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,...     

主奇异子空间跟踪算法与性能分析

主奇异子空间分析是一种自适应的神经网络信号处理技术,广泛应用于现代信号处理中.本文提出一种新的主奇异子空间跟踪信息准则,并以此为基础推导出一种在线的梯度流神经网络算法.理论分析表明,信息准则具有唯一的全局最小值,且最小值对应的状态矩阵能够恰好张成输入信号的主奇异子空间.该算法具有良好的收敛能力,强大的自稳定性能,且当输入信号呈现出奇异互相关特性时,仍呈现出良好的跟踪效果.分别采用李雅普诺夫函数方法和常微分方程方法分析算法的收敛性能和自稳定性. MATLAB仿真算例验证了算法的性能.     

A new subspace identification approach based on principal component analysis

Principal component analysis (PCA) has been widely used for monitoring complex industrial processes with multiple variables and diagnosing process and sensor faults. The objective of this paper is to develop a new subspace identification algorithm that gives consistent model estimates under the errors-in-variables (EIV) situation. In this paper, we propose a new subspace identification approach using principal component analysis. PCA naturally falls into the category of EIV formulation, which resembles total least squares and allows for errors in both process input and output. We propose to use PCA to determine the system observability subspace, the A, B, C, and D matrices and the system order for an EIV formulation. Standard PCA is modified with instrumental variables in order to achieve consistent estimates of the system matrices. The proposed subspace identification method is demonstrated using a simulated process and a real industrial process for model identification and order determination. For comparison the MOESP algorithm and N4SID algorithm are used as benchmarks to demonstrate the advantages of the proposed PCA based subspace model identification (SMI) algorithm.     

An adaptive learning algorithm for principal component analysis

Principal component analysis (PCA) is one of the most general purpose feature extraction methods. A variety of learning algorithms for PCA has been proposed. Many conventional algorithms, however, will either diverge or converge very slowly if learning rate parameters are not properly chosen. In this paper, an adaptive learning algorithm (ALA) for PCA is proposed. By adaptively selecting the learning rate parameters, we show that the m weight vectors in the ALA converge to the first m principle component vectors with almost the same rates. Comparing with the Sanger's generalized Hebbian algorithm (GHA), the ALA can quickly find the desired principal component vectors while the GHA fails to do so. Finally, simulation results are also included to illustrate the effectiveness of the ALA.     

Online nonparametric discriminant analysis for incremental subspace learning and recognition

This paper presents a novel approach for online subspace learning based on an incremental version of the nonparametric discriminant analysis (NDA). For many real-world applications (like the study of visual processes, for instance) it is impossible to know beforehand the number of total classes or the exact number of instances per class. This motivated us to propose a new algorithm, in which new samples can be added asynchronously, at different time stamps, as soon as they become available. The proposed technique for NDA-eigenspace representation has been used in pattern recognition applications, where classification of data has been performed based on the nearest neighbor rule. Extensive experiments have been carried out both in terms of classification accuracy and execution time. On the one hand, the results show that the Incremental NDA converges towards the classical NDA at the end of the learning process and furthermore. On the other hand, Incremental NDA is suitable to update a large knowledge representation eigenspace in real-time. Finally, the use of our method on a real-world application is presented.     

CBIR with a subspace tree: principal component analysis versus averaging

The subspace tree is an indexing method for large multi-media databases. The search in such a tree starts at the subspace with the lowest dimension. In this subspace, the set of all possible similar images is determined. In the next subspace, additional metric information corresponding to a higher dimension is used to reduce this set. We compare theoretically and empirically data-dependent mappings into subspaces (principal component analysis) with data-independent mapping (averaging). The empirical experiments are performed on an image collection of 30,000 images.     

Face recognition based on random subspace method and tensor subspace analysis

In this paper, we propose a novel method, called random subspace method (RSM) based on tensor (Tensor-RS), for face recognition. Different from the traditional RSM which treats each pixel (or feature) of the face image as a sampling unit, thus ignores the spatial information within the face image, the proposed Tensor-RS regards each small image region as a sampling unit and obtains spatial information within small image regions by using reshaping image and executing tensor-based feature extraction method. More specifically, an original whole face image is first partitioned into some sub-images to improve the robustness to facial variations, and then each sub-image is reshaped into a new matrix whose each row corresponds to a vectorized small sub-image region. After that, based on these rearranged newly formed matrices, an incomplete random sampling by row vectors rather than by features (or feature projections) is applied. Finally, tensor subspace method, which can effectively extract the spatial information within the same row (or column) vector, is used to extract useful features. Extensive experiments on four standard face databases (AR, Yale, Extended Yale B and CMU PIE) demonstrate that the proposed Tensor-RS method significantly outperforms state-of-the-art methods.

     

User modeling: Through statistical analysis and subspace learning

One of the challenges which must be faced in the field of the information processing is the need to cope with huge amounts of data. There exist many different environments in which large quantities of information are produced. For example, in a command-line interface, a computer user types thousands of commands which can hide information about the behavior of her/his. However, processing this kind of streaming data on-line is a hard problem.This paper addresses the problem of the classification of streaming data from a dimensionality reduction perspective. We propose to learn a lower dimensionality input model which best represents the data and improves the prediction performance versus standard techniques. The proposed method uses maximum dependence criteria as distance measurement and finds the transformation which best represents the command-line user. We also make a comparison between the dimensionality reduction approach and using the full dataset. The results obtained give some deeper understanding in advantages and drawbacks of using both perspectives in this user classifying environment.     

Online multi-view subspace learning via group structure analysis for visual object tracking

In this paper, we focus on incrementally learning a robust multi-view subspace representation for visual object tracking. During the tracking process, due to the dynamic background variation and target appearance changing, it is challenging to learn an informative feature representation of tracking object, distinguished from the dynamic background. To this end, we propose a novel online multi-view subspace learning algorithm (OMEL) via group structure analysis, which consistently learns a low-dimensional representation shared across views with time changing. In particular, both group sparsity and group interval constraints are incorporated to preserve the group structure in the low-dimensional subspace, and our subspace learning model will be incrementally updated to prevent repetitive computation of previous data. We extensively evaluate our proposed OMEL on multiple benchmark video tracking sequences, by comparing with six related tracking algorithms. Experimental results show that OMEL is robust and effective to learn dynamic subspace representation for online object tracking problems. Moreover, several evaluation tests are additionally conducted to validate the efficacy of group structure assumption.     

A class of learning algorithms for principal component analysis andminor component analysis

In this paper, we first propose a differential equation for the generalized eigenvalue problem. We prove that the stable points of this differential equation are the eigenvectors corresponding to the largest eigenvalue. Based on this generalized differential equation, a class of principal component analysis (PCA) and minor component analysis (MCA) learning algorithms can be obtained. We demonstrate that many existing PCA and MCA learning algorithms are special cases of this class, and this class includes some new and simpler MCA learning algorithms. Our results show that all the learning algorithms of this class have the same order of convergence speed, and they are robust to implementation error.     

A class of learning algorithms for principal component analysis andminor component analysis

Principal component analysis (PCA) and minor component analysis (MCA) are a powerful methodology for a wide variety of applications such as pattern recognition and signal processing. In this paper, we first propose a differential equation for the generalized eigenvalue problem. We prove that the stable points of this differential equation are the eigenvectors corresponding to the largest eigenvalue. Based on this generalized differential equation, a class of PCA and MCA learning algorithms can be obtained. We demonstrate that many existing PCA and MCA learning algorithms are special cases of this class, and this class includes some new and simpler MCA learning algorithms. Our results show that all the learning algorithms of this class have the same order of convergence speed, and they are robust to implementation error.     

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。     

非监督子空间学习中关联度量多维尺度分析

多维尺度分析已经在维度约减和数据挖掘领域得到了广泛应用。MDS的主要缺点是其定义在训练数据上,对于新的测试样本无法直接获得映射结果。另外,MDS基于欧氏距离度量,不适合获取相似数据中的非线性流形结构。将MDS扩展到关联度量空间,称为关联度量多维尺度分析(CMDS)。与传统MDS在训练数据中完成映射,进而缩小空间范围相比,CMDS 能够直接获得测试样本映射结果。此外,CMDS基于关联度量,能够有效学习相似数据中的非线性流形结构。理论分析表明,CMDS可以利用核方法扩展到新特征空间,解决非线性问题。实验结果表明,CMDS及其核形式KG-CMDS性能优于常用传统降维方法。     

Akin-based Orthogonal Space (AOS): a subspace learning method for face recognition

A projection learning space is an approach to mapping a high-dimensional vector space to a lower dimensional vector space. In this paper, we proposed an algorithm, namely, AOS: Akin based Orthogonal Space. The algorithm is driven with two major targets - (i) to choose most representative image(s) from a group of face images of an individual, (ii) finally to produce a learning space which follows a Gaussian distribution to reduce the influence of grosses like non-Gaussianly distributed data noises, variations in facial expression and illumination. To improve the recognition performance, we proposed another approach i.e. fusion between AOS features and a custom VGG features. We justify the effectiveness of the proposed approaches over five benchmark face datasets using two classifiers. Experimental results show that the proposed learning algorithm has obtained maximum of 92.22% recognition rate, as well deep learning based fusion approch greatly improves the recognition accuracy. The comparative performances demonstrate that the proposed method could significantly outperform other relevant subspace learning methods.

     

Robust hebbian learning and noisy principal component analysis

The classical analysis of a stochastic signal into principal components compresses the signal using an optimal selection of linear features. Noisy Principal Component Analysis (NPCA) is an extension of PCA under the assumption that the extracted features are unreliable, and the unreliability is modeled by additive noise. The applications of this assumption appear for instance, in communications problems with noisy channels. The level of noise in the NPCA features affects the reconstruction error in a way resembling the water-filling analogy in information theory. Robust neural network models for Noisy PCA can be defined with respect to certain synaptic weight constraints. In this paper we present the NPCA theory related to a particularly simple and tractable constraint which allows us to evaluate the robustness of old PCA Hebbian learning rules. It turns out that those algorithms are not optimally robust in the sense that they produce a zero solution when the noise power level reaches half the limit set by NPCA. In fact, they are not NPCA-optimal for any other noise levels except zero. Finally, we propose new NPCA-optimal robust Hebbian learning algorithms for multiple adaptive noisy principal component extraction.     

Charting-based subspace learning for video-based human action classification

We use charting, a non-linear dimensionality reduction algorithm, for articulated human motion classification in multi-view sequences or 3D data. Charting estimates automatically the intrinsic dimensionality of the latent subspace and preserves local neighbourhood and global structure of high-dimensional data. We classify human actions sub-sequences of varying lengths of skeletal poses, adopting a multi-layered subspace classification scheme with layered pruning and search. The sub-sequences of varying lengths of skeletal poses can be extracted using either markerless articulated tracking algorithms or markerless motion capture systems. We present a qualitative and quantitative comparison of single-subspace and multiple-subspace classification algorithms. We also identify the minimum length of action skeletal poses, required for accurate classification, using competing classification systems as the baseline. We test our motion classification framework on HumanEva, CMU, HDM05 and ACCAD mocap datasets and achieve similar or better classification accuracy than various comparable systems.     

Towards learning a semantic-consistent subspace for cross-modal retrieval

A great many of approaches have been developed for cross-modal retrieval, among which subspace learning based ones dominate the landscape. Concerning whether using the semantic label information or not, subspace learning based approaches can be categorized into two paradigms, unsupervised and supervised. However, for multi-label cross-modal retrieval, supervised approaches just simply exploit multi-label information towards a discriminative subspace, without considering the correlations between multiple labels shared by multi-modalities, which often leads to an unsatisfactory retrieval performance. To address this issue, in this paper we propose a general framework, which jointly incorporates semantic correlations into subspace learning for multi-label cross-modal retrieval. By introducing the HSIC-based regularization term, the correlation information among multiple labels can be not only leveraged but also the consistency between the modality similarity from each modality is well preserved. Besides, based on the semantic-consistency projection, the semantic gap between the low-level feature space of each modality and the shared high-level semantic space can be balanced by a mid-level consistent one, where multi-label cross-modal retrieval can be performed effectively and efficiently. To solve the optimization problem, an effective iterative algorithm is designed, along with its convergence analysis theoretically and experimentally. Experimental results on real-world datasets have shown the superiority of the proposed method over several existing cross-modal subspace learning methods.

     

Regularized nonnegative shared subspace learning

Joint modeling of related data sources has the potential to improve various data mining tasks such as transfer learning, multitask clustering, information retrieval etc. However, diversity among various data sources might outweigh the advantages of the joint modeling, and thus may result in performance degradations. To this end, we propose a regularized shared subspace learning framework, which can exploit the mutual strengths of related data sources while being immune to the effects of the variabilities of each source. This is achieved by further imposing a mutual orthogonality constraint on the constituent subspaces which segregates the common patterns from the source specific patterns, and thus, avoids performance degradations. Our approach is rooted in nonnegative matrix factorization and extends it further to enable joint analysis of related data sources. Experiments performed using three real world data sets for both retrieval and clustering applications demonstrate the benefits of regularization and validate the effectiveness of the model. Our proposed solution provides a formal framework appropriate for jointly analyzing related data sources and therefore, it is applicable to a wider context in data mining.     

基于子空间学习的快速自适应局部比值和判别分析

降维是处理高维数据的一项关键技术,其中线性判别分析及其变体算法均为有效的监督算法。然而大多数判别分析算法存在以下缺点：a)无法选择更具判别性的特征;b)忽略原始空间中噪声和冗余特征的干扰;c)更新邻接图的计算复杂度高。为了克服以上缺点,提出了基于子空间学习的快速自适应局部比值和判别分析算法。首先,提出了统一比值和准则及子空间学习的模型,以在子空间中探索数据的潜在结构,选择出更具判别信息的特征,避免受原始空间中噪声的影响;其次,采用基于锚点的策略构造邻接图来表征数据的局部结构,加速邻接图学习;然后,引入香农熵正则化,以避免平凡解;最后,在多个数据集上进行了对比实验,验证了算法的有效性。