基于迁移子空间的半监督领域自适应方法

传统子空间学习方法在对齐领域总体分布时往往忽略样本类别信息,若原始样本判别力不足,将难以保证投影后子空间中样本的判别性.针对该问题,提出迁移子空间的半监督领域自适应方法.通过充分利用样本类别标签先验信息,在得到具有判别性子空间的同时充分挖掘重构矩阵中蕴含的鉴别信息,增强子空间跨领域特征表达的鉴别力和鲁棒性,提高模型的分类性能.在领域自适应问题常用的基准图像数据集上进行实验,其结果表明,该算法有较好的分类效果.     

引入低秩约束先验的深度子空间聚类

大多数子空间聚类算法将高维数据映射到低维子空间时不能较好捕获数据间几何结构.针对上述问题,文中提出引入低秩约束先验的深度子空间聚类算法,兼顾数据全局和局部结构信息.算法结合低秩表示与深度自编码器,利用低秩约束捕获数据全局结构,并将约束神经网络的潜在特征表示为低秩.自编码通过最小化重构误差进行非线性低维子空间映射,保留数据的局部特性.以多元逻辑回归函数作为判别模型,预测子空间分割.整个算法在无监督联合学习框架下进行优化.在5个数据集上的实验验证文中方法的有效性.     

烟花算法优化的软子空间MR图像聚类算法

现有的软子空间聚类算法在分割MR图像时易受随机噪声的影响,而且算法因依赖于初始聚类中心的选择而容易陷入局部最优,导致分割效果不理想.针对这一问题,提出一种基于烟花算法的软子空间MR图像聚类算法.算法首先设计一个结合界约束与噪声聚类的目标函数,弥补现有算法对噪声数据敏感的缺陷,并提出一种隶属度计算方法,快速、准确地寻找簇类所在子空间;然后,在聚类过程中引入自适应烟花算法,有效地平衡局部与全局搜索,弥补现有算法容易陷入局部最优的不足.EWKM,FWKM,FSC,LAC算法在UCI数据集、人工合成图像、Berkeley图像数据集以及临床乳腺MR图像、脑部MR图像上的聚类结果表明,所提出的算法不仅在UCI数据集上能够取得较好的结果,而且对图像聚类也具有较好的抗噪性能,尤其是对MR图像的聚类具有较高的精度和鲁棒性,能够较为有效地实现MR图像的分割.     

一种基于融合重构的子空间学习的零样本图像分类方法

图像分类是计算机视觉中一个重要的研究子领域.传统的图像分类只能对训练集中出现过的类别样本进行分类.然而现实应用中,新的类别不断涌现,因而需要收集大量新类别带标记的数据,并重新训练分类器.与传统的图像分类方法不同,零样本图像分类能够对训练过程中没有见过的类别的样本进行识别,近年来受到了广泛的关注.零样本图像分类通过语义空间建立起已见类别和未见类别之间的关系,实现知识的迁移,进而完成对训练过程中没有见过的类别样本进行分类.现有的零样本图像分类方法主要是根据已见类别的视觉特征和语义特征,学习从视觉空间到语义空间的映射函数,然后利用学习好的映射函数,将未见类别的视觉特征映射到语义空间,最后在语义空间中用最近邻的方法实现对未见类别的分类.但是由于已见类和未见类的类别差异,以及图像的分布不同,从而容易导致域偏移问题.同时直接学习图像视觉空间到语义空间的映射会导致信息损失问题.为解决零样本图像分类知识迁移过程中的信息损失以及域偏移的问题,本文提出了一种图像分类中基于子空间学习和重构的零样本分类方法.该方法在零样本训练学习阶段,充分利用未见类别已知的信息,来减少域偏移,首先将语义空间中的已见类别和未见类别之间的关系迁移到视觉空间中,学习获得未见类别视觉特征原型.然后根据包含已见类别和未见类别在内的所有类别的视觉特征原型所在的视觉空间和语义特征原型所在的语义空间,学习获得一个潜在类别原型特征空间,并在该潜在子空间中对齐视觉特征和语义特征,使得所有类别在潜在子空间中的表示既包含视觉空间下的可分辨性信息,又包含语义空间下的类别关系信息,同时在子空间的学习过程中利用重构约束,减少信息损失,同时也缓解了域偏移问题.最后零样本分类识别阶段,在不同的空间下根据最近邻算法对未见类别样本图像进行分类.本文的主要贡献在于:一是通过对语义空间中类别间关系的迁移,学习获得视觉空间中未见类别的类别原型,使得在训练过程中充分利用未见类别的信息,一定程度上缓解域偏移问题.二是通过学习一个共享的潜在子空间,该子空间既包含了图像视觉空间中丰富的判别性信息,也包含了语义空间中的类别间关系信息,同时在子空间学习过程中,通过重构,缓解知识迁移过程中信息损失的问题.本文在四个公开的零样本分类数据集上进行对比实验,实验结果表明本文提出的零样本分类方法取得了较高的分类平均准确率,证明了本文方法的有效性.     

基于L2,1模和图正则化的低秩迁移子空间学习

本文提出一种基于L_(2,1)模和图正则化的低秩迁移子空间学习方法.首先,在低秩重构过程中通过对重构矩阵施加具有旋转不变性的L_(2,1)模约束,可在挖掘目标域数据的关键特征的同时提高算法对不同姿态图片分类的鲁棒性.其次,在目标函数中引入图结构的正则化,使得迁移时数据中的局部几何结构信息得以充分利用,进一步提高了分类性能.最后,为解决源域数据较少导致的欠完备特征空间覆盖问题,在公共子空间中利用源域数据和目标域数据联合构造字典,保证了重构的鲁棒性.在Caltech256, Office, CMU–PIE, COIL20, USPS, MNIST, VOC2007和MSRC数据库上的大量对比实验验证了本文方法的有效性和鲁棒性.     

基于线性判别回归的最近-最远子空间分类鲁棒人脸识别

针对人脸识别中小样本问题导致类依赖子空间不完善而严重影响识别性能的问题,提出一种基于线性判别回归的最近-最远子空间分类算法。首先,基于线性判别回归,利用最近子空间分类器度量测试图像与单一类之间的关系;然后,利用所提出的最远子空间分类器度量测试图像与训练图像之间的关系;最后,结合最近、最远子空间分类器,利用类依赖子空间的不同特性完成人脸的分类识别。在三个公开的人脸数据库ORL、AR及扩展Yale B上的实验验证了该算法的有效性。实验结果表明,相比其他几种分类算法,该算法取得了更好的识别效果。     

丰富图像标签的正则化非负矩阵分解方法

目的 随着Web2.0技术的进步,以用户生成内容为中心的社交网站蓬勃发展,也使得基于图像标签的图像检索技术越来越重要。但是,由于用户标注时的随意性和个性化,导致用户提交的图像标签不够完备,降低了图像检索的准确性。方法 针对这一问题,提出一种正则化的非负矩阵分解方法来丰富图像欠完备的标签,提高图像标签的完备性。利用非负矩阵分解的方法将原始的标签-图像矩阵投影到潜在的低秩空间里消除噪声,同时利用图像的类内视觉离散度作为正则化项提高消除噪声、丰富标签的效果。结果 利用从社交网站Flickr上下载的大量社交图像进行对比实验,验证了本文方法对丰富图像标签的有效性。通过对比目前流行的优化算法,本文算法获得较高的性能提升,算法平均准确度提高了12.3%。结论 将图像类内视觉离散度作为正则化项的非负矩阵分解算法,能较好地丰富社交图像的标签,解决网络图像标签的欠完备问题。     

结合Fisher判别分析和稀疏编码的图像场景分类

视觉词典法是当前广泛使用的一种图像表示方法,针对传统视觉词典法存在的表示误差大、空间信息丢失以及判别性弱等问题,提出一种基于Fisher判别稀疏编码的图像场景分类算法.首先利用近邻视觉词汇重构局部特征点,构建局部特征点的非负稀疏局部线性编码,从而有效地利用图像的空间信息;然后在非负稀疏局部线性编码的基础上引入Fisher判别约束准则,构建基于Fisher判别约束的非负稀疏局部线性编码模型,以获得图像的判别稀疏向量表示,增强图像稀疏表示的判别性;最后结合支持向量机(SVM)分类器实现场景分类.实验结果表明,该算法提高了图像稀疏表示的特征分类能力以及分类性能,更有利于场景分类任务.     

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。     

子空间搜索广义主成分分析

GPCA(Generalized Principal Component Analysis)是近几年提出的一种数据聚类和降维方法,它通过将样本聚类为不同的子空间得到样本的低维表达.GPCA方法已经被应用于图像分割、图像聚类等问题.原有的GPCA算法具有指数计算复杂度,很难应用于高维数据的实际处理.文中针对此问题,提出了基于子空间搜索的SGPCA算法,将聚类问题分解为单个平面的单个垂直向量的搜索问题,对不同子空间分别搜索,从而实现多项式复杂度算法.实验表明,新方法不仅计算复杂度低,而且对噪声的鲁棒性也更强.     

局部子空间聚类

现有子空间聚类方法通常以数据全局线性为前提,将每个样本点表示为其他样本点的线性组合,因而导致常见子空间聚类方法不能很好地应用于非线性数据.为克服全局线性表示的局限,借鉴流形学习思想,用k近邻局部线性表示代替全局线性表示,与稀疏子空间聚类和最小二乘子空间聚类方法相结合,提出局部稀疏子空间聚类和局部最小二乘子空间聚类方法,统称局部子空间聚类方法.在双月形数据、6个图像数据集和4个基因表达数据集上进行实验,实验结果表明该方法是有效的.     

Modified Oja's Algorithms For Principal Subspace and Minor Subspace extraction

Principal component extraction and minor component extraction are well known and powerful techniques in time series. Modified Oja's algorithms for extracting principal and minor component subspaces are proposed. The only difference between them is the sign of the first term in the iteration equations. Simulations show that the algorithms are effective.     

Quantum Subspace Measurements

Fundamental studies of quantum measurements and their capacity to acquire information are typically based on scenarios in which the full Hilbert space of the measured quantum system is open to measurement interactions. In this work, we consider a class of incomplete quantum measurements – quantum subspace measurements (QSM’s) – for which all measurement interactions are restricted to an arbitrary but specified subspace of the measured system Hilbert space. We define QSM’s formally through a condition on the measurement Hamiltonian, obtain forms for the post-measurement states and positive operators (POVM elements) associated with QSM’s acting in a specified subspace, and upper bound the accessible information for such measurements. Characteristic features of QSM’s are identified and discussed.     

Subspace Procrustes Analysis

Procrustes analysis (PA) has been a popular technique to align and build 2-D statistical models of shapes. Given a set of 2-D shapes PA is applied to remove rigid transformations. Later, a non-rigid 2-D model is computed by modeling the residual (e.g., PCA). Although PA has been widely used, it has several limitations for modeling 2-D shapes: occluded landmarks and missing data can result in local minima solutions, and there is no guarantee that the 2-D shapes provide a uniform sampling of the 3-D space of rotations for the object. To address previous issues, this paper proposes subspace PA (SPA). Given several instances of a 3-D object, SPA computes the mean and a 2-D subspace that can model rigid and non-rigid deformations of the 3-D object. We propose a discrete (DSPA) and continuous (CSPA) formulation for SPA, assuming that 3-D samples of an object are provided. DSPA extends the traditional PA, and produces unbiased 2-D models by uniformly sampling different views of the 3-D object. CSPA provides a continuous approach to uniformly sample the space of 3-D rotations, being more efficient in space and time. We illustrate the benefits of SPA in two different applications. First, SPA is used to learn 2-D face and body models from 3-D datasets. Experiments on the FaceWarehouse and CMU motion capture (MoCap) datasets show the benefits of our 2-D models against the state-of-the-art PA approaches and conventional 3-D models. Second, SPA learns an unbiased 2-D model from CMU MoCap dataset and it is used to estimate the human pose on the Leeds Sports dataset.     

Incremental Deformation Subspace Reconstruction

Recalculating the subspace basis of a deformable body is a mandatory procedure for subspace simulation, after the body gets modified by interactive applications. However, using linear modal analysis to calculate the basis from scratch is known to be computationally expensive. In the paper, we show that the subspace of a modified body can be efficiently obtained from the subspace of its original version, if mesh changes are small. Our basic idea is to approximate the stiffness matrix by its low‐frequency component, so we can calculate new linear deformation modes by solving an incremental eigenvalue decomposition problem. To further handle nonlinear deformations in the subspace, we present a hybrid approach to calculate modal derivatives from both new and original linear modes. Finally, we demonstrate that the cubature samples trained for the original mesh can be reused in fast reduced force and stiffness matrix evaluation, and we explore the use of our techniques in various simulation problems. Our experiment shows that the updated subspace basis still allows a simulator to generate visual plausible deformation effects. The whole system is efficient and it is compatible with other subspace construction approaches.     

Multi-geometric Sparse Subspace Clustering

Neural Processing Letters - Recently, the Riemannian manifold has received special attention in unsupervised clustering since the real-world visual data usually resides on a special manifold where...     

Local Adaptive Subspace Regression

Incremental learning of sensorimotor transformations in high dimensional spaces is one of the basic prerequisites for the success of autonomous robot devices as well as biological movement systems. So far, due to sparsity of data in high dimensional spaces, learning in such settings required a significant amount of prior knowledge about the learning task, usually provided by a human expert. In this paper we suggest a partial revision of the view. Based on empirical studies, we observed that, despite being globally high dimensional and sparse, data distributions from physical movement systems are locally low dimensional and dense. Under this assumption, we derive a learning algorithm, Locally Adaptive Subspace Regression, that exploits this property by combining a dynamically growing local dimensionality reduction technique as a preprocessing step with a nonparametric learning technique, locally weighted regression, that also learns the region of validity of the regression. The usefulness of the algorithm and the validity of its assumptions are illustrated for a synthetic data set, and for data of the inverse dynamics of human arm movements and an actual 7 degree-of-freedom anthropomorphic robot arm.     

弹性核子空间聚类*

现有子空间聚类算法通常假设数据来自多个线性子空间,无法处理时间序列聚类中存在的非线性和时间轴弯曲问题.为了克服这些局限,通过引入核技巧和弹性距离,提出弹性核低秩表示子空间聚类和弹性核最小二乘回归子空间聚类,统称为弹性核子空间聚类,并从理论上证明弹性核最小二乘回归子空间算法的组效应和弹性核低秩表示子空间聚类算法的收敛性.在5个UCR时间序列数据集上的实验表明本文算法的有效性.     

分块子空间追踪算法

压缩传感理论是一种充分利用信号稀疏性或者可压缩性的全新信号采样理论。该理论表明,通过采集少量的信号测量值就能够实现可稀疏信号的精确重构。本文在研究现有经典重构算法的基础上,提出结合图像分块思想和回溯思想的分块子空间追踪算法（Block Subspace Pursuit, B_SP）用于压缩传感信号的重构。该算法以块结构获取图像,利用回溯过程实现支撑集的自适应筛选,最终实现图像信号的精确重构。实验结果表明,在相同测试条件下,该算法的重构效果无论从主观视觉上还是客观数据上都有不同程度的提高。     

Subspace identification of circulant systems

This article concerns the identification of a class of large scale systems called “circulant systems”. Circulant systems have a special property that allows them to be decomposed into simpler subsystems through a state transformation. This property has been used in literature for control design, and here we show how it can be used for system identification. The approach that is proposed here will both reduce the complexity of the problem as well as provide models which have a circulant structure that can be exploited for control design. A novel identification algorithm for circulant systems based on subspace identification is presented. The algorithm is then tested in simulation on an academic example of circulant system and on a realistic finite element model of a vibrating plate.