基于广义主成分分析的重构故障子空间建模方法

在线故障诊断是工业过程中十分重要的问题.相比传统贡献图而言,基于重构的故障诊断受到特别关注.传统的主元分析方法没有考虑故障数据中同时包含正常工况信息和故障信息,因而提取出故障子空间对故障的描述准确性不足.为提高故障子空间的准确性,提出一种基于广义主成分分析的重构故障子空间建模方法.首先,同时考虑正常工况数据和故障数据,...     

Face recognition using direct, weighted linear discriminant analysis and modular subspaces

We present a modular linear discriminant analysis (LDA) approach for face recognition. A set of observers is trained independently on different regions of frontal faces and each observer projects face images to a lower-dimensional subspace. These lower-dimensional subspaces are computed using LDA methods, including a new algorithm that we refer to as direct, weighted LDA or DW-LDA. DW-LDA combines the advantages of two recent LDA enhancements, namely direct LDA (D-LDA) and weighted pairwise Fisher criteria. Each observer performs recognition independently and the results are combined using a simple sum-rule. Experiments compare the proposed approach to other face recognition methods that employ linear dimensionality reduction. These experiments demonstrate that the modular LDA method performs significantly better than other linear subspace methods. The results also show that D-LDA does not necessarily perform better than the well-known principal component analysis followed by LDA approach. This is an important and significant counterpoint to previously published experiments that used smaller databases. Our experiments also indicate that the new DW-LDA algorithm is an improvement over D-LDA.     

Affine feature extraction: A generalization of the Fukunaga–Koontz transformation

Dimension reduction methods are often applied in machine learning and data mining problems. Linear subspace methods are the commonly used ones, such as principal component analysis (PCA), Fisher's linear discriminant analysis (FDA), common spatial pattern (CSP), et al. In this paper, we describe a novel feature extraction method for binary classification problems. Instead of finding linear subspaces, our method finds lower-dimensional affine subspaces satisfying a generalization of the Fukunaga–Koontz transformation (FKT). The proposed method has a closed-form solution and thus can be solved very efficiently. Under normality assumption, our method can be seen as finding an optimal truncated spectrum of the Kullback–Leibler divergence. Also we show that FDA and CSP are special cases of our proposed method under normality assumption. Experiments on simulated data show that our method performs better than PCA and FDA on data that is distributed on two cylinders, even one within the other. We also show that, on several real data sets, our method provides statistically significant improvement on test set accuracy over FDA, CSP and FKT. Therefore the proposed method can be used as another preliminary data-exploring tool to help solve machine learning and data mining problems.     

基于快速凸无穷范数极小化的 大量子空间的子空间分割

摘 要：子空间分割是计算机视觉和机器学习中的一个基本问题。由于实际问题中的数据 往往类数较多,使得大量子空间的子空间分割问题显得尤为重要。近年来基于谱聚类的方法在 子空间分割领域得到了越来越多的关注,但是在相关工作的实验中,子空间的个数却往往不超 过 10 个。无穷范数极小化是近年来提出的一个专门针对大量子空间的子空间分割问题的方法, 其通过降低表示系数矩阵的差异性能有效地处理该问题,但是仍有一定的局限,例如计算速度 仍不够快,缺乏针对独立子空间问题的理论保证。为此,提出快速凸无穷范数极小化,该个方 法不仅能够降低表示系数矩阵的差异性,而且能够对独立子空间情况提供理论保障且计算速度 更快,大量的实验证明了该方法的有效性。     

基于自动子空间划分的高光谱数据特征提取

针对遥感高光谱图像数据量大、维数高的特点,提出了一种自动子空间划分方法用于高光谱图像数据量减小处理。该方法主要包括3个处理步骤:数据空间划分,子空间主成分分析和基于类别可分性准则的特征选择。该方法充分利用了高光谱图像各波段数据之间的局部相关性,将整个数据划分为若干个具有较强相关性的独立子空间,然后在子空间内利用主成分分析进行特征提取,根据各类地物间的类别可分性选择有效特征,最后利用地物分类来验证该方法的有效性。实验结果表明,该方法能够有效地实现高光谱图像数据维数减小和特征提取,同现有的自适应子空间分解方法和分段主成分变换方法相比,该方法所提取的特征用于分类时能获得较好的分类精度。利用该方法进行处理,当高光谱数据维数降低了90%时,9类地物分类实验的总体分类精度可以达到80.2%。     

The common vector approach and its comparison with other subspace methods in case of sufficient data

This paper presents an application of the common vector approach (CVA), an approach mainly used for speech recognition problems when the number of data items exceeds the dimension of the feature vectors. The calculation of a unique common vector for each class involves the use of principal component analysis. CVA and other subspace methods are compared both theoretically and experimentally. TI-digit database is used in the experimental study to show the practical use of CVA for the isolated word recognition problems. It can be concluded that CVA results are higher in terms of recognition rates when compared with those of other subspace methods in training and test sets. It is also seen that the consideration of only within-class scatter in CVA gives better performance than considering both within- and between-class scatters in Fisher’s linear discriminant analysis. The recognition rates obtained for CVA are also better than those obtained with the HMM method.     

基于改进结构保持数据降维方法的故障诊断研究

传统基于核主成分分析(Kernel principal component analysis, KPCA)的数据降维方法在提取有效特征信息时只考虑全局结构保持而未考虑样本间的局部近邻结构保持问题, 本文提出一种改进全局结构保持算法的特征提取与降维方法.改进的特征提取与降维方法将流形学习中核局部保持投影(Kernel locality preserving projection, KLPP)的思想融入核主成分分析的目标函数中, 使样本投影后的特征空间不仅保持原始样本空间的整体结构, 还保持样本空间相似的局部近邻结构, 包含更丰富的特征信息.上述方法通过同时进行的正交化处理可避免局部子空间结构发生失真, 并能够直观显示出低维结果, 将低维数据输入最近邻分类器, 以识别率和聚类分析结果作为衡量指标, 同时将所提方法应用于故障诊断中.使用AVL Boost软件模拟的柴油机故障数据和田纳西(Tennessee Eastman, TE)化工数据仿真, 验证了所提方法的有效性.     

Perceptual video hashing based on Tucker decomposition with application to indexing and retrieval of near-identical videos

The perceptual video hash function defines a feature vector that characterizes a video depending on its perceptual contents. This function must be robust to the content preserving manipulations and sensitive to the content changing manipulations. In the literature, the subspace projection techniques such as the reduced rank PARAllel FACtor analysis (PARAFAC), have been successfully applied to extract perceptual hash for the videos. We propose a robust perceptual video hash function based on Tucker decomposition, a multi-linear subspace projection method. We also propose a method to find the optimum number of components in the factor matrices of the Tucker decomposition. The Receiver Operating Characteristics (ROC) curves are used to evaluate the performance of the proposed algorithm compared to the other state-of-the-art projection techniques. The proposed algorithm shows superior performance for most of the image processing attacks. An application for indexing and retrieval of near-identical videos is developed using the proposed algorithm and the performance is evaluated using average recall/precision curves. The experimental results show that the proposed algorithm is suitable for indexing and retrieval of near-identical videos.     

Multibody grouping by inference of multiple subspaces from high-dimensional data using oriented-frames

Recently, subspace constraints have been widely exploited in many computer vision problems such as multibody grouping. Under linear projection models, feature points associated with multiple bodies reside in multiple subspaces. Most existing factorization-based algorithms can segment objects undergoing independent motions. However, intersections among the correlated motion subspaces will lead most previous factorization-based algorithms to erroneous segmentation. To overcome this limitation, in this paper, we formulate the problem of multibody grouping as inference of multiple subspaces from a high-dimensional data space. A novel and robust algorithm is proposed to capture the configuration of the multiple subspace structure and to find the segmentation of objects by clustering the feature points into these inferred subspaces, no matter whether they are independent or correlated. In the proposed method, an oriented-frame (OF), which is a multidimensional coordinate frame, is associated with each data point indicating the point's preferred subspace configuration. Based on the similarity between the subspaces, novel mechanisms of subspace evolution and voting are developed. By filtering the outliers due to their structural incompatibility, the subspace configurations will emerge. Compared with most existing factorization-based algorithms that cannot correctly segment correlated motions, such as motions of articulated objects, the proposed method has a robust performance in both independent and correlated motion segmentation. A number of controlled and real experiments show the effectiveness of the proposed method. However, the current approach does not deal with transparent motions and motion subspaces of different dimensions.     

基于改进子空间追踪算法的稀疏信道估计

由于许多通信系统的信道具有稀疏多径的特性,因此可以将信道估计问题归结为稀疏信号的恢复问题,继而应用压缩感知理论(CS)的算法求解。针对CS中现存的信号重构方法——子空间追踪法(SP)需要对稀疏度有先验知识的缺点,提出一种改进的子空间追踪法(MSP)。该方法的反馈和精选过程与SP算法一致,不同之处是MSP算法每次迭代时向备选组合中反馈添加的向量个数是随着迭代次数而逐一增加的,而SP算法中备选组合被添加的向量个数与稀疏度相同。仿真结果表明,基于MSP方法所得到的稀疏多径信道估计结果优于基于传统SP的方法,且无需已知信道的多径个数。     

Contextual constraints based linear discriminant analysis

Linear feature extraction methods such as LDA have achieved great success in pattern recognition and image processing area. For most existing methods, the image data is usually transformed into a vector representation and the contextual information among pixels is not exploited. However, image data distribute sparsely in high-dimension feature space and the dependence among neighboring pixels is important to represent a natural image. Therefore, in this paper, we propose a novel image contextual constraint based linear discriminant analysis (CCLDA) method by taking into account the pixel dependence of an image in subspace learning process. In this way, a more discriminative subspace could be learned especially in the case of small sample size. Extensive experiments on ORL, Extended Yale-B, PIE and FRGC databases validate the efficacy of the proposed method.     

哈夫曼编码乘积量化的图像哈希检索方法

目的 基于哈希编码的检索方法是图像检索领域中的经典方法。其原理是将原始空间中相似的图片经哈希函数投影、量化后,在汉明空间中得到相近的哈希码。此类方法一般包括两个过程：投影和量化。投影过程大多采用主成分分析法对原始数据进行降维,但不同方法的量化过程差异较大。对于信息量不均衡的数据,传统的图像哈希检索方法采用等长固定编码位数量化的方式,导致出现低编码效率和低量化精度等问题。为此,本文提出基于哈夫曼编码的乘积量化方法。方法 首先,利用乘积量化法对降维后的数据进行量化,以便较好地保持数据在原始空间中的分布情况。然后,采用子空间方差作为衡量信息量的标准,并以此作为编码位数分配的依据。最后,借助于哈夫曼树,给方差大的子空间分配更多的编码位数。结果 在常用公开数据集MNIST、NUS-WIDE和22K LabelMe上进行实验验证,与原始的乘积量化方法相比,所提出方法能平均降低49%的量化误差,并提高19%的平均准确率。在数据集MNIST上,与同类方法的变换编码方法（TC）进行对比,比较了从32 bit到256 bit编码时的训练时间,本文方法的训练时间能够平均缩短22.5 s。结论 本文提出了一种基于多位编码乘积量化的哈希方法,该方法提高了哈希编码的效率和量化精度,在平均准确率、召回率等性能上优于其他同类算法,可以有效地应用到图像检索相关领域。     

对步态空时数据的连续特征子空间分析

提出一种基于空时特征提取的人体步态识别算法。连续的特征子空间学习依次提取出步态的时间与空间特征：第一次特征子空间学习对步态的频域数据进行主成分分析,步态数据被转化为周期特征矢量;第二次特征子空间学习对步态数据的周期特征矢量形式进行主成分分析加线性判别分析的联合分析,步态数据被进一步转化为步态特征矢量。步态特征矢量同时包含运动的周期特征以及人体的形态特征,具有很强的识别能力。在USF步态数据库上的实验结果显示,该算法识别率较其他同类算法有明显提升。     

rs-Sparse principal component analysis: A mixed integer nonlinear programming approach with VNS

Principal component analysis is a popular data analysis dimensionality reduction technique, aiming to project with minimum error for a given dataset into a subspace of smaller number of dimensions.In order to improve interpretability, different variants of the method have been proposed in the literature, in which, besides error minimization, sparsity is sought. In this paper we formulate as a mixed integer nonlinear program the problem of finding a subspace with a sparse basis minimizing the sum of squares of distances between the points and their projections. Contrary to other attempts in the literature, with our model the user can fix the level of sparseness of the resulting basis vectors. Variable neighborhood search is proposed to solve the problem obtained this way.Our numerical experience on test sets shows that our procedure outperforms benchmark methods in the literature, both in terms of sparsity and errors.     

基于动态主成分子空间的人脸识别算法

在基于子空间分析的人脸识别中,通常是按照特征值的大小来确认主成分的重要性,并以此为基础构造一个固定的特征子空间.通过人脸图像重建分析,发现固定的特征子空间会给人脸识别带来误差,于是采用多元线性回归分析理论,提出一个动态主成分子空间构造算法.在此基础上,得到了动态PCA(主成分分析)算法和基于Gabor特征的动态PCA算法.由ORL和Georgia Tech人脸数据库上的实验结果表明,该算法不仅减少了主成分数目,而且提高了识别率.     

Sparse sample self-representation for subspace clustering

This paper proposes a new subspace clustering method based on sparse sample self-representation (SSR). The proposed method considers SSR to solve the problem that affinity matrix does not strictly follow the structure of subspace, and also utilizes sparse constraint to ensure the robustness to noise and outliers in subspace clustering. Specifically, we propose to first construct a self-representation matrix for all samples and combine an l ₁-norm regularizer with an l _2,1-norm regularizer to guarantee that each sample can be represented as a sparse linear combination of its related samples. Then, we conduct the resulting matrix to build an affinity matrix. Finally, we apply spectral clustering on the affinity matrix to conduct clustering. In order to validate the effectiveness of the proposed method, we conducted experiments on UCI datasets, and the experimental results showed that our proposed method reduced the minimal clustering error, outperforming the state-of-the-art methods.

     

Single-channel source separation of multi-component radar signal based on EVD and ICA

This study explored a novel method based on eigenvalue decomposition (EVD) and independent component analysis (ICA) to separate the multi-component radar signal in the single channel. By exploiting the generalized periodicity of the radar signal, the proposed method structures the multi-dimensional matrix from the observed signal in single-channel through EVD, then applies ICA to the matrix to determine the basic waveform of each component, and finally reconstructs the component signals. Simulation results confirmed the effectiveness of the proposed method and compared it with other methods, although the performance of proposed approach is a bit worse than some other method when processing radar signals, the most outstanding advantage of the proposed approach is that it does not require any other known conditions, and it can recover the component signals with a satisfactory level, so it can yet be regarded as an effective method.     

一种人脸本征空间的特征提取算法

传统线性子空间算法在提取类内散度矩阵的特征向量时,存在偏差、过拟合和推广能力差的问题。为此,提出一种新的子空间算法。将类内散度矩阵的特征空间分解为2个子解空间,即主成分空间和零空间,再利用本征谱模型对2个空间分别进行正则化。在ORL人脸库上的实验表明,该算法使用较少的特征维数就能达到与传统算法相同的识别率。     

基于\begin{document}$ \pmb k $\end{document}近邻主元得分差分的故障检测策略

针对具有非线性和多模态特征过程的故障检测问题, 本文提出一种基于k近邻主元得分差分的故障检测策略.首先, 通过主元分析(Principal component analysis, PCA)方法计算样本的真实得分.然后, 应用样本的k近邻均值计算样本估计得分.接下来, 通过上述两种得分计算样本的得分差分矩阵和残差矩阵, 其中残差矩阵由样本的估计得分计算得到,这区别于传统方法.最后, 在差分子空间和残差子空间中分别建立新的统计指标进行故障检测.值得注意的是本文的得分差分方法能够消除数据结构对过程故障检测的影响, 同时, 新的统计量能够提高过程的故障检测率.将本文方法在两个模拟例子和Tennessee Eastman (TE)过程中进行测试, 并与传统方法如PCA、KPCA、DPCA和~FD-kNN等进行对比分析, 测试结果证明了本文方法的有效性.