基于L1-范数的最大间距准则

在进行线性投影降维时,由于传统的最大间距准则(Maximum Margin Criterion,MMC)算法基于L2-范数,易于受到野值(outliers)及噪声的影响.该文提出一种基于L1-范数的最大间距准则(L1-norm-based MMC,MMC-L1)降维方法,它充分利用L1-范数对野值及噪声的强鲁棒性以及最大间距准则,提出了一种快速迭代优化算法,并给出了其单调收敛到局部最优的证明.在多个图像数据库上的实验验证了该方法的鲁棒性与高效性.     

单训练样本条件下的人脸识别算法研究

由于主成分分析法和线性判别分析法等传统方法对单训练样本的识别能力弱,甚至直接失效。本文提出了二维小波变换与矩阵的最大间距准则或矩阵的线性判别分析相融合的人脸特征提取算法。即首先将原图像进行三层二维小波变换,然后对每层的近似分量分别进行最大间距准则或线性判别分析处理,最后用欧氏距离判别。在ORL人脸数据库上取得的实验结果表明,本文提出的算法能够提高单训练样本条件下的人脸识别率,同时也满足实时性要求。     

Robust L1-norm two-dimensional collaborative representation-based projection for dimensionality reduction

Collaborative representation-based projection (CRP) is a well-known dimensionality reduction technique, which has been proved to have better performance than sparse representation-based projection (SRP) in the fields of recognition and computer vision. However, classical CRP is sensitive to noises and outliers since its objective function is based on L2-norm, and it will suffer from the curse of dimensionality as it is used for images processing. In this paper, a novel CRP model, named L1-norm two-dimensional collaborative representation-based projection (L1-2DCRP) and an efficient iterative algorithm to solve it are proposed. Different from conventional CRP, the optimal problem in our proposed model is a L1-norm-based maximization and the vector data is extended to matrix date. The proposed algorithm is theoretically proved to be monotonously convergent, and more robust to noises and outliers since L1-norm is used. Experimental results on CMU Multi-PIE, COIL20, FERET and ORL face databases validate the effectiveness of L1-2DCRP compared with several state-of-the-art approaches.     

基于戴帽L1范数的双支持向量机

针对双支持向量机模型易受异常点影响导致泛化性能较低的问题,提出了一种基于戴帽L1范数的双支持向量机模型.采用带有上限值的戴帽L1范数代替L2范数来构造最优化问题,一定程度上削弱了离群点、噪音点对于两个超平面构造的影响,增强了模型的鲁棒性.另外,针对构造的新的双支持向量机模型最优化问题提出了一个简单有效的迭代算法并且在理论上证明了该算法的收敛性.在无噪以及有噪UCI数据集上的实验结果表明,与其它支持向量机模型相比,该模型有着更强的鲁棒性以及稳定性.     

A NEURAL-BASED NONLINEAR L_1-NORM OPTIMIZATION ALGORITHM FOR DIAGNOSIS OF NETWORKS*

Based on exact penalty function, a new neural network for solving the L1-norm optimization problem is proposed. In comparison with Kennedy and Chua's network(1988), it has better properties.Based on Bandler's fault location method(1982), a new nonlinearly constrained L1-norm problem is developed. It can be solved with less computing time through only one optimization processing. The proposed neural network can be used to solve the analog diagnosis L1 problem. The validity of the proposed neural networks and the fault location L1 method are illustrated by extensive computer simulations.     

基于间隔损失和L1范数调节的特征选择方法研究

特征评价和选择是机器学习和模式识别的重要步骤。为了获得稀疏特征子集,结合间隔损失评估策略和L1范数调节技术来获得一种有效的特征选择方法(MLFWL-L1),并将其应用到RBFSVM分类器。实验中,在UCI数据集上将提出的算法与Simba和ReliefF对比表明,验证所提出的算法是一种有效的特征选择方法。     

基于L1-范数的二维线性判别分析

为了避免图像数据向量化后的维数灾难问题,以及增强对野值(outliers)及噪声的鲁棒性,该文提出一种基于L1-范数的2维线性判别分析(L1-norm-based Two-Dimensional Linear Discriminant Analysis, 2DLDA-L1)降维方法。它充分利用L1-范数对野值及噪声的强鲁棒性,并且直接在图像矩阵上进行投影降维。该文还提出一种快速迭代优化算法,并给出了其单调收敛到局部最优的证明。在多个图像数据库上的实验验证了该方法的鲁棒性与高效性。     

基于非负稀疏表示的SAR图像目标识别方法

针对合成孔径雷达(SAR)图像目标识别中存在物体遮挡的情况,该文提出一种基于非负稀疏表示的分类方法。通过分析L0范数和L1范数最小化在求解非负稀疏表示问题上的区别,证明在一定条件下,L1范数最小化方法除了保持解的稀疏性还能得到与输入信号更加相似的原子集合,因此也更加适用于分类问题中。在运动和静止目标获取与识别(MSTAR)数据集上的识别实验结果表明,采用L1范数的非负稀疏表示分类方法能达到较好的识别性能,并且相对传统方法对存在遮挡情况下的识别问题更稳健。     

一种基于L_∞范式的求解已知旋转相机重建算法

基于多幅图像序列的三维重建过程中,相机模型的坐标统一是非常重要的基础。在已知两两相机之间的相对关系的情况下,将相机模型统一至同一世界坐标系,并恢复特征点的三维坐标。本文给出了一种基于L∞范式的求解已知旋转相机重建方法。给出了一种基于L∞范式的几何结构和运动问题的新框架,并用实验证明了算法能够达到很好的性能。     

L2范数正则化鲁棒编码视觉跟踪

针对基于稀疏表示的视觉跟踪计算效率低和易于产生模型漂移的不足,该文提出一种基于L2范数正则化鲁棒编码的视觉跟踪方法。该方法利用L2范数正则化鲁棒编码求解候选目标的编码系数,以粒子滤波为框架,利用候选目标的加权重建误差建立似然模型跟踪目标。为了适应目标的变化并克服模型漂移问题,利用L2范数正则化鲁棒编码估计当前目标的加权矩阵用于遮挡检测,根据遮挡检测结果实现模型更新。对提出的跟踪方法进行实验的结果表明:与现有跟踪方法相比,该方法具有较优的跟踪性能。     

基于无穷范数的二值线性判别分析

线性判别分析（LDA）是监督式的特征提取方法,在人脸识别等领域得到了广泛应用。为了提高特征提取速度,提出了基于无穷范数的线性判别分析方法。传统LDA方法将目标函数表示为类内散布矩阵和类间散布矩阵之差的或者商的L2范数,且通常需要涉及到矩阵求逆和特征值分解问题。与传统方法不同,这里所提方法将目标函数表示为类内散布矩阵和类间散布矩阵之差的无穷范数,而且最优解是以迭代形式得到,避免了耗时的特征值分解。无穷范数使得到的基向量实现了二值化,即元素仅在-1和1两个数字内取值,避免了特征提取时的浮点型点积运算,从而降低了测试时间,提高了效率。在ORL人脸数据库和Yale数据库上的实验表明所提算法是有效的。     

Robust locality preserving projection based on maximum correntropy criterion

Conventional local preserving projection (LPP) is sensitive to outliers because its objective function is based on the L2-norm distance criterion and suffers from the small sample size (SSS) problem. To improve the robustness of LPP against outliers, LPP-L1 uses L1-norm distance metric. However, LPP-L1 does not work ideally when there are larger outliers. We propose a more robust version of LPP, called LPP-MCC, which formulates the objective problem based on maximum correntropy criterion (MCC). The objective problem is efficiently solved via a half-quadratic optimization procedure and the complicated non-linear optimization procedure can thereby be reduced to a simple quadratic optimization at each iteration. Moreover, LPP-MCC avoids the SSS problem because the generalized eigenvalues computation is not involved in the optimization procedure. The experimental results on both synthetic and real-world databases demonstrate that the proposed method can outperform LPP and LPP-L1 when there are large outliers in the training data.     

A Novel Method for the Diagnosis of the Incipient Faults in Analog Circuits Based on LDA and HMM

Diagnosis of incipient faults for electronic systems, especially for analog circuits, is very important, yet very difficult. The methods reported in the literature are only effective on hard faults, i.e., short-circuit or open-circuit of the components. For a soft fault, the fault can only be diagnosed under the occurrence of large variation of component parameters. In this paper, a novel method based on linear discriminant analysis (LDA) and hidden Markov model (HMM) is proposed for the diagnosis of incipient faults in analog circuits. Numerical simulations show that the proposed method can significantly improve the recognition performance. First, to include more fault information, three kinds of original feature vectors, i.e., voltage, autoregression-moving average (ARMA), and wavelet, are extracted from the analog circuits. Subsequently, LDA is used to reduce the dimensions of the original feature vectors and remove their redundancy, and thus, the processed feature vectors are obtained. The LDA is further used to project three kinds of the processed feature vectors together, to obtain the hybrid feature vectors. Finally, the hybrid feature vectors are used to form the observation sequences, which are sent to HMM to accomplish the diagnosis of the incipient faults. The performance of the proposed method is tested, and it indicates that the method has better recognition capability than the popularly used backpropagation (BP) network.     

在小样本条件下直接LDA的理论分析

直接线性鉴别分析(DLDA)是一种以克服小样本问题而提出的LDA扩展方法,被声明利用了包含类内散布矩阵零空间外的所有信息。然而,很多反例表明事实并非如此。为了更深入地了解DLDA的特性,该文从理论上对其进行了分析,得出结论:基于传统Fisher准则的DLDA几乎没利用零空间,将丢失一些有用的鉴别信息;而基于广义Fisher准则的DLDA,若满足一定条件(在高维小样本数据应用中一般都满足)且最优鉴别矢量正交约束,则其等价于零空间LDA和正交LDA。在人脸数据库ORL和YALE上的比较实验结果亦与理论分析一致。     

任意稀疏结构的多量测向量快速稀疏重构算法研究

目前的稀疏重构算法求解多量测向量时存在两个问题:一是计算复杂度高;二是不能实现任意稀疏结构的多量测向量重构.为此,本文提出一种多量测向量快速重构算法.该算法首先构建矩阵平滑零范数法,实现对具有任意稀疏结构的多量测向量的重构,并获得多量测向量的初始支撑集;其次根据稀疏度与量测维度的关系,对初始支撑集进行筛选获得预选支撑集;然后采用贝叶斯组检验方式得到信号重构所需的最终支撑集;最后通过最终支撑集实现信号的重构.该算法充分利用了矩阵平滑零范数法的高效性以及贝叶斯组检验对冗余支撑集的剔除功能,不但实现了稀疏位置随机变化的多量测向量的高效重构,而且保证了算法的精度,并对噪声具有一定的鲁棒性,基于实测数据的ISAR成像实验验证了所提算法的有效性.     

L1-norm-based common spatial patterns

Common spatial patterns (CSP) is a commonly used method of spatial filtering for multichannel electroencephalogram (EEG) signals. The formulation of the CSP criterion is based on variance using L2-norm, which implies that CSP is sensitive to outliers. In this paper, we propose a robust version of CSP, called CSP-L1, by maximizing the ratio of filtered dispersion of one class to the other class, both of which are formulated by using L1-norm rather than L2-norm. The spatial filters of CSP-L1 are obtained by introducing an iterative algorithm, which is easy to implement and is theoretically justified. CSP-L1 is robust to outliers. Experiment results on a toy example and datasets of BCI competitions demonstrate the efficacy of the proposed method.     

Relevance‐Weighted (2D)2LDA Image Projection Technique for Face Recognition

In this paper, a novel image projection technique for face recognition application is proposed which is based on linear discriminant analysis (LDA) combined with the relevance‐weighted (RW) method. The projection is performed through 2‐directional and 2‐dimensional LDA, or (2D)²LDA, which simultaneously works in row and column directions to solve the small sample size problem. Moreover, a weighted discriminant hyperplane is used in the between‐class scatter matrix, and an RW method is used in the within‐class scatter matrix to weigh the information to resolve confusable data in these classes. This technique is called the relevance‐weighted (2D)²LDA, or RW(2D)²LDA, which is used for a more accurate discriminant decision than that produced by the conventional LDA or 2DLDA. The proposed technique has been successfully tested on four face databases. Experimental results indicate that the proposed RW(2D)²LDA algorithm is more computationally efficient than the conventional algorithms because it has fewer features and faster times. It can also improve performance and has a maximum recognition rate of over 97%.     

采用自适应正则参数的超分辨率加权重建

采用L1(一阶)、L2(二阶)范数是当前较为流行的2种图像超分辨率重建算法。在对这2种算法的优缺点进行分析的基础上,提出了一种采用L1和L2范数混合加权的参数自适应双边全变差正则化重建算法,将正则化参数作为重建图像的一个函数。实验证明这种算法有很好的边缘保持和去除椒盐噪声的能力,重建图像的质量有显著提高。     

Automatic image orientation detection

We present an algorithm for automatic image orientation estimation using a Bayesian learning framework. We demonstrate that a small codebook (the optimal size of codebook is selected using a modified MDL criterion) extracted from a learning vector quantizer (LVQ) can be used to estimate the class-conditional densities of the observed features needed for the Bayesian methodology. We further show how principal component analysis (PCA) and linear discriminant analysis (LDA) can be used as a feature extraction mechanism to remove redundancies in the high-dimensional feature vectors used for classification. The proposed method is compared with four different commonly used classifiers, namely k-nearest neighbor, support vector machine (SVM), a mixture of Gaussians, and hierarchical discriminating regression (HDR) tree. Experiments on a database of 16 344 images have shown that our proposed algorithm achieves an accuracy of approximately 98% on the training set and over 97% on an independent test set. A slight improvement in classification accuracy is achieved by employing classifier combination techniques.     

冲击噪声背景下基于稀疏表示的双基地MIMO雷达多目标定位

该文研究了对称稳定分布(SS)冲击噪声下双基地MIMO雷达的多目标定位问题。针对SS噪声下因二阶矩不存在而造成子空间类算法估计性能下降的不足,提出了矩阵行2范数最大的预处理方法对接收数据进行归一化,使得归一化后的协方差矩阵有界,并以拉直后的协方差矩阵构造稀疏线性模型,提出了基于协方差矩阵-近似零范数(Covariance Matrix Smoothed L0 norm, CMSL0)算法进行目标的发射角和接收角估计。仿真实验表明:通过矩阵行2范数最大化预处理之后,MUSIC(Multiple Signal Classification)和CMSL0算法均能有效地估计出目标的角度,并且CMSL0算法的估计精度及对冲击噪声的稳健性均优于MUSIC算法。此外,与MUSIC算法相比,CMSL0算法不要预先估计目标源的数目,且收发阵元不受半波长间隔的限制。