A novel semi-supervised canonical correlation analysis and extensions for multi-view dimensionality reduction

Canonical correlation analysis (CCA) is an efficient method for dimensionality reduction on two-view data. However, as an unsupervised learning method, CCA cannot utilize partly given label information in multi-view semi-supervised scenarios. In this paper, we propose a novel two-view semi-supervised learning method, called semi-supervised canonical correlation analysis based on label propagation (LPbSCCA). LPbSCCA incorporates a new sparse representation based label propagation algorithm to infer label information for unlabeled data. Specifically, it firstly constructs dictionaries consisting of all labeled samples; and then obtains reconstruction coefficients of unlabeled samples using sparse representation technique; at last, by combining given labels of labeled samples, estimates label information for unlabeled ones. After that, it constructs soft label matrices of all samples and probabilistic within-class scatter matrices in each view. Finally, in order to enhance discriminative power of features, it is formulated to maximize the correlations between samples of the same class from cross views, while minimizing within-class variations in the low-dimensional feature space of each view simultaneously. Furthermore, we also extend a general model called LPbSMCCA to handle data from multiple (more than two) views. Extensive experimental results from several well-known datasets demonstrate that the proposed methods can achieve better recognition performances and robustness than existing related methods.     

Semi-Supervised Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a popular method for low-rank approximation of nonnegative matrix, providing a useful tool for representation learning that is valuable for clustering and classification. When a portion of data are labeled, the performance of clustering or classification is improved if the information on class labels is incorporated into NMF. To this end, we present semi-supervised NMF (SSNMF), where we jointly incorporate the data matrix and the (partial) class label matrix into NMF. We develop multiplicative updates for SSNMF to minimize a sum of weighted residuals, each of which involves the nonnegative 2-factor decomposition of the data matrix or the label matrix, sharing a common factor matrix. Experiments on document datasets and EEG datasets in BCI competition confirm that our method improves clustering as well as classification performance, compared to the standard NMF, stressing that semi-supervised NMF yields semi-supervised feature extraction.     

Joint feature representation and classification via adaptive graph semi-supervised nonnegative matrix factorization

As an effective feature representation method, non-negative matrix factorization (NMF) cannot utilize the label information sufficiently, which makes it not be suitable for the classification task. In this paper, we propose a joint feature representation and classification framework named adaptive graph semi-supervised nonnegative matrix factorization (AGSSNMF). Firstly, to enhance the discriminative ability of feature representation and accomplish the classification task, a regression model with nonnegative matrix factorization (called as RNMF) is proposed, which exploits the relation between the label information and feature representation. Secondly, to overcome the drawback of insufficient labels, an adaptive graph-based label propagation (refereed as AGLP) model is established, which adopts a local constraint to reflect the local structure of data. Then, we integrate RNMF and AGLP into a unified framework for feature representation and classification. Finally, an iterative optimization algorithm is used to solve the objective function. Extensive experiments show that the proposed framework has excellent performance compared with some well-known methods.     

Sparsity in optical flow and trajectories

In this article, we apply sparse constraints to improve optical flow and trajectories. We apply sparsity in two ways. First, with two-frame optical flow, we enforce a sparse representation of flow patches using a learned overcomplete dictionary. Second, we apply a low-rank constraint to trajectories via robust coupling. Optical flow is an ill-posed underconstrained inverse problem. Many recent approaches use total variation to constrain the flow solution to satisfy color constancy. In our first results presented, we find that learning a 2D overcomplete dictionary from the total variation result and then enforcing a sparse constraint on the flow improves the result. A new technique using partially overlapping patches accelerates the calculation. This approach is implemented in a coarse-to-fine strategy. Our results show that combining total variation and a sparse constraint from a learned dictionary is more effective than total variation alone. In the second part, we compute optical flow and trajectories from an image sequence. Sparsity in trajectories is measured by matrix rank. We introduce a low-rank constraint of linear complexity using random subsampling of the data. We demonstrate that, by using a robust coupling with the low-rank constraint, our approach outperforms baseline methods on general image sequences.     

Towards robust subspace recovery via sparsity-constrained latent low-rank representation

Robust recovery of subspace structures from noisy data has received much attention in visual analysis recently. To achieve this goal, previous works have developed a number of low-rank based methods, among of which Low-Rank Representation (LRR) is a typical one. As a refined variant, Latent LRR constructs the dictionary using both observed and hidden data to relieve the insufficient sampling problem. However, they fail to consider the observation that each data point can be represented by only a small subset of atoms in a dictionary. Motivated by this, we present the Sparse Latent Low-rank representation (SLL) method, which explicitly imposes the sparsity constraint on Latent LRR to encourage a sparse representation. In this way, each data point can be represented by only selecting a few points from the same subspace. Its objective function is solved by the linearized Augmented Lagrangian Multiplier method. Favorable experimental results on subspace clustering, salient feature extraction and outlier detection have verified promising performances of our method.     

基于最大范数的低秩稀疏分解模型

为了更好地解决高维数据矩阵低秩稀疏分解问题,该文提出以Max-范数凸化秩函数的Max极小化模型,并给出该模型的相应算法。在对新模型计算复杂性分析的基础上,该文进一步提出了Max约束模型,改进模型不仅在分解问题中效果良好,且相应的投影梯度算法具有更强的时效性。实验结果表明,该文提出的两组模型对于低秩稀疏分解问题均行之有效。     

基于l0正则化的增量低秩特征学习目标跟踪

为了提高生成型目标跟踪算法在遮挡、背景干扰 等复杂条件下的性能,在稀疏编码模型中引入l₀范数正 则化约束,以减少冗余编码信息并改善目标表观重构效果。同时提出一种新的基于非凸近端 加速梯度的快速迭代算法, 解决由此产生的非凸非光滑优化问题。设计了一种增量低秩学习策略,和传统方法需 要将目标观测数据作为 一个整体进行低秩学习不同,本文方法通过l₀正则化稀疏编码能够有效地对目标低秩特 征子空间进行在线学习和更 新。在多个视频序列上的实验表明:基于l₀正则化的增量低秩学习方法能有效提高目标 跟踪算法的准确率和鲁棒性; 和8种优秀的跟踪算法相比,本文算法在中心误差稳健性和重叠率稳健性两个指标上都取得 了最好结果。     

基于低秩子空间恢复的联合稀疏表示人脸识别算法

 针对阴影、反光及遮挡等原因破坏图像低秩结构这一问题,提出基于低秩子空间恢复的联合稀疏表示识别算法.首先将每个个体的所有训练样本图像看作矩阵 D ,将矩阵 D 分解为低秩矩阵 A 和稀疏误差矩阵 E ,其中 A 表示某类个体的'干净’人脸,严格遵循子空间结构, E 表示由阴影、反光、遮挡等引起的误差项,这些误差项破坏了人脸图像的低秩结构.然后用低秩矩阵 A 和误差矩阵 E 构造训练字典,将测试样本表示为低秩矩阵 A 和误差矩阵 E 的联合稀疏线性组合,利用这两部分的稀疏逼近计算残差,进行分类判别.实验证明该稀疏表示识别算法有效,识别精度得到了有效提高.     

基于低秩表示和学习字典的高光谱图像异常探测

提出一种基于低秩表示和学习字典的高光谱遥感图像异常探测算法.相对于其它低秩矩阵分解方法如鲁棒主成分分析,低秩表示方法更为契合高光谱图像的线性混合模型.该算法将低秩表示模型应用到高光谱图像异常探测问题上来,引入表征背景信息的学习字典,大大增强了低秩表示模型对初始参数的鲁棒性.仿真和实际高光谱数据的实验结果表明,所提出的算法有效地提高了异常的探测率,同时对初始参数具有较好的鲁棒性,可以作为一种解决高光谱图像异常探测的有效手段.     

结合潜在低秩分解和稀疏表示的脑部图像融合

针对低秩分解和稀疏表示(space representation,SR) 造成融合图像信息缺失的问题,提出一种结合潜在低秩分解和SR的脑部图像融合算法。首先,将源图像分解为低秩、稀疏和噪声3种成分,面对不同分解成分特性间的差异,分别构造低秩字典和稀疏字典进行描述:采用加权灰度值的方法处理低秩成分,以保持其轮廓和亮度特征;对于稀疏成分,设计一种多范数加权度量的方法对SR进行改进,以保持其高维信息,剔除噪声成分。比对当前主流的5种算法,在视觉效果和客观指标上,本文方法效果最优。     

Cooperative sparse representation in two opposite directions for semi-supervised image annotation

Recent studies have shown that sparse representation (SR) can deal well with many computer vision problems, and its kernel version has powerful classification capability. In this paper, we address the application of a cooperative SR in semi-supervised image annotation which can increase the amount of labeled images for further use in training image classifiers. Given a set of labeled (training) images and a set of unlabeled (test) images, the usual SR method, which we call forward SR, is used to represent each unlabeled image with several labeled ones, and then to annotate the unlabeled image according to the annotations of these labeled ones. However, to the best of our knowledge, the SR method in an opposite direction, that we call backward SR to represent each labeled image with several unlabeled images and then to annotate any unlabeled image according to the annotations of the labeled images which the unlabeled image is selected by the backward SR to represent, has not been addressed so far. In this paper, we explore how much the backward SR can contribute to image annotation, and be complementary to the forward SR. The co-training, which has been proved to be a semi-supervised method improving each other only if two classifiers are relatively independent, is then adopted to testify this complementary nature between two SRs in opposite directions. Finally, the co-training of two SRs in kernel space builds a cooperative kernel sparse representation (Co-KSR) method for image annotation. Experimental results and analyses show that two KSRs in opposite directions are complementary, and Co-KSR improves considerably over either of them with an image annotation performance better than other state-of-the-art semi-supervised classifiers such as transductive support vector machine, local and global consistency, and Gaussian fields and harmonic functions. Comparative experiments with a nonsparse solution are also performed to show that the sparsity plays an important role in the cooperation of image representations in two opposite directions. This paper extends the application of SR in image annotation and retrieval.     

Graph-based semi-supervised learning with multiple labels

Conventional graph-based semi-supervised learning methods predominantly focus on single label problem. However, it is more popular in real-world applications that an example is associated with multiple labels simultaneously. In this paper, we propose a novel graph-based learning framework in the setting of semi-supervised learning with multiple labels. This framework is characterized by simultaneously exploiting the inherent correlations among multiple labels and the label consistency over the graph. Based on the proposed framework, we further develop two novel graph-based algorithms. We apply the proposed methods to video concept detection over TRECVID 2006 corpus and report superior performance compared to the state-of-the-art graph-based approaches and the representative semi-supervised multi-label learning methods.     

基于Sinkhorn距离特征缩放的多约束非负矩阵分解算法

为了减少原始特征对非负矩阵分解(NMF)算法的共适应性干扰,并提高NMF的子空间学习能力与聚类性能,该文提出一种基于Sinkhorn距离特征缩放的多约束半监督非负矩阵分解算法。首先该算法通过Sinkhorn距离对原始输入矩阵进行特征缩放,提高空间内同类数据特征之间的关联性,然后结合样本标签信息的双图流形结构与范数稀疏约束作为双正则项,使分解后的基矩阵具有稀疏特性和较强的空间表达能力,最后,通过KKT条件对所提算法目标函数的进行优化推导,得到有效的乘法更新规则。通过在多个图像数据集以及平移噪声数据上的聚类实验结果对比分析,该文所提算法具有较强的子空间学习能力,且对平移噪声有更强的鲁棒性。     

基于低秩分解的联合动态稀疏表示多观测样本分类算法

通过互联网易获得同一对象的多个无约束的观测样本,针对如何解决无约束观测样本带来的识别困难及充分利用多观测样本数据信息提高其分类性能问题,提出基于低秩分解的联合动态稀疏表示多观测样本分类算法.该算法首先寻找到一组最佳的图像变换域,使得变换图像可以分解成一个低秩矩阵和一个相关的稀疏误差矩阵;然后对低秩矩阵和稀疏误差矩阵分别进行联合动态稀疏表示,以便充分利用类级的相关性和原子级的差异性,即使多观测样本的稀疏表示向量在类级别上分享相同的稀疏模型,而在原子级上采用不同的稀疏模型;最后利用总的稀疏重建误差进行类别判决.在CMU-PIE人脸数据库、ETH-80物体识别数据库、USPS手写体数字数据库和UMIST人脸数据库上进行对比实验,实验结果表明本方法的优越性.     

Spectral clustering steered low-rank representation for subspace segmentation

Low-rank representation (LRR) and its variations have achieved great successes in subspace segmentation tasks. However, the segmentation processes of the existing LRR-related methods are all divided into two separated steps: affinity graphs construction and segmentation results obtainment. In the second step, normalize cut (Ncut) algorithm is used to get the final results based on the constructed graphs. This implies that the affinity graphs obtained by LRR-related algorithms may not be most suitable for Ncut, and the best results are not guaranteed to be achieved. In this paper, we propose a spectral clustering steered LRR representation algorithm (SCSLRR) which combines the objection functions of Ncut, K-means and LRR together. By solving a joint optimization problem, SCSLRR is able to find low-rank affinity matrices which are most beneficial for Ncut to get best segmentation results. The extensive experiments of subspace segmentation on several benchmark datasets show that SCSLRR dominates the related methods.     

基于信号暂态稀疏表示的AIS辐射源个体识别方法

针对民用船舶自动报告系统通信辐射源个体识别问题,该文提出一种基于信号暂态稀疏表示的个体识别方法。该算法求解一个充分利用信号暂态样本类别信息且可保持样本稀疏表示结构的投影变换,来提取低维个体特征矢量。该算法通过最大化类间特征的重构误差和最小化类内特征的重构误差来构造目标函数求解投影变换,并在低维辨别子空间以最小稀疏表示重构误差准则来判定测试样本类别属性。对实际数据处理结果表明该文提出的新算法可有效识别不同辐射源个体;对辐射源暂态信号建模仿真结果,验证了该文算法的正确性和有效性,且平均正确识别率优于现有算法。      

有监督低秩子空间恢复的正则鲁棒稀疏表示人脸识别算法

针对训练样本和测试样本均存在光照及遮挡时,破坏图像低秩结构问题,本文提出基于监督低秩子空间恢复的正则鲁棒稀疏表示人脸识别算法。首先,将所有训练样本构造成矩阵D,对矩阵D进行监督低秩矩阵分解,分解为低秩类相关结构A,低秩类内差异结构B和稀疏误差结构E;然后用主成分分析方法找到类相关结构A低秩子空间的变换矩阵;再通过变换矩阵将训练样本和测试样本投影到低秩子空间;最后,在低秩子空间中,通过正则鲁棒稀疏编码进行加权分类识别。在AR和Extended Yale B公开人脸数据库上的实验结果验证本文算法的有效性及鲁棒性。      

Sparse representation for face recognition by discriminative low-rank matrix recovery

This paper proposes a discriminative low-rank representation (DLRR) method for face recognition in which both the training and test samples are corrupted owing to variations in occlusion and disguise. The proposed method extends the sparse representation-based classification algorithm by incorporating the low-rank structure of data representation. The DLRR algorithm recovers a clean dictionary with enhanced discrimination ability from the corrupted training samples for sparse representation. Simultaneously, it learns a low-rank projection matrix to correct corrupted test samples by projecting them onto their corresponding underlying subspaces. The dictionary elements from different classes are encouraged to be as independent as possible by regularizing the structural incoherence of the original training samples. This leads to a compact representation of a corrected test sample by a linear combination of more dictionary elements from the corrected class. The experimental results on benchmark databases show the effectiveness and robustness of our face recognition technique.     

Indoor localization via -graph regularized semi-supervised manifold learning

In this paper,a new l1-graph regularized semi-supervised manifold learning(LRSML) method is proposed for indoor localization.Due to noise corruption and non-linearity of received signal strength(RSS),traditional approaches always fail to deliver accurate positioning results.The l1-graph is constructed by sparse representation of each sample with respect to remaining samples.Noise factor is considered in the construction process of l1-graph,leading to more robustness compared to traditional k-nearest-neighbor graph(KNN-graph).The KNN-graph construction is supervised,while the l1-graph is assumed to be unsupervised without harnessing any data label information and uncovers the underlying sparse relationship of each data.Combining KNN-graph and l1-graph,both labeled and unlabeled information are utilized,so the LRSML method has the potential to convey more discriminative information compared to conventional methods.To overcome the non-linearity of RSS,kernel-based manifold learning method(K-LRSML) is employed through mapping the original signal data to a higher dimension Hilbert space.The efficiency and superiority of LRSML over current state of art methods are verified with extensive experiments on real data.     

Denoising by low-rank and sparse representations

Due to the ill-posed nature of image denoising problem, good image priors are of great importance for an effective restoration. Nonlocal self-similarity and sparsity are two popular and widely used image priors which have led to several state-of-the-art methods in natural image denoising. In this paper, we take advantage of these priors and propose a new denoising algorithm based on sparse and low-rank representation of image patches under a nonlocal framework. This framework consists of two complementary steps. In the first step, noise removal from groups of matched image patches is formulated as recovery of low-rank matrices from noisy data. This problem is then efficiently solved under asymptotic matrix reconstruction model based on recent results from random matrix theory which leads to a parameter-free optimal estimator. Nonlocal learned sparse representation is adopted in the second step to suppress artifacts introduced in the previous estimate. Experimental results, demonstrate the superior denoising performance of the proposed algorithm as compared with the state-of-the-art methods.