结构化稀疏低秩子空间聚类

通过定义子空间结构化低秩正则项,将其与子空间结构化稀疏子空间聚类模型相结合,给出一个新的统一优化模型。新模型利用数据的类别属性和相似度互相引导,使得相似度具有判别性和一致性,类别属性具有一致性。相似度的判别性有利于将不同子空间的数据分为不同类,而一致性有利于将同一子空间的数据聚为一类。大量实验表明提出的方法优于一些典型的两步法和子空间结构化稀疏子空间聚类模型。     

完全判别分析

针对现有的线性判别分析算法中存在的降维舍弃空间的判别信息丢失问题,以及秩空间和零空间的判别信息难以兼顾的问题,本文提出了一种完全判别分析算法.算法通过新构建一个子空间以及其中的判别矩阵,实现了可以充分使用全空间的判别信息;且新空间的维数较低,算法流程简单,计算代价较小.相关实验结果证实了本文算法较传统判别分析算法有更好的性能和效率.     

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.     

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。     

基于补集零空间与最近空间距离的人脸识别

针对人脸识别中在分类器判别时没有充分利用类间差异的问题,提出一种补集零空间（CNS）算法,并进一步提出结合CNS算法与最近空间距离的人脸识别算法——补集零空间与最近空间距离算法（CNSD）。首先,在训练样本中,对每一种类别的人脸样本,构建其子空间并计算其补集的零空间;其次,计算测试样本与所有子空间和补集零空间的距离,找到最小的子空间距离与最大的补集零空间距离对应的类别,将其判别为测试样本的类别。算法在ORL与AR人脸数据集上进行了测试,当训练样本数较小时,CNS算法与CNSD算法识别率远高于最近邻分类器（NN）算法、最近空间距离（NS）算法、最近最远空间距离（NFS）算法;训练样本数较大时,CNS算法与CNSD算法识别率也略高于NN算法、NS算法、NFS算法。实验结果表明,所提算法能充分利用图像的类间差异,提高人脸识别的成功率。     

语义相似性保持的判别式跨模态哈希

针对跨模态哈希检索方法中存在标签语义利用不充分,从而导致哈希码判别能力弱、检索精度低的问题,提出了一种语义相似性保持的判别式跨模态哈希方法.该方法将异构模态的特征数据投影到一个公共子空间,并结合多标签核判别分析方法将标签语义中的判别信息和潜在关联嵌入到公共子空间中;通过最小化公共子空间与哈希码之间的量化误差提高哈希码的判别能力;此外,利用标签构建语义相似性矩阵,并将语义相似性保留到所学的哈希码中,进一步提升哈希码的检索精度.在LabelMe、MIRFlickr-25k、NUS-WIDE三个基准数据集上进行了大量实验,其结果验证了该方法的有效性.     

基于余类零空间与最近距离的人脸识别算法

提出了一种新的人脸识别算法,即基于余类零空间与最近距离的人脸识别算法. 通过构建不同类别的人脸图像的余类零空间与子空间,可以将不同类别的人脸最大化地区别出来. 本算法的主要思想在于：测试图像与所属类别图像的子空间之间的距离最小,而与所属类别的图像的余类零空间距离最大. 本算法基于ORL数据集与AR数据集进行了测试. 从这些人脸数据集上的测试结果可以看出,本文提出的算法在PCA降维方法的基础上,比一些常见的算法所使用的判别方式更有效,如最近邻分类器（NN）所使用的最近距离判别方式、最近空间分类器（NS）所使用的最近空间距离判别方式、最近最远子空间分类器（NFS）所使用的最近最远空间距离判别方式等.     

广义区间动力系统的能控性

讨论了广义区间动力系统正则性、I-能控与C-能控问题.由于上述问题等价于判别某 个区间矩阵为列满秩,首先得到判别区间矩阵为列满秩的充分条件与充分必要条件,进一步得 到了判别广义区间系统为正则的充分必要条件、I-能控的充分条件与C-能控的充分必要条件. 通过数值实例说明所得到的结果相对于已有结果更具有一般性及有效性.由对偶原理,得到相 应的能观性的判据.     

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。     

基于正则化最小二乘的局部判别投影的人脸识别

受子空间学习和正则化技术的启发,提出正则化最小二乘的局部判别投影,为了获得投影子空间,首先构建类内和类间图,然后推导出计算公式,再使用正则化最小二乘法解出子空间,与普通算法相比,该算法既保持了流形的局部几何结构,又保持了判别结构,在标准人脸数据库上的实验表明该算法有效.     

Dynamic Output Feedback Consensualization of Uncertain Swarm Systems with Time Delays

Consensus analysis and design problems of high‐dimensional discrete‐time swarm systems in directed networks with time delays and uncertainties are dealt with by using output information. Two subspaces are introduced, namely a consensus subspace and a complement consensus subspace. By projecting the state of a swarm system onto the two subspaces, a necessary and sufficient condition for consensus is presented, and based on different influences of time delays and uncertainties, an explicit expression of the consensus function is given which is very important in applications of swarm systems. A method to determine gain matrices of consensus protocols is proposed. Numerical simulations are presented to demonstrate theoretical results.     

Classification by nearness in complementary subspaces

This study introduces a classifier founded on k-nearest neighbours in the complementary subspaces (NCS). The global space, spanned by all training samples, can be decomposed into the direct sum of two subspaces in terms of one class: the projection vectors of this class into one subspace are nonzero, and that into another subspace are zero. A query sample is projected into the two subspaces for each class, respectively. In each subspace, the distance from the projection vector to the mean of its k-nearest neighbours can be calculated, and the final classification rules are designed in terms of the two distances calculated in the two complementary subspaces, respectively. Allowing for the geometric meaning of Gram determinant and kernel trick, the classifier is naturally implemented in the kernel space. The experimental results on 1 synthetic, 13 IDA binary class, and five UCI multi-class data sets show that NCS compares favourably to the comparing classifiers, which is founded on the k-nearest neighbours or the nearest subspace, on almost all the data sets. The classifier can straightforwardly solve multi-classification problems, and the performance is promising.     

Subspace controllability of Boolean networks

Many Boolean control networks contain independent uncontrollable subnetworks, which may affect other nodes; and the rest of the system is called subspace of sub‐controllable states. This paper investigates the problem of subspace controllability under free input sequences, while the presumption that the initial states of those independent subnetworks are designable is canceled. An algorithm based on the common asymptotic periodic properties of the states is developed to find the reachable sets. Accordingly, the existing controllability criteria for subspaces when initial states of subnetworks are designable is improved, and a necessary and sufficient condition of subspace controllability via subnetworks and free inputs is derived. A design technique involving a kind of newly defined addition is presented to construct desired controls.     

Disturbance localization with dead-beat control for linear periodic discrete-time systems

In this paper the classical notion of a controlled invariant subspace, together with its main properties, is extended to the case of linear periodic discrete-time systems, and used for deriving necessary and sufficient solvability conditions for the disturbance-localization problem and a synthesis procedure for the solution. Moreover, the notions of outer and inner controllable subspaces are introduced and studied for the same class of system, thus allowing the derivation of necessary and sufficient solvability conditions for the disturbance-localization problem with output or state dead-beat control and to give synthesis procedures for the solutions.     

Further decomposition for singular systems and its properties on geometric subspace

This paper focuses on the relationship between the geometric subspaces and the structural decomposition of continuous-time singular systems. The original structural decomposition is not capable of revealing explicitly the invariant geometric subspaces for singular systems. As such, a further decomposition is necessary and is thus investigated in this paper. Under a new decomposition proposed, the supremal output-nulling (A,E, ImB)-invariant subspace of singular systems can be clearly expressed in an explicit form, and some of its applications are also addressed.     

Output consensus analysis and design for high-order linear swarm systems: Partial stability method

Output consensus analysis and design problems for high-order linear time-invariant swarm systems with directed interaction topologies are investigated. Firstly, as foundations of our approaches, several conclusions about partial stability are given. Then, two subspaces of the output space of swarm systems, namely an output consensus subspace and a complement output consensus subspace, are introduced. Based on output projection onto the two subspaces and partial stability, necessary and/or sufficient conditions for output consensus and limited-control-energy consensus are proposed respectively, an explicit expression of the output consensus function is presented based on the different contributions of initial states of agents and protocols, and an approach independent of the number of agents is shown to determine the gain matrices of output consensus protocols. Finally, a numerical example is given to demonstrate the theoretical results.     

On almost invariant subspaces for implicit linear discrete-time systems

The concept of almost invariant subspace for an implicit linear discrete-time system is introduced and studied in detail. It is shown also that for regular homogeneous implicit systems the so-called deflating subspaces can be identified with almost invariant subspaces.     

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality.

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.     

深度连接的超轻量化子空间注意模块

针对紧凑型卷积神经网络在部署现有注意力机制存在计算量或参数开销大的问题,提出一种改进的超轻量化子空间注意模块。首先,深度连接的子空间注意模块(Deep Connected Subspace Attention Mechanism, DCSAM)划分特征图为若干特征子空间,为每个特征子空间推导不同的注意特征图;其次,改进特征子空间进行空间校准的方式;最后,建立前后特征子空间的连接,实现前后特征子空间的信息流动。该子空间注意机制能够学习到多尺度、多频率的特征表示,更适合细粒度分类任务,且与现有视觉模型中的注意力机制是正交和互补的。实验结果表明,在ImageNet-1K和Stanford Cars数据集上,MobileNetV2在参数量和浮点运算数分别减少12%和24%的情况下,最高精度分别提高了0.48和约2个百分点。