Block Incremental Dense Tucker Decomposition with Application to Spatial and Temporal Analysis of Air Quality Data

How can we efficiently store and mine dynamically generated dense tensors for modeling the behavior of multidimensional dynamic data?Much of the multidimensional dynamic data in the real world is generated in the form of time-growing tensors.For example,air quality tensor data consists of multiple sensory values gathered from wide locations for a long time.Such data,accumulated over time,is redundant and consumes a lot ofmemory in its raw form.We need a way to efficiently store dynamically generated tensor data that increase over time and to model their behavior on demand between arbitrary time blocks.To this end,we propose a Block IncrementalDense Tucker Decomposition(BID-Tucker)method for efficient storage and on-demand modeling ofmultidimensional spatiotemporal data.Assuming that tensors come in unit blocks where only the time domain changes,our proposed BID-Tucker first slices the blocks into matrices and decomposes them via singular value decomposition(SVD).The SVDs of the time×space sliced matrices are stored instead of the raw tensor blocks to save space.When modeling from data is required at particular time blocks,the SVDs of corresponding time blocks are retrieved and incremented to be used for Tucker decomposition.The factor matrices and core tensor of the decomposed results can then be used for further data analysis.We compared our proposed BID-Tucker with D-Tucker,which our method extends,and vanilla Tucker decomposition.We show that our BID-Tucker is faster than both D-Tucker and vanilla Tucker decomposition and uses less memory for storage with a comparable reconstruction error.We applied our proposed BID-Tucker to model the spatial and temporal trends of air quality data collected in South Korea from 2018 to 2022.We were able to model the spatial and temporal air quality trends.We were also able to verify unusual events,such as chronic ozone alerts and large fire events.

Bispectrum Feature Extraction of Gearbox Faults Based on Nonnegative Tucker3 Decomposition with 3D Calculations

Nonnegative Tucker3 decomposition（NTD） has attracted lots of attentions for its good performance in 3D data array analysis. However, further research is still necessary to solve the problems of overfitting and slow convergence under the anharmonic vibration circumstance occurred in the field of mechanical fault diagnosis. To decompose a large-scale tensor and extract available bispectrum feature, a method of conjugating Choi-Williams kernel function with Gauss-Newton Cartesian product based on nonnegative Tucker3 decomposition（NTD_EDF） is investigated. The complexity of the proposed method is reduced from o（nNlgn） in 3D spaces to o（RiR2nlgn） in 1D vectors due to its low rank form of the Tucker-product convolution. Meanwhile, a simultaneously updating algorithm is given to overcome the overfitting, slow convergence and low efficiency existing in the conventional one-by-one updating algorithm. Furthermore, the technique of spectral phase analysis for quadratic coupling estimation is used to explain the feature spectrum extracted from the gearbox fault data by the proposed method in detail. The simulated and experimental results show that the sparser and more inerratic feature distribution of basis images can be obtained with core tensor by the NTD EDF method compared with the one by the other methods in bispectrum feature extraction, and a legible fault expression can also be performed by power spectral density（PSD） function. Besides, the deviations of successive relative error（DSRE） of NTD_EDF achieves 81.66 dB against 15.17 dB by beta-divergences based on NTD（NTD_Beta） and the time-cost of NTD EDF is only 129.3 s, which is far less than 1 747.9 s by hierarchical alternative least square based on NTD （NTD_HALS）. The NTD_EDF method proposed not only avoids the data overfitting and improves the computation efficiency but also can be used to extract more inerratic and sparser bispectrum features of the gearbox fault.

Multispectral image compression and encryption method based on tensor decomposition in wavelet domain

Multispectral image compression and encryption algorithms commonly suffer from issues such as low compression efficiency,lack of synchronization between the compression and encryption proces-ses,and degradation of intrinsic image structure.A novel approach is proposed to address these is-sues.Firstly,a chaotic sequence is generated using the Lorenz three-dimensional chaotic mapping to initiate the encryption process,which is XORed with each spectral band of the multispectral image to complete the initial encryption of the image.Then,a two-dimensional lifting 9/7 wavelet transform is applied to the processed image.Next,a key-sensitive Arnold scrambling technique is employed on the resulting low-frequency image.It effectively eliminates spatial redundancy in the multispectral image while enhancing the encryption process.To optimize the compression and encryption processes further,fast Tucker decomposition is applied to the wavelet sub-band tensor.It effectively removes both spectral redundancy and residual spatial redundancy in the multispectral image.Finally,the core tensor and pattern matrix obtained from the decomposition are subjected to entropy encoding,and real-time chaotic encryption is implemented during the encoding process,effectively integrating compression and encryption.The results show that the proposed algorithm is suitable for occasions with high requirements for compression and encryption,and it provides valuable insights for the de-velopment of compression and encryption in multispectral field.

Randomized Generalized Singular Value Decomposition

The generalized singular value decomposition(GSVD)of two matrices with the same number of columns is a very useful tool in many practical applications.However,the GSVD may suffer from heavy computational time and memory requirement when the scale of the matrices is quite large.In this paper,we use random projections to capture the most of the action of the matrices and propose randomized algorithms for computing a low-rank approximation of the GSVD.Serval error bounds of the approximation are also presented for the proposed randomized algorithms.Finally,some experimental results show that the proposed randomized algorithms can achieve a good accuracy with less computational cost and storage requirement.

Electrical Data Matrix Decomposition in Smart Grid

As the development of smart grid and energy internet, this leads to a significantincrease in the amount of data transmitted in real time. Due to the mismatch withcommunication networks that were not designed to carry high-speed and real time data,data losses and data quality degradation may happen constantly. For this problem,according to the strong spatial and temporal correlation of electricity data which isgenerated by human’s actions and feelings, we build a low-rank electricity data matrixwhere the row is time and the column is user. Inspired by matrix decomposition, we dividethe low-rank electricity data matrix into the multiply of two small matrices and use theknown data to approximate the low-rank electricity data matrix and recover the missedelectrical data. Based on the real electricity data, we analyze the low-rankness of theelectricity data matrix and perform the Matrix Decomposition-based method on the realdata. The experimental results verify the efficiency and efficiency of the proposed scheme.

Parallel Active Subspace Decomposition for Tensor Robust Principal Component Analysis

Tensor robust principal component analysis has received a substantial amount of attention in various fields.Most existing methods,normally relying on tensor nuclear norm minimization,need to pay an expensive computational cost due to multiple singular value decompositions at each iteration.To overcome the drawback,we propose a scalable and efficient method,named parallel active subspace decomposition,which divides the unfolding along each mode of the tensor into a columnwise orthonormal matrix(active subspace)and another small-size matrix in parallel.Such a transformation leads to a nonconvex optimization problem in which the scale of nuclear norm minimization is generally much smaller than that in the original problem.We solve the optimization problem by an alternating direction method of multipliers and show that the iterates can be convergent within the given stopping criterion and the convergent solution is close to the global optimum solution within the prescribed bound.Experimental results are given to demonstrate that the performance of the proposed model is better than the state-of-the-art methods.

基于张量Tucker分解的高光谱图像异常目标识别

高光谱图像每个像素点的光谱信息包含数百甚至数千个波段,使得高光谱图像在维度上具有高度的复杂性,且由于光谱波段众多,其中存在大量的冗余信息,加大了异常目标识别计算的负担。为此,文中提出基于张量Tucker分解的高光谱图像异常目标识别方法。通过张量Tucker分解压缩高光谱图像后,采用依据高光谱图像数据样本学习的构造方法,构建压缩后高光谱图像的字典,获取高光谱图像数据的稀疏表示形式后,通过RX异常检测方法检测出高光谱图像中的异常目标。实验结果表明:所提方法张量分解重构高光谱图像后,可以缩短压缩时间,减少算法复杂度;重构后的高光谱图像清晰度高,且高光谱图像异常目标检测虚警率低。

基于小波变换和Tucker分解的彩色图像数字水印

提出了一种通过小波变换和Tucker分解将水印信息同时嵌入彩色图像R、G、B通道的水印算法。首先对彩色图像R、G、B三通道进行小波变换,然后将获得的三个低频系数构成三阶张量,再经过Tucker分解后获得核心张量,通过在核心张量中嵌入水印信息使得水印信息扩散到原彩色图像的R、G、B三个分量中。通过实验表明,本算法对于压缩、噪声、滤波、缩放等攻击具有一定的鲁棒性,并与在同样嵌入规则下,直接将Tucker分解应用于彩色图像的算法比较,该算法具有更好的稳定性。

基于张量Tucker分解的发动机故障诊断

传统的发动机故障诊断方法通常基于向量模式进行数据特征的提取,可能丢失数据之间的结构信息及破坏数据间相关性。针对此问题,提出了一种张量模式下提取发动机数据特征的方法,构建了"信号类别×曲轴转角×转速"的三阶张量形式的发动机状态样本,基于交替投影的思想,使用HOSVDHOOI张量Tucker分解的联立求解算法,对数据特征进行提取。分别以不进行数据特征提取和基于张量Tucker分解进行数据特征提取两种情况,对发动机正常工作、单缸失火和轴系不对中三种状态下的实验数据进行处理,并分别采用网格参数优化法、遗传算法、粒子群算法对分类模型中的参数进行优化。以预测准确率和模型学习时间为评价指标进行对比分析,实验结果表明,基于张量Tucker分解的发动机数据特征提取及诊断方法预测准确率更高,分类模型学习时间更短。

基于Tucker分解的音频分类研究

提出一种利用Tucker分解获得鲁棒性较强的音频信号不同属性的特征,在高斯混合模型上测试音频信号分类性能的方法。音频信号经过预处理后,提取其不同类型特征集合,包括常规声学特征参数集合、听觉感知特征参数集合、心理声学特征参数集合;然后由三种特征集合构建三阶特征张量,通过Tucker分解得到每一类特征阶投影矩阵并进行主分量分析;最后使用包括音乐、语音、噪声3种类型的300条音频数据测试不同特征集合的分类效果,在此过程中使用了有监督学习的高斯混合模型作为分类器。实验中比较了不同特征集合使用高斯混合模型的分类正确率。实验结果表明,Tucker分解获得的特征集合实现了较好的分类,说明该方法性能优于传统特征集合。

基于快速层次交替最小二乘非负张量Tucker分解的干涉高光谱图像光谱信息压缩方法

提出一种基于快速层次交替最小二乘非负张量Tucker分解的高光谱图像光谱信息压缩算法。首先,将干涉高光谱图像光程差方向的三维信息采用三维光程差方向提升小波变换(3DOPT-LDWT)进行分解,将三维小波子带系数看作三阶非负张量,采用快速层次交替最小二乘非负张量Tucker分解(FHALS-NTD)算法对进行分解,得到核心张量和模式矩阵。对每个模式矩阵进行量化,对核心张量采用比特平面重要系数编码算法进行编码,得出最终的压缩码流。结果表明,此压缩算法可以稳定可靠地工作。与传统压缩算法比较,平均信噪比提高了1.23dB。有效的提高了干涉高光谱图像压缩性能。

基于张量Tucker分解的智能配电网大数据压缩

为了解决智能配电网中由海量异构数据引发的存储问题,提出一种基于张量Tucker分解的智能配电网数据压缩方法。首先,针对配电网异构数据建立配电网结构化SCADA数据与非结构化视频、图片数据的张量标准化处理模型。然后,提出基于张量Tucker分解的配电网大数据压缩方法,该方法可以在保留数据空间本征结构的情况下对配电网异构数据进行压缩。最后,采用真实的配电网数据验证了所提出方法可以有效削减数据量以应对数据存储问题。对比结果表明,所提出方法优于奇异值分解方法。

基于张量Tucker分解的配电网红外图像监测数据压缩

对于配电网设备在线监测,逐渐增多的红外图像数据在远程传输时会对信道带宽产生极大压力。为解决这一问题,提升传输效率,以张量Tucker分解为基础,结合同一配电室内设备间的温度信息相关性提出一种红外图像监测数据压缩方法。将现场采集的配电室内多设备红外图像数据,根据其宽、高、颜色空间及设备编号建立四阶张量模型,并进行压缩和性能分析。通过压缩比、峰值信噪比和均方差3个指标评价所提出图像数据压缩方法的性能,该压缩方法能够利用设备间温度数据相关性,保留多设备红外图像数据的空间本征结构,降低了压缩图像的信息丢失。在与单幅图像压缩以及奇异值分解方法的对比结果表明,所提出的方法具有高压缩比和低图像压缩失真的优点,可以有效缓解在线红外图像监测数据传输过程中对信道带宽的压力。

基于非负Tucker 3分解的稀疏分量分析在故障信号提取中的应用

针对初始故障信号不稀疏难于判断的问题,在非负Tucker 3分解(NTD)的基础上,提出了一种基于NTD的稀疏分量分析(SCA)处理二次特征信号的方法.同时,为了克服NTD算法收敛慢、易陷入过拟合等局限性,对分解因子增加了非负约束,并提出了对分解因子一次更新的算法.对比传统的最小交替二乘法,该更新算法能一次性地计算所有分解因子,避免了计算大规模的Jacobian矩阵,从而较大地提高了算法的效率.实验结果表明:NTD和SCA相结合的方法(SCA_NTD)只需迭代约150步可达到收敛,而且在频谱稀疏性处理方面优于NTF等传统的方法;在分解相同维数张量的条件下,SCA_NTD的最高精度达到了97.16%.因此,SCA_NTD不仅能够改善信号特征的稀疏性,而且对提高算法的收敛速度和精度也具有重要的意义.

基于Tucker分解的音频分类方法的研究

提出了一种基于张量分解的音频信号的分类方法.首先,通过张量建模与Tucker分解挖掘出信号潜在的结构信息,当作音频信号的有效特征信息,然后利用支持向量机作为分类器完成分类.实验结果表明:通过张量分析提取的特征具有更好的区分度,分类的正确率达到了91.3%,相较于传统方法音频分类的正确率有了明显的提高,说明张量分析方法在音频信号分类中的有效性.

基于CUDA与CUBLAS的Tucker分解模块设计与实现

由于张量Tucker分解在图像处理、人脸识别与信号处理等领域中的大量应用,使得Tucker分解算法成为目前重点研究对象。但是当前流行的Tucker分解算法需要对张量进行多次展开,导致算法加速效率降低。针对上述问题,提出一种应用于统一计算设备架构(CUDA)平台上的改进Tucker分解模块,通过对Tucker分解算法与CUDA平台进行优化,在省略张量展开过程的同时,提高加速效率,从而降低对加速系统的要求。实验结果表明,改进Tucker分解算法在CUDA平台上的加速性能具有明显提高。

基于分块DCT和Tucker分解的彩色图像数字水印

提出了一种通过分块DCT和Tucker分解将水印信息同时嵌入彩色图像R、G、B通道的离散余弦变换(DCT)直流系数中的水印算法。首先对彩色图像R、G、B通道进行8×8分块DCT,然后将各分块系数矩阵的直流系数分量构成三阶张量,再经过Tucker分解后获得核心张量,通过在核心张量中嵌入水印信息使得水印信息同时扩散到三通道的直流系数中。通过实验表明,该算法对于压缩、噪声、滤波、缩放等攻击具有一定的鲁棒性。与传统的基于YCbCr颜色空间的算法比较,该算法具有更好的不可见性。

分布式的增量式张量Tucker分解方法

随着社交网络、电商系统、移动终端设备的快速发展,海量且高维的数据正以前所未有的速度不断地增长和积累.高维数据可以自然地表示为张量.张量的Tucker分解方法是一种常用且经典的高维数据分析机器学习方法,被广泛地应用于推荐系统、图像压缩、计算机视觉等多个领域.然而,传统的张量分解方法大多只能处理静态的数据,并不适用于动态增长的数据.当处理不断增长的数据时,传统方法大多只能低效地重新开始计算,以完成张量分解.针对增量式数据对传统张量分解方法带来的挑战,本文提出了一种分布式的增量式张量Tucker分解方法DITTD,首次解决了海量高维且动态增长数据上高效的分布式张量Tucker分解问题.该方法首先根据增量数据相对原始数据的位置关系对其进行分类处理.为了实现分布式节点的负载均衡,本文指出张量的最优划分是NP-难问题,并使用启发式方法以实现尽可能均匀的张量划分.为了避免张量Tucker分解的中间结果爆炸问题,本文提出了一种新颖的增量式张量Tucker分解计算方法.该方法减少了中间结果的计算和网络传输通信量,以提升分布式的增量式张量Tucker分解效率.最后,本文在真实与合成数据集上进行了大量的实验.实验结果验证了本文方法的运行效率比基准方法提升了至少1个数量级,并具有良好的可扩展性.

一种基于Tucker分解的等矩形全景图像水印算法

随着全景图像的应用与发展,全景图像的版权保护成为了亟待解决的问题。针对这一问题,提出了一种基于Tucker分解的等矩形全景图像水印算法。首先,根据图像的分辨率求得权重因子以此确定嵌入强度;其次,利用Tucker分解得到等矩形全景图像的核心张量,并选择核心张量的第一子带作为水印的嵌入区域;最后,将第一子带进行不重叠分块,并对图像块使用奇异值分解(SVD),继而对最大奇异值以量化方式嵌入水印,并根据图像的局部特性以及嵌入强度来自适应地确定量化步长。实验结果表明,未经攻击的含水印图像的平均WSPSNR为40. 318 3 dB且水印提取的平均误码率为0. 11%;对多种投影转换攻击,水印提取的平均误码率低于13. 06%,说明水印具有较好的鲁棒性,并实现了水印的盲提取。

基于DWT和Tucker分解的超光谱图像压缩技术研究

由于超光谱图像(HSI)的大数据量,HSI压缩技术的研究近年来越来越受到关注。鉴于此,提出了一种基于离散小波变换(DWT)和Tucker分解的HSI压缩方法。充分利用HSI频域和空域的信息,对HSI频带的小波变换系数进行Tucker分解,先利用小波变换将HSI分解为不同的子图像,然后利用Tucker分解实现子图像的压缩;最后用实际的HSI对算法的有效性进行评估。与其他算法的比较结果表明该算法具有更好的性能;实验还显示了压缩HSI在监督分类方法中的作用。