一种基于数据补全的大象流检测方法

由于在网络测量中存在不可避免的数据损失,网络监测数据通常是不完备的甚至是稀疏的,这使得大象流的精确检测成为一个具有挑战性的问题.本文提出了一种基于数据补全的离线大象流检测方法.为实现对于大象流的精准检测,首先实现了一个基于矩阵分解的数据补全算法,将流量数据补全问题转化为一个低秩矩阵奇异值分解问题.其次,在此基础上进行高阶扩展,引申出张量补全模型,利用张量CP分解实现数据补全,将原问题转化为通过最小化张量秩来恢复缺失条目的张量补全问题.最后对上面使用的矩阵补全算法和张量补全算法进行了仿真实验,对比了各算法精准度,评估了超参数,并展示了张量补全算法的时间开销.实验结果证明该方法取得了较好的效果.     

非负张量补全算法

近年来矩阵补全已成为一种重要的信号采集方式。将矩阵补全推广到非负张量情形,并提出了非负张量补全算法。该算法先将非负张量补全问题转化为交替求解一系列非负矩阵补全问题,再使用非负最小二乘方法求解这些问题。由于充分利用了数据的空时结构,所提的非负张量补全算法比非负矩阵补全算法有更好的恢复性能。实验结果证实了该方法的优越性。     

一种基于张量分解的医学数据缺失模态的补全算法

多模态磁共振影像数据采集过程中会出现不同程度的模态数据缺失,现有的补全方法大多只针对随机缺失,无法较好地恢复条状及块状缺失.针对此问题,本文提出了一种基于多向延迟嵌入的平滑张量补全算法分类框架.首先,对缺失数据进行多向延迟嵌入操作,得到折叠后的张量;然后通过平滑张量CP分解,得到补全的张量;最后利用多向延迟嵌入的逆向操...     

基于张量奇异值理论的交通数据重构方法

由于探测器和通信设备的故障,交通数据的缺失是不可避免的,这种缺失给智能交通系统（ITS）带来了不利的影响。针对此问题,运用张量平均秩的概念,对张量核范数进行最小化,从而构建了新的低秩张量补全模型,并且在此基础上,基于张量奇异值分解（T-SVD）和阈值分解（TSVT）理论,分别使用坐标梯度下降法（CGD）和交替乘子法（ADMM）对模型进行求解,提出两个张量补全算法LRTC-CGD和LRTC-TSVT。在公开的真实时空交通数据集上进行实验。结果表明,LRTC-CGD和LRTC-TSVT算法在不同的缺失场景和缺失率条件下,补全精度要优于现行的其他补全算法,并且在数据极端缺失情况下（70%~80%）,补全的效果更加稳定。     

基于线性 Bregman 迭代的结构化噪声矩阵补全算法

通过采样部分元素补全低秩矩阵的缺失元素是许多实际应用如图像修复、无线传感网数据收集和推荐系统等经常遇到的一个颇具挑战性的难题。在机器学习领域,这类问题通常能刻画成矩阵补全问题。虽然现有研究针对矩阵补全问题已提出了许多有效算法,但这些算法通常仅限于采样元素要么无噪要么仅含少量随机高斯噪声的补全情形,难以处理实际问题中常见的行结构化噪声。为了解决这个问题,该文首先借助分类器设计中流行的 L2,1范数正则化技术来平滑此类噪声,并将该问题建模为一类基于 L2,1范数正则化的凸约束优化问题。其次,为了快速有效地求解,我们将向量空间的线性 Bregman 迭代算法和近邻算子技术拓展到矩阵空间,进一步设计了一种鲁棒的基于线性 Bregman 迭代的结构化噪声矩阵补全算法（LiBIMC）。严格的理论分析证明了 LiBIMC 迭代算法的不动点正是结构化噪声矩阵补全问题的全局最优解。数值实验结果表明,和已有的矩阵补全算法相比,LiBIMC 算法不仅能更好地恢复结构化噪声矩阵的缺失元素,还能精确地辨识出采样矩阵中被污染的元素所在行的位置信息。     

异常值自识别的低秩矩阵补全方法

低秩矩阵补全的相关问题在机器学习、图像处理、视频去噪等领域受到极大关注,在假设数据低秩的情况下,使用矩阵补全可以估计缺失数据的值,得到满足约束条件情况下最接近目标矩阵的结果矩阵。然而,在加入非高斯噪声的情况下,目前大部分矩阵补全算法的鲁棒性并不理想。为了增加矩阵补全算法的鲁棒性并避免算法过拟合,讨论了几种较为经典的矩阵补全算法,并提出了一种新的鲁棒性矩阵补全方法。该算法可以识别异常值的位置并用近似数据替换异常数据,降低异常值对算法的影响,增加精确度。模拟数据和真实数据的实验结果均显示,该算法在处理数据被高斯噪声毁坏的情况下有较好的鲁棒性和准确性。     

基于非凸张量环秩最小化的张量补全算法研究

在实际应用中,恢复缺失的高阶数据一直是重要的研究热点,而基于张量分解的方法能够有效地提取数据的低秩结构,预测丢失的数据,为该问题提供了新的思路.针对传统张量环补全模型的秩松弛问题,建立了基于Lp(0相似文献   

基于低管秩张量分解的互质阵列自适应波束成形算法

互质阵列因其大阵列孔径和高自由度特性在波束成形领域受到广泛关注.为了充分利用该特性,近年来学者们提出了基于孔洞填充的算法,有效提高了互质阵列波束成形的性能.然而,这些算法存在计算量大、噪声鲁棒性弱等缺点,难以适应复杂多变的实际环境.为此,本文利用张量的多维结构在参数估计上的性能优势,提出了一种基于低管秩张量分解的互质阵列自适应波束成形算法.首先将互质阵列的多采样虚拟信号矩阵重排为张量形式,利用其低管秩特性补全缺失的互相关信息;然后从补全后的张量数据中提取信号参数,并与目标先验进行匹配,最终得到波束成形权矢量.本算法分别利用ADMM和Tucker分解提高了张量补全和分解的运算效率;所设计的目标匹配方案也有效控制了算法误差.仿真结果展示了本算法在性能和计算复杂度相对于现有方法的优势,尤其是在低信噪比和少采样数的情况下.     

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.     

基于NSGA2的参数自确定数据补全模型

基于分解的数据补全模型在补全缺失元素问题的研究中被广泛应用。然而,参数低秩与参数最大迭代次数作为模型的输入,其合理性直接影响补全模型的性能。参数低秩设定不合理将导致数据补全模型出现过拟合或者欠拟合问题。此外,参数最大迭代次数选取不合理将导致计算资源的浪费或者数据补全精度的下降。基于此论文提出一种基于进化算法NSGA2的参数自确定数据补全模型。该模型通过构建多目标函数执行遗传进化操作确定合理的参数值,确保数据补全模型的性能。对比试验结果表明,该模型通过进化算法确定合理参数值有效避免了过拟合与欠拟合问题的发生,同时也避免了计算资源的浪费,确保了数据补全结果的精度。     

基于低秩表示与矩阵填充的人脸识别方法

基于回归分析的人脸识别方法在处理不完备数据矩阵时,先对矩阵进行填充,再使用人脸识别方法,因此会降低分类性能.为了更有效地执行关于不完备数据的识别,文中将低秩矩阵填充和低秩表示学习整合在同一个模型,提出基于低秩表示和低秩矩阵填充的人脸识别方法.通过最小化表示系数和矩阵秩交替计算样本低秩表示系数矩阵和恢复矩阵缺失项,再使用最近邻分类器实现分类.在一些公开人脸数据集上的实验表明,在训练样本矩阵元素随机缺失时,文中方法可以有效提高识别精度及降低填充误差.     

结合稀疏先验与多模式分解的低秩张量恢复方法

目的 各类终端设备获取的大量数据往往由于信息丢失而导致数据不完整,或经常受到降质问题的困扰。为有效恢复缺损或降质数据,低秩张量补全备受关注。张量分解可有效挖掘张量数据的内在特征,但传统分解方法诱导的张量秩函数无法探索张量不同模式之间的相关性;另外,传统张量补全方法通常将全变分约束施加于整体张量数据,无法充分利用张量低维子空间的平滑先验。为解决以上两个问题,提出了基于稀疏先验与多模式张量分解的低秩张量恢复方法。方法 在张量秩最小化模型基础上,融入多模式张量分解技术以及分解因子局部稀疏性。首先对原始张量施加核范数约束,以此捕获张量的全局低秩性,然后,利用多模式张量分解将整体张量沿着每个模式分解为一组低维张量和一组因子矩阵,以探索不同模式之间的相关性,对因子矩阵施加因子梯度稀疏正则化约束,探索张量子空间的局部稀疏性,进一步提高张量恢复性能。结果 在高光谱图像、多光谱图像、YUV（也称为YCbCr）视频和医学影像数据上,将本文方法与其他8种修复方法在3种丢失率下进行定量及定性比较。在恢复4种类型张量数据方面,本文方法与深度学习GP-WLRR方法（global prior refined weighted low-rank representation）的修复效果基本持平,本文方法的MPSNR（mean peak signal-to-noise ratio）在所有丢失率及张量数据上的总体平均高0.68dB,MSSIM（mean structural similarity）总体平均高0.01;与其他6种张量建模方法相比,本文方法的MPSNR及MSSIM均取得最优结果。结论 提出的基于稀疏先验与多模式张量分解的低秩张量恢复方法,可同时利用张量的全局低秩性与局部稀疏性,能够对受损的多维视觉数据进行有效修复。     

基于大间距准则和图像矩阵双向投影的人脸特征提取方法

传统基于降维技术的人脸特征提取需要将图像转换成更高维的向量, 从而加剧维数灾难问题, 对于采用Fisher优化准则的特征提取, 这也会使小样本问题更加突出. 基于图像的矩阵表示, 本文提出了一种新的基于大间距准则和矩阵双向投影技术的人脸特征提取方法(Maximum margin criterion and image matrix bidirectional projection, MMC-MBP). 该方法一方面在计算散度矩阵时引入了能保持数据局部性的Laplacian矩阵, 以保持数据的流形结构, 从而提高识别正确率; 另一方面采用了有效且稳定的大间距的优化准则即最大化矩阵迹差, 能克服利用Fisher准则所带来的小样本问题; 更重要的, MMC-MBP方法给出了求解最优双向投影矩阵的迭代计算过程, 该迭代求解过程能保证目标函数的单调递增性、收敛性以及投影矩阵的收敛性, 从而成功解决了传统基于张量(矩阵)投影技术的特征提取方法特征维数过高或者无收敛解的问题. 最后广泛而系统的人脸识别实验表明, MMC-MBP的迭代求解过程能很快收敛, 且相比Eigenfaces, Fisherfaces, Laplacianfaces等脸识别方法, 具有更高的识别正确率, 是一种有效的人脸特征提取方法.     

基于非局部张量火车分解的彩色图像修补

数据在采集和转换的过程中通常存在部分数据丢失的问题,丢失数据的补全直接影响后续的识别、跟踪等高层任务的结果.自然图像中经常存在许多具有重复特性的相似结构,利用该类冗余信息,文中提出基于非局部张量火车分解的张量补全方法.利用图像的非局部相似性,挖掘其中蕴含的低秩特性,并通过张量火车分解模型进行建模及升阶,将低阶张量转化为高阶以进行低秩信息的进一步挖掘利用,从而进行图像中缺失数据的修补.实验验证文中方法在图像修补上的有效性.     

Algorithms for sparse nonnegative Tucker decompositions

There is a increasing interest in analysis of large-scale multiway data. The concept of multiway data refers to arrays of data with more than two dimensions, that is, taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions for tensors are the Tucker model and the more restricted PARAFAC model. Both models can be viewed as generalizations of the regular factor analysis to data of more than two modalities. Nonnegative matrix factorization (NMF), in conjunction with sparse coding, has recently been given much attention due to its part-based and easy interpretable representation. While NMF has been extended to the PARAFAC model, no such attempt has been done to extend NMF to the Tucker model. However, if the tensor data analyzed are nonnegative, it may well be relevant to consider purely additive (i.e., nonnegative) Tucker decompositions). To reduce ambiguities of this type of decomposition, we develop updates that can impose sparseness in any combination of modalities, hence, proposed algorithms for sparse nonnegative Tucker decompositions (SN-TUCKER). We demonstrate how the proposed algorithms are superior to existing algorithms for Tucker decompositions when the data and interactions can be considered nonnegative. We further illustrate how sparse coding can help identify what model (PARAFAC or Tucker) is more appropriate for the data as well as to select the number of components by turning off excess components. The algorithms for SN-TUCKER can be downloaded from M?rup (2007).     

MPCA: Multilinear Principal Component Analysis of Tensor Objects

This paper introduces a multilinear principal component analysis (MPCA) framework for tensor object feature extraction. Objects of interest in many computer vision and pattern recognition applications, such as 2-D/3-D images and video sequences are naturally described as tensors or multilinear arrays. The proposed framework performs feature extraction by determining a multilinear projection that captures most of the original tensorial input variation. The solution is iterative in nature and it proceeds by decomposing the original problem to a series of multiple projection subproblems. As part of this work, methods for subspace dimensionality determination are proposed and analyzed. It is shown that the MPCA framework discussed in this work supplants existing heterogeneous solutions such as the classical principal component analysis (PCA) and its 2-D variant (2-D PCA). Finally, a tensor object recognition system is proposed with the introduction of a discriminative tensor feature selection mechanism and a novel classification strategy, and applied to the problem of gait recognition. Results presented here indicate MPCA's utility as a feature extraction tool. It is shown that even without a fully optimized design, an MPCA-based gait recognition module achieves highly competitive performance and compares favorably to the state-of-the-art gait recognizers.     

Parallel algorithms for tensor completion in the CP format

Low-rank tensor completion addresses the task of filling in missing entries in multi-dimensional data. It has proven its versatility in numerous applications, including context-aware recommender systems and multivariate function learning. To handle large-scale datasets and applications that feature high dimensions, the development of distributed algorithms is central. In this work, we propose novel, highly scalable algorithms based on a combination of the canonical polyadic (CP) tensor format with block coordinate descent methods. Although similar algorithms have been proposed for the matrix case, the case of higher dimensions gives rise to a number of new challenges and requires a different paradigm for data distribution. The convergence of our algorithms is analyzed and numerical experiments illustrate their performance on distributed-memory architectures for tensors from a range of different applications.     

最小二乘半监督支持张量机学习算法*

支持张量机(STM)受限于迭代操作,训练时间较长.针对这一缺点,改进STM的目标规划,将训练过程由解决一组二次规划改为计算线性方程组,并引入直推式的思想解决半监督问题,提出最小二乘半监督支持张量机学习算法.在人脸识别和时间序列分类上对比文中算法与传统算法,实验证明文中算法不仅减少运算时间,而且提高识别率.     

Individual Kernel Tensor-subspaces for robust face recognition: a computationally efficient tensor framework without requiring mode factorization.

Facial images change appearance due to multiple factors such as different poses, lighting variations, and facial expressions. Tensors are higher order extensions of vectors and matrices, which make it possible to analyze different appearance factors of facial variation. Using higher order tensors, we can construct a multilinear structure and model the multiple factors of face variation. In particular, among the appearance factors, the factor of a person's identity modeled by a tensor structure can be used for face recognition. However, this tensor-based face recognition creates difficulty in factorizing the unknown parameters of a new test image and solving for the person-identity parameter. In this paper, to break this limitation of applying the tensor-based methods to face recognition, we propose a novel tensor approach based on an individual-modeling method and nonlinear mappings. The proposed method does not require the problematic tensor factorization and is more efficient than the traditional TensorFaces method with respect to computation and memory. We set up the problem of solving for the unknown factors as a least squares problem with a quadratic equality constraint and solve it using numerical optimization techniques. We show that an individual-multilinear approach reduces the order of the tensor so that it makes face-recognition tasks computationally efficient as well as analytically simpler. We also show that nonlinear kernel mappings can be applied to this optimization problem and provide more accuracy to face-recognition systems than linear mappings. In this paper, we show that the proposed method, Individual Kernel TensorFaces, produces the better discrimination power for classification. The novelty in our approach as compared to previous work is that the Individual Kernel TensorFaces method does not require estimating any factor of a new test image for face recognition. In addition, we do not need to have any a priori knowledge of or assumption about the factors of a test image when using the proposed method. We can apply Individual Kernel TensorFaces even if the factors of a test image are absent from the training set. Based on various experiments on the Carnegie Mellon University Pose, Illumination, and Expression database, we demonstrate that the proposed method produces reliable results for face recognition.     

Multiple rank multi-linear SVM for matrix data classification

Matrices, or more generally, multi-way arrays (tensors) are common forms of data that are encountered in a wide range of real applications. How to classify this kind of data is an important research topic for both pattern recognition and machine learning. In this paper, by analyzing the relationship between two famous traditional classification approaches, i.e., SVM and STM, a novel tensor-based method, i.e., multiple rank multi-linear SVM (MRMLSVM), is proposed. Different from traditional vector-based and tensor based methods, multiple-rank left and right projecting vectors are employed to construct decision boundary and establish margin function. We reveal that the rank of transformation can be regarded as a tradeoff parameter to balance the capacity of learning and generalization in essence. We also proposed an effective approach to solve the proposed non-convex optimization problem. The convergence behavior, initialization, computational complexity and parameter determination problems are analyzed. Compared with vector-based classification methods, MRMLSVM achieves higher accuracy and has lower computational complexity. Compared with traditional supervised tensor-based methods, MRMLSVM performs better for matrix data classification. Promising experimental results on various kinds of data sets are provided to show the effectiveness of our method.