Low-rank Decomposition Algorithm Research Articles

Exploration of the influence of early rehabilitation training on circulating endothelial progenitor cell mobilization in patients with acute ischemic stroke and its related mechanism under a lightweight artificial intelligence algorithm.

This work aimed to explore the application of lightweight artificial intelligence algorithms in magnetic resonance imaging (MRI) image processing of patients with acute ischemic stroke (AIS) to clarify the effect and mechanism of early rehabilitation training on the mobilization of circulating endothelial progenitor cells (EPCs) in AIS. A total of 98 AIS patients undergoing MRI examination were selected as the research objects and were randomly divided into a rehabilitation group (early rehabilitation training, 50 cases) and a routine group (conventional treatment, 48 cases) by random number table method and lottery method. In this work, based on the convolutional neural network (CNN) algorithm, a low-rank decomposition algorithm was introduced to optimize it, and a lightweight MRI image computer intelligent segmentation model (LT-RCNN) was established. The LT-RCNN model was used in the MRI image processing of AIS patients, and the role of the model in AIS image segmentation and lesion localization was analyzed. Furthermore, flow cytometry was used to detect the number of peripheral circulating EPCs and CD34+KDR+ cells in the two groups of patients before and after treatment. The serum levels of vascular endothelial growth factor (VEGF), tumor necrosis factor-α (TNF-α), interleukin 10 (IL-10), and stromal cell-derived factor-1α (SDF-1α) content were detected by Enzyme-Linked Immunosorbent Assay (ELISA). In addition, the correlation between each factor and CD34+KDR+ was analyzed by Pearson linear correlation. The diffusion-weighted imaging (DWI) signal of MRI images of AIS patients under the LT-RCNN model was high. The location of the lesion could be accurately detected, and the contour of the lesion could be displayed and segmented, and the segmentation accuracy and sensitivity were significantly better than before optimization. The number of EPCs and CD34+KDR+ cells in the rehabilitation group was increased compared with the control group (p<0.01); the expression levels of VEGF, IL-10, and SDF-1α were higher than those of the control group (p<0.001), and TNF-α content was lower than the control group (p<0.001). The number of CD34+KDR+ cells was positively correlated with VEGF, IL-10, and TNF-α contents (p<0.01). The results showed that the computer-intelligent segmentation model LT-RCNN could accurately locate, and segment AIS lesions and the early rehabilitation training could change the expression level of inflammatory factors and further promote the mobilization of AIS circulation EPCs.

The Compression Techniques Applied on Deep Learning Model

In recent years, the penetration rate of smartphones has gradually completed, artificial intelligence is the cutting-edge technology that can trigger disruptive changes. Deep learning neural networks are also starting to appear on mobile devices. In order to obtain better performance, more complex networks need to be designed, and the corresponding models, computation and storage space are increasing, however, the challenges of resource allocation and energy consumption still exist in mobile. The techniques for compressing deep learning models are quite important, and this paper studies a series of related literatures. This paper reviews deep learning-based deep neural network compression techniques and introduces the key operational points of knowledge extraction and network model on the learning performance of Resolution-Aware Knowledge Distillation. In this paper, a low-rank decomposition algorithm is evaluated based on sparse parameters and rank using the extended BIC for tuning parameter selection. This paper discusses the reduction of redundancy in the fully connected and constitutive layers of the training network model by pruning strategies.Moreover, this paper presents the quantization techniques and a neural network that quantifies weights and activations by applying differentiable nonlinear functions.

A simple and effective spectral-spatial method for mapping large-scale coastal wetlands using China ZY1-02D satellite hyperspectral images

This paper proposes a simple and effective spatial-spectral (SESS) method for mapping large-scale coastal wetlands using China ZY1-02D satellite hyperspectral data. First, the improved sparse subspace clustering algorithm is implemented to select presentative bands, and then the multi-scale low-rank decomposition algorithm is employed to extract multi-scale spatial features. After that, the extracted spatial and selected spectral features are stacked and fused using presented Landmark-neighborhood preserving embedding algorithm. Finally, the low-dimensional fused features are classified with two popular classifiers (i.e., random forest and support vector machine) to map coastal wetlands. Experiments results show that the SESS obtains the highest classification accuracy of 96.92% and 94.84% on Yellow River Delta and Yancheng coastal wetlands of China, respectively, exhibiting good capability in accurately identifying complicated ground objects. This paper is the first attempt to investigate the potentials of China ZY1-02D satellite hyperspectral data, and the SESS can also be applied into other hyperspectral data.

Viscoelastic Wave Simulation with High Temporal Accuracy Using Frequency-Dependent Complex Velocity

In recent decades, the study of seismic attenuation has received more and more concerns because it can stimulate the development of wave propagation simulation and improve the accuracy of structure imaging and reservoir prediction. In this paper, we review the attenuation theory and the development of high temporal accuracy wave simulation. The conventional mathematical models to describe the characteristics of viscoelastic are based on constant-Q model or standard linear solids theory. However, these approaches possess some noticeable shortcomings. Therefore, we introduce a frequency-dependent complex velocity to derive the novel viscoelastic wave equations with decoupled amplitude dissipation and phase dispersion. To obtain high temporal accuracy viscoelastic wave simulation, we adopt the normalized pseudo-Laplacian to compensate for the temporal dispersion errors caused by the second-order finite-difference discretization in the time domain. During the implementation, we incorporate the normalized pseudo-Laplacian into the optimized staggered-grid finite-difference coefficients. Therefore, it can greatly reduce the times of low-rank decomposition and Fourier transform and largely improve the computational efficiency. Based on this strategy, we can implement the high temporal accuracy viscoelastic wavefield extrapolation by comprehensively exploiting the staggered-grid finite-difference scheme, pseudo-spectral method and low-rank decomposition algorithm. Meanwhile, a linear velocity model is employed to evaluate the accuracy of low-rank approximation. Furthermore, we use several numerical examples to carry out the comparison between our scheme and other conventional methods. The numerical results reveal that our proposed scheme can effectively compensate for temporal dispersion errors and help generate high temporal accuracy viscoelastic wave solutions.

A parallel hierarchical blocked adaptive cross approximation algorithm

This article presents a low-rank decomposition algorithm based on subsampling of matrix entries. The proposed algorithm first computes rank-revealing decompositions of submatrices with a blocked adaptive cross approximation (BACA) algorithm, and then applies a hierarchical merge operation via truncated singular value decompositions (H-BACA). The proposed algorithm significantly improves the convergence of the baseline ACA algorithm and achieves reduced computational complexity compared to the traditional decompositions such as rank-revealing QR. Numerical results demonstrate the efficiency, accuracy, and parallel scalability of the proposed algorithm.

Application of adaptive iterative low-rank algorithm based on transform domain in desert seismic signal analysis

Elimination of random noise is crucial in seismic data processing. Especially in desert area, field record generally has problems of weak effective reflection wave and strong noise due to its special surface factors. Besides, desert noise has characteristics of low-frequency, non-stationary and non-Gaussian. Thus, it is difficult to separate the effective signal from desert noise in low-frequency band. In order to solve these problems, this paper proposes an iterative low-rank denoising method based on synchrosqueezed wavelet transform (SWT). The algorithm first transforms seismic signal into time–frequency domain by SWT, then the signal is decomposed by iterative low-rank decomposition. Different from a traditional low-rank algorithm, this paper performs an adaptive iterative convergence on low-rank decomposition algorithm. When the error of decomposition reaches the predetermined range, the effective low-rank component is extracted. In the end, the low-rank matrix is converted back to time domain by inverse SWT to achieve the denoising. The results of the synthetic and field records verify the effectiveness of the proposed method so that it can be applied to the denoising of desert seismic data. In addition, the surface waves in real desert seismic record have obvious suppression effects and the advantages of the algorithm are shown in the comparison experiments.

Spatiotemporal Feature Learning Based Hour-Ahead Load Forecasting for Energy Internet

In this paper, we analyze the characteristics of the load forecasting task in the Energy Internet context and the deficiencies of existing methods and then propose a data driven approach for one-hour-ahead load forecasting based on the deep learning paradigm. The proposed scheme involves three aspects. First, we formulate a historical load matrix (HLM) with spatiotemporal correlation combined with the EI scenario and then create a three-dimensional historical load tensor (HLT) that contains the HLMs for multiple consecutive time points before the forecasted hour. Second, we preprocess the HLT leveraging a novel low rank decomposition algorithm and different load gradients, aiming to provide a forecasting model with richer input data. Third, we develop a deep forecasting framework (called the 3D CNN-GRU) featuring a feature learning module followed by a regression module, in which the 3D convolutional neural network (3D CNN) is used to extract the desired feature sequences with time attributes, while the gated recurrent unit (GRU) is responsible for mapping the sequences to the forecast values. By feeding the corresponding load label into the 3D CNN-GRU, our proposed scheme can carry out forecasting tasks for any zone covered by the HLM. The results of self-evaluation and a comparison with several state-of-the-art methods demonstrate the superiority of the proposed scheme.

Occlusion expression recognition based on non-convex low-rank double dictionaries and occlusion error model

Aiming at effectively correcting recognition error caused by partial facial occlusion, and simultaneously reducing the influence of facial individual′s difference on expression recognition, a novel method based on double dictionaries got by non-convex low-rank decomposition and occlusion error model is proposed in this paper. There are two steps in the training stage: 1° we use logarithmic determinant function for rank minimization problem of facial feature matrix, whose singular value fluctuates rather largely among different dimensions and causes that normal nuclear norm function cannot effectively estimate the minimal rank of the matrix. 2° non-convex low-rank decomposition algorithm is used to learn double dictionaries for expression features and individual identity features, respectively, and then an intra-class related dictionary and an inter-class structured dictionary are obtained. Three steps are taken in test stage: 1° we establish an occlusion error model to represent bias information of an occluded test sample, which is represented in a single matrix and added into iteration reconstructing process of the occluded test sample, based on double dictionaries obtained in the training stage. 2° The occluded test sample is decomposed into three sub-images, including expression feature, identity feature and occlusion error. 3° The occluded test sample is represented by the decomposed expression feature sub-image and then is classified into corresponding expression category. The following experiments in CK+ and KDEF expression databases show that, the proposed method is robust to the recognition of random occlusion facial expression images.

Spike-Like Blending Noise Attenuation Using Structural Low-Rank Decomposition

Spikelike noise is a common type of random noise existing in many geoscience and remote sensing data sets. The attenuation of spike-like noise has become extremely important recently, because it is the main bottleneck when processing the simultaneous source data that are generated from the modern seismic acquisition. In this letter, we propose a novel low-rank decomposition algorithm that is effective in rejecting the spike-like noise in the seismic data set. The specialty of the low-rank decomposition algorithm is that it is applied along the morphological direction of the seismic data sets with a prior knowledge of the morphology of the seismic data, which we call local slope. The seismic data are of much lower rank along the morphological direction than along the space direction. The morphology of the seismic data (local slope) is obtained via a robust plane-wave destruction method. We use two simulated field data examples to illustrate the algorithm workflow and its effective performance.

Learning Low-Rank Decomposition for Pan-Sharpening With Spatial-Spectral Offsets.

Finding accurate injection components is the key issue in pan-sharpening methods. In this paper, a low-rank pan-sharpening (LRP) model is developed from a new perspective of offset learning. Two offsets are defined to represent the spatial and spectral differences between low-resolution multispectral and high-resolution multispectral (HRMS) images, respectively. In order to reduce spatial and spectral distortions, spatial equalization and spectral proportion constraints are designed and cast on the offsets, to develop a spatial and spectral constrained stable low-rank decomposition algorithm via augmented Lagrange multiplier. By fine modeling and heuristic learning, our method can simultaneously reduce spatial and spectral distortions in the fused HRMS images. Moreover, our method can efficiently deal with noises and outliers in source images, for exploring low-rank and sparse characteristics of data. Extensive experiments are taken on several image data sets, and the results demonstrate the efficiency of the proposed LRP.

GoDec+: Fast and Robust Low-Rank Matrix Decomposition Based on Maximum Correntropy.

GoDec is an efficient low-rank matrix decomposition algorithm. However, optimal performance depends on sparse errors and Gaussian noise. This paper aims to address the problem that a matrix is composed of a low-rank component and unknown corruptions. We introduce a robust local similarity measure called correntropy to describe the corruptions and, in doing so, obtain a more robust and faster low-rank decomposition algorithm: GoDec+. Based on half-quadratic optimization and greedy bilateral paradigm, we deliver a solution to the maximum correntropy criterion (MCC)-based low-rank decomposition problem. Experimental results show that GoDec+ is efficient and robust to different corruptions including Gaussian noise, Laplacian noise, salt & pepper noise, and occlusion on both synthetic and real vision data. We further apply GoDec+ to more general applications including classification and subspace clustering. For classification, we construct an ensemble subspace from the low-rank GoDec+ matrix and introduce an MCC-based classifier. For subspace clustering, we utilize GoDec+ values low-rank matrix for MCC-based self-expression and combine it with spectral clustering. Face recognition, motion segmentation, and face clustering experiments show that the proposed methods are effective and robust. In particular, we achieve the state-of-the-art performance on the Hopkins 155 data set and the first 10 subjects of extended Yale B for subspace clustering.

A Random Algorithm for Low-Rank Decomposition of Large-Scale Matrices With Missing Entries.

A random submatrix method (RSM) is proposed to calculate the low-rank decomposition U(m×r)V(n×r)(T) (r < m, n) of the matrix Y∈R(m×n) (assuming m > n generally) with known entry percentage 0 < ρ ≤ 1. RSM is very fast as only O(mr(2)ρ(r)) or O(n(3)ρ(3r)) floating-point operations (flops) are required, compared favorably with O(mnr+r(2)(m+n)) flops required by the state-of-the-art algorithms. Meanwhile, RSM has the advantage of a small memory requirement as only max(n(2),mr+nr) real values need to be saved. With the assumption that known entries are uniformly distributed in Y, submatrices formed by known entries are randomly selected from Y with statistical size k×nρ(k) or mρ(l)×l , where k or l takes r+1 usually. We propose and prove a theorem, under random noises the probability that the subspace associated with a smaller singular value will turn into the space associated to anyone of the r largest singular values is smaller. Based on the theorem, the nρ(k)-k null vectors or the l-r right singular vectors associated with the minor singular values are calculated for each submatrix. The vectors ought to be the null vectors of the submatrix formed by the chosen nρ(k) or l columns of the ground truth of V(T). If enough submatrices are randomly chosen, V and U can be estimated accordingly. The experimental results on random synthetic matrices with sizes such as 13 1072 ×10(24) and on real data sets such as dinosaur indicate that RSM is 4.30 ∼ 197.95 times faster than the state-of-the-art algorithms. It, meanwhile, has considerable high precision achieving or approximating to the best.

Oct-Tree-Based Multilevel Low-Rank Decomposition Algorithm for Rapid 3-D Parasitic Extraction

Fast parasitic extraction is an integral part of high-speed microelectronic simulation at the package and on-chip level. Integral equation methods and related fast solvers for the iterative solution of the resulting dense matrix systems have enabled linear time complexity and memory usage. However, these methods tend to have large disparities between setup and matrix-vector product times that affect their efficiency when applied to multiple excitation problems, i.e., problems with a large number of nets. For example, FastCap, which is based on the fast multipole method, has a significantly faster setup time than the multilevel QR decomposition-based IES/sup 3/, but relatively slow matrix-vector products. In this paper, we present a novel oct-tree-based QR compression technique for fast iterative solution. The regular cube structure of the fast multipole method and the QR compression scheme for interaction submatrices as in IES/sup 3/ are combined to achieve a predetermined compressible matrix-block structure and, consequently, superior memory, setup, and solve time efficiencies.