A new approach to the cheap LQ regulator exploiting the geometric properties of the Hamiltonian system

The cheap LQ regulator is reinterpreted as an output nulling problem which is a basic problem of the geometric control theory. In fact, solving the LQ regulator problem is equivalent to keep the output of the related Hamiltonian system identically zero. The solution lies on a controlled invariant subspace whose dimension is characterized in terms of the minimal conditioned invariant of the original system, and the optimal feedback gain is computed as the friend matrix of the resolving subspace. This study yields a new computational framework for the cheap LQ regulator, relying only on the very basic and simple tools of the geometric approach, namely the algorithms for controlled and conditioned invariant subspaces and invariant zeros.     

A hybrid differential evolution algorithm integrated with an ant system and its application

A new hybrid differential evolution algorithm, in which an ant system is used to select the optimal base vector of mutation operation, named the ant system differential evolution (ASDE), is proposed. In ASDE, each dimension in the feasible solution space is divided into several subspaces evenly, and each subspace is marked with the same initial intensity of pheromone trails. The probability of choosing an individual as the base vector is influenced by the visibility and pheromone quantity of the individual. The trail of the selected base vector’s location subspaces will be reinforced with some pheromones, when the offspring is better than its parent. The experimental results show that the ASDE generally outperforms the other differential evolution algorithms for nine benchmark functions. Furthermore, the ASDE is applied to develop the global kinetic model for SO₂ oxidation on the Cs-Rb-V catalyst, and satisfactory results are obtained.     

Discriminative common vectors for face recognition

In face recognition tasks, the dimension of the sample space is typically larger than the number of the samples in the training set. As a consequence, the within-class scatter matrix is singular and the linear discriminant analysis (LDA) method cannot be applied directly. This problem is known as the "small sample size" problem. In this paper, we propose a new face recognition method called the discriminative common vector method based on a variation of Fisher's linear discriminant analysis for the small sample size case. Two different algorithms are given to extract the discriminative common vectors representing each person in the training set of the face database. One algorithm uses the within-class scatter matrix of the samples in the training set while the other uses the subspace methods and the Gram-Schmidt orthogonalization procedure to obtain the discriminative common vectors. Then, the discriminative common vectors are used for classification of new faces. The proposed method yields an optimal solution for maximizing the modified Fisher's linear discriminant criterion given in the paper. Our test results show that the discriminative common vector method is superior to other methods in terms of recognition accuracy, efficiency, and numerical stability.     

Multibody grouping by inference of multiple subspaces from high-dimensional data using oriented-frames

Recently, subspace constraints have been widely exploited in many computer vision problems such as multibody grouping. Under linear projection models, feature points associated with multiple bodies reside in multiple subspaces. Most existing factorization-based algorithms can segment objects undergoing independent motions. However, intersections among the correlated motion subspaces will lead most previous factorization-based algorithms to erroneous segmentation. To overcome this limitation, in this paper, we formulate the problem of multibody grouping as inference of multiple subspaces from a high-dimensional data space. A novel and robust algorithm is proposed to capture the configuration of the multiple subspace structure and to find the segmentation of objects by clustering the feature points into these inferred subspaces, no matter whether they are independent or correlated. In the proposed method, an oriented-frame (OF), which is a multidimensional coordinate frame, is associated with each data point indicating the point's preferred subspace configuration. Based on the similarity between the subspaces, novel mechanisms of subspace evolution and voting are developed. By filtering the outliers due to their structural incompatibility, the subspace configurations will emerge. Compared with most existing factorization-based algorithms that cannot correctly segment correlated motions, such as motions of articulated objects, the proposed method has a robust performance in both independent and correlated motion segmentation. A number of controlled and real experiments show the effectiveness of the proposed method. However, the current approach does not deal with transparent motions and motion subspaces of different dimensions.     

Random Sampling for Subspace Face Recognition

Subspace face recognition often suffers from two problems: (1) the training sample set is small compared with the high dimensional feature vector; (2) the performance is sensitive to the subspace dimension. Instead of pursuing a single optimal subspace, we develop an ensemble learning framework based on random sampling on all three key components of a classification system: the feature space, training samples, and subspace parameters. Fisherface and Null Space LDA (N-LDA) are two conventional approaches to address the small sample size problem. But in many cases, these LDA classifiers are overfitted to the training set and discard some useful discriminative information. By analyzing different overfitting problems for the two kinds of LDA classifiers, we use random subspace and bagging to improve them respectively. By random sampling on feature vectors and training samples, multiple stabilized Fisherface and N-LDA classifiers are constructed and the two groups of complementary classifiers are integrated using a fusion rule, so nearly all the discriminative information is preserved. In addition, we further apply random sampling on parameter selection in order to overcome the difficulty of selecting optimal parameters in our algorithms. Then, we use the developed random sampling framework for the integration of multiple features. A robust random sampling face recognition system integrating shape, texture, and Gabor responses is finally constructed.     

A parameter free Continuous Ant Colony Optimization Algorithm for the optimal design of storm sewer networks: Constrained and unconstrained approach

This paper describes the application of the newly introduced Continuous Ant Colony Optimization Algorithm (CACOA) to optimal design of sewer networks. Two alternative approaches to implement the algorithm is presented and applied to a storm sewer network in which the nodal elevations of the network are considered as the decision variables of the optimization problem. In the first and unconstrained approach, a Gaussian probability density function is used to represent the pheromone concentration over the allowable range of each decision variable. The pheromone concentration function is used by each ant to randomly sample the nodal elevations of the trial networks. This method, however, will lead to solutions which may be infeasible regarding some or all of the constraints of the problem and in particular the minimum slope constraint. In the second and constrained approach, known value of the elevation at downstream node of a pipe is used to define new bounds on the elevation of the upstream node satisfying the explicit constraints on the pipe slopes. Two alternative formulations of the constrained algorithm are used to solve a test example and the results are presented and compared with those of unconstrained approach. The methods are shown to be very effective in locating the optimal solution and efficient in terms of the convergence characteristics of the resulting algorithms. The proposed algorithms are also found to be relatively insensitive to the initial colony and size of the colony used compared to the original algorithm.     

Using In-frame Shear Constraints for Monocular Motion Segmentation of Rigid Bodies

It is a well known result in the vision literature that the motion of independently moving objects viewed by an affine camera lie on affine subspaces of dimension four or less. As a result a large number of the recently proposed motion segmentation algorithms model the problem as one of clustering the trajectory data to its corresponding affine subspace. While these algorithms are elegant in formulation and achieve near perfect results on benchmark datasets, they fail to address certain very key real-world challenges, including perspective effects and motion degeneracies. Within a robotics and autonomous vehicle setting, the relative configuration of the robot and moving object will frequently be degenerate leading to a failure of subspace clustering algorithms. On the other hand, while gestalt-inspired motion similarity algorithms have been used for motion segmentation, in the moving camera case, they tend to over-segment or under-segment the scene based on their parameter values. In this paper we present a principled approach that incorporates the strengths of both approaches into a cohesive motion segmentation algorithm capable of dealing with the degenerate cases, where camera motion follows that of the moving object. We first generate a set of prospective motion models for the various moving and stationary objects in the video sequence by a RANSAC-like procedure. Then, we incorporate affine and long-term gestalt-inspired motion similarity constraints, into a multi-label Markov Random Field (MRF). Its inference leads to an over-segmentation, where each label belongs to a particular moving object or the background. This is followed by a model selection step where we merge clusters based on a novel motion coherence constraint, we call in-frame shear, that tracks the in-frame change in orientation and distance between the clusters, leading to the final segmentation. This oversegmentation is deliberate and necessary, allowing us to assess the relative motion between the motion models which we believe to be essential in dealing with degenerate motion scenarios.We present results on the Hopkins-155 benchmark motion segmentation dataset [27], as well as several on-road scenes where camera and object motion are near identical. We show that our algorithm is competitive with the state-of-the-art algorithms on [27] and exceeds them substantially on the more realistic on-road sequences.     

Bi-objective optimisation model for installation scheduling in offshore wind farms

A bi-objective optimisation using a compromise programming approach is proposed for installation scheduling of an offshore wind farm. As the installation cost and the completion period of the installation are important aspects in the construction of an offshore wind farm, the proposed method is used to deal with those conflicting objectives. We develop a mathematical model using integer linear programming (ILP) to determine the optimal installation schedule considering several constraints such as weather condition and the availability of vessels. We suggest two approaches to deal with the multi-objective installation scheduling problem, namely compromise programming with exact method and with metaheuristic techniques. In the exact method the problem is solved by CPLEX whereas in the metaheuristic approach we propose Variable Neighbourhood Search (VNS) and Simulated Annealing (SA). Moreover, greedy algorithms and a local search for solving the scheduling problem are introduced. Two generated datasets are used for testing our approaches. The computational experiments show that the proposed metaheuristic approaches produce interesting results as the optimal solution for some cases is obtained.     

Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA

We consider the problem of segmenting multiple rigid-body motions from point correspondences in multiple affine views. We cast this problem as a subspace clustering problem in which point trajectories associated with each motion live in a linear subspace of dimension two, three or four. Our algorithm involves projecting all point trajectories onto a 5-dimensional subspace using the SVD, the PowerFactorization method, or RANSAC, and fitting multiple linear subspaces representing different rigid-body motions to the points in ℝ⁵ using GPCA. Unlike previous work, our approach does not restrict the motion subspaces to be four-dimensional and independent. Instead, it deals gracefully with all the spectrum of possible affine motions: from two-dimensional and partially dependent to four-dimensional and fully independent. Our algorithm can handle the case of missing data, meaning that point tracks do not have to be visible in all images, by using the PowerFactorization method to project the data. In addition, our method can handle outlying trajectories by using RANSAC to perform the projection. We compare our approach to other methods on a database of 167 motion sequences with full motions, independent motions, degenerate motions, partially dependent motions, missing data, outliers, etc. On motion sequences with complete data our method achieves a misclassification error of less that 5% for two motions and 29% for three motions.     

一种遗传搜索块匹配运动估计算法

运动估计是帧间视频编码中的关键技术,但现有的快速搜索算法中大都是次优算法,且易陷于局部极小点,针对此问题,提出了将一种遗传算法应用于块运动估计中的遗传搜索匹配估计算法（GSAME）,该方法把块运动向量作为遗传染色体,经过杂交、变异等操作,以便得到全局意义上的最优解,并与经典的全局搜索法和三步搜索法进行了比较,实验结果显示,该算法不仅有效地解决了局部极小问题,而且计算量也较少。     

Numerical techniques for the inverse optimal control problem in limited state feedback systems

The numerical problem of finding the performance index parameters {Q}, for which a given control {u = fx} is optimal, is studied. Two successful algorithms are described for the single input case. Both apply to systems which are optimal within the constraint of limited state availability. The structure of Q must be prespecified to allow only r free parameters (where r is the dimension of the feedback vector). This ensures that the solution is unique. Numerical examples and program listings are included.     

Feature space locality constraint for kernel based nonlinear discriminant analysis

Subspace learning is an important approach in pattern recognition. Nonlinear discriminant analysis (NDA), due to its capability of describing nonlinear manifold structure of samples, is considered to be more powerful to undertake classification tasks in image related problems. In kernel based NDA representation, there are three spaces involved, i.e., original data space, implicitly mapped high dimension feature space and the target low dimension subspace. Existing methods mainly focus on the information in original data space to find the most discriminant low dimension subspace. The implicit high dimension feature space plays a role that connects the original space and the target subspace to realize the nonlinear dimension reduction, but the sample geometric structure information in feature space is not involved. In this work, we try to utilize and explore this information. Specifically, the locality information of samples in feature space is modeled and integrated into the traditional kernel based NDA methods. In this way, both the sample distributions in original data space and the mapped high dimension feature space are modeled and more information is expected to be explored to improve the discriminative ability of the subspace. Two algorithms, named FSLC-KDA and FSLC-KSR, are presented. Extensive experiments on ORL, Extended-YaleB, PIE, Multi-PIE and FRGC databases validate the efficacy of the proposed method.     

一种基于协方差阵拟合的解测向模糊算法

流形模糊发生的原因是阵列流形上的多个矢量线性相关,子空间类算法无法靠自身解模糊。为解决子空间类算法中的模糊问题,提出了一种新的基于协方差阵拟合的解模糊算法。该方法用预估的导向矢量与入射波功率来拟合协方差阵,用最陡下降法寻找最优的功率参数,认定功率较大的入射波为真实来波。与子空间算法结合,可解决测向模糊问题。数值仿真表明,此方法在阵元数量较多时仍能有效工作。     

On utilizing search methods to select subspace dimensions for kernel-based nonlinear subspace classifiers

In kernel-based nonlinear subspace (KNS) methods, the subspace dimensions have a strong influence on the performance of the subspace classifier. In order to get a high classification accuracy, a large dimension is generally required. However, if the chosen subspace dimension is too large, it leads to a low performance due to the overlapping of the resultant subspaces and, if it is too small, it increases the classification error due to the poor resulting approximation. The most common approach is of an ad hoc nature, which selects the dimensions based on the so-called cumulative proportion computed from the kernel matrix for each class. We propose a new method of systematically and efficiently selecting optimal or near-optimal subspace dimensions for KNS classifiers using a search strategy and a heuristic function termed the overlapping criterion. The rationale for this function has been motivated in the body of the paper. The task of selecting optimal subspace dimensions is reduced to find the best ones from a given problem-domain solution space using this criterion as a heuristic function. Thus, the search space can be pruned to very efficiently find the best solution. Our experimental results demonstrate that the proposed mechanism selects the dimensions efficiently without sacrificing the classification accuracy.     

一种基于极大熵的快速无监督线性降维方法

现实世界中高维数据无处不在,然而在高维数据中往往存在大量的冗余和噪声信息,这导致很多传统聚类算法在对高维数据聚类时不能获得很好的性能.实践中发现高维数据的类簇结构往往嵌入在较低维的子空间中.因而,降维成为挖掘高维数据类簇结构的关键技术.在众多降维方法中,基于图的降维方法是研究的热点.然而,大部分基于图的降维算法存在以下两个问题:(1)需要计算或者学习邻接图,计算复杂度高;(2)降维的过程中没有考虑降维后的用途.针对这两个问题,提出一种基于极大熵的快速无监督降维算法MEDR. MEDR算法融合线性投影和极大熵聚类模型,通过一种有效的迭代优化算法寻找高维数据嵌入在低维子空间的潜在最优类簇结构. MEDR算法不需事先输入邻接图,具有样本个数的线性时间复杂度.在真实数据集上的实验结果表明,与传统的降维方法相比, MEDR算法能够找到更好地将高维数据投影到低维子空间的投影矩阵,使投影后的数据有利于聚类.     

一种改进遗传搜索块匹配运动估计算法

运动估计是帧间视频编码中的关键技术,但现有的快速搜索算法中大都是次优算法,且易陷于局部极小点。针对此问题,提出了一种改进型遗传算法应用于块运动估计中的遗传搜索块匹配运动估计算法(MGSAME)。该方法把块运动向量作为遗传染色体,经过杂交、变异等操作,以便得到全局意义上的最优解,并与经典的全局搜索法、三步搜索法和传统遗传算法(SGA)进行了比较。实验结果显示,该算法不仅有效地解决了局部极小问题,而且计算量也较少。     

On simultaneous on-line state and parameter estimation in non-linear state-space models

On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex multi-dimensional integrals that are not amenable to analytical solution. While basic sequential Monte-Carlo (SMC) or particle filtering (PF) algorithms for simultaneous estimation exist, it is well recognized that there is a need for making these on-line algorithms non-degenerate, fast and applicable to processes with missing measurements. To overcome the deficiencies in traditional algorithms, this work proposes a Bayesian approach to on-line state and parameter estimation. Its extension to handle missing data in real-time is also provided. The simultaneous estimation is performed by filtering an extended vector of states and parameters using an adaptive sequential-importance-resampling (SIR) filter with a kernel density estimation method. The approach uses an on-line optimization algorithm based on Kullback–Leibler (KL) divergence to allow adaptation of the SIR filter for combined state-parameter estimation. An optimal tuning rule to control the width of the kernel and the variance of the artificial noise added to the parameters is also proposed. The approach is illustrated through numerical examples.     

束搜索算法的候选选取方法研究

在假设空间中进行爬山搜索是机器学习算法中常用的策略，爬山算法不能保证得到全局最优解，为了减少收敛到局部最优解的风险，束搜索应用而生。宽度为k的束搜索，在每一步以k个最佳候选为入口进行搜索(产生分支)，并从结果集中再次选取k个候选作为下一步的搜索入口。但目前多数算法只是在结果集中简单选取具有最大启发式性能量度值的k个成员。该文讨论了束搜索算法，提出了几种合理的候选选取方法，并在UCI数据库上进行对比实验测试，给出了实验结果。     

一种基于新型遗传算法的块运动估计算法

提出了一种基于新型遗传算法的块匹配运动估计算法。该算法把块运动向量作为遗传染色体,经过选择变异等操作,将随机搜索与特定目标搜索相结合,解决了以往快速搜索算法易陷于局部最优的问题,同时该算法中所带的模糊评价函数使得对个体的评价更合理、客观,该算法还将运动矢量空间偏置特性用于初始种群的选取,进一步提高了算法性能。实验结果表明,该算法性能上接近于FSA,速度却接近于TSS。     

An affine subspace clustering algorithm based on ridge regression

Recent subspace clustering algorithms, which use sparse or low-rank representations, conduct clustering by considering the errors and noises into their objective functions. Then, the similarity matrix is solved via alternating direction method of multipliers. However, these approaches are subject to the restriction that the characteristic of errors and outliers in sample points should be known as the prior information. Furthermore, these algorithms are time-consuming during the iterative process. Motivated by this observation, this paper proposes a new subspace clustering algorithm: an affine subspace clustering algorithm based on ridge regression. The method introduces ridge regression as objective function which applies affine criteria into subspace clustering. An analytic solution to the problem has been determined for the coefficient matrix. Experimental results obtained on face datasets demonstrate that the proposed method not only improves the accuracy of the clustering results, but also enhances the robustness. Furthermore, the proposed method reduces the computational complexity.