMP) optimization technique to demonstrate the accuracy and reliability of the algorithm. Moreover, as the wavelet basis matrix is another sparsifying basis to sparse representations of ECG signals, the compressed sensing is applied to the ECG signals using the wavelet basis matrix. The simulation results indicated that the proposed algorithm with Gaussian basis matrix reduces the reconstruction error and increases the compression ratio.