Approximative model reconstruction of cascade systems

This letter considers how to approximately reconstruct a cascade system from a given unstructured system estimate. Many system identification methods, including subspace methods, provide reliable but generally unstructured black-box models. The problem we consider is how to find cascade systems that are close to such black-box models. For this, we use model matching techniques and optimal weighted Hankel-norm approximation to obtain accurate low-order cascade systems. We show that it is possible to bound the reconstruction error in terms of an error tolerance parameter and weighted Hankel singular values. The suggested methods are illustrated on both a numerical example and a real double tank system with experimental data.     

Hardness and approximation of minimum maximal matchings

In this paper, we consider the minimum maximal matching problem in some classes of graphs such as regular graphs. We show that the minimum maximal matching problem is NP-hard even in regular bipartite graphs, and a polynomial time exact algorithm is given for almost complete regular bipartite graphs. From the approximation point of view, it is well known that any maximal matching guarantees the approximation ratio of 2 but surprisingly very few improvements have been obtained. In this paper we give improved approximation ratios for several classes of graphs. For example any algorithm is shown to guarantee an approximation ratio of (2-o(1)) in graphs with high average degree. We also propose an algorithm guaranteeing for any graph of maximum degree Δ an approximation ratio of (2?1/Δ), which slightly improves the best known results. In addition, we analyse a natural linear-time greedy algorithm guaranteeing a ratio of (2?23/18k) in k-regular graphs admitting a perfect matching.     

Structure and attribute index for approximate graph matching in large graphs

The increasing popularity of graph data in various domains has lead to a renewed interest in developing efficient graph matching techniques, especially for processing large graphs. In this paper, we study the problem of approximate graph matching in a large attributed graph. Given a large attributed graph and a query graph, we compute a subgraph of the large graph that best matches the query graph. We propose a novel structure-aware and attribute-aware index to process approximate graph matching in a large attributed graph. We first construct an index on the similarity of the attributed graph, by partitioning the large search space into smaller subgraphs based on structure similarity and attribute similarity. Then, we construct a connectivity-based index to give a concise representation of inter-partition connections. We use the index to find a set of best matching paths. From these best matching paths, we compute the best matching answer graph using a greedy algorithm. Experimental results on real datasets demonstrate the efficiency of both index construction and query processing. We also show that our approach attains high-quality query answers.     

Improving an Algorithm for Approximate Pattern Matching

We study a recent algorithm for fast on-line approximate string matching. This is the problem of searching a pattern in a text allowing errors in the pattern or in the text. The algorithm is based on a very fast kernel which is able to search short patterns using a nondeterministic finite automaton, which is simulated using bit-parallelism. A number of techniques to extend this kernel for longer patterns are presented in that work. However, the techniques can be integrated in many ways and the optimal interplay among them is by no means obvious. The solution to this problem starts at a very low level, by obtaining basic probabilistic information about the problem which was not previously known, and ends integrating analytical results with empirical data to obtain the optimal heuristic. The conclusions obtained via analysis are experimentally confirmed. We also improve many of the techniques and obtain a combined heuristic which is faster than the original work. This work shows an excellent example of a complex and theoretical analysis of algorithms used for design and for practical algorithm engineering, instead of the common practice of first designing an algorithm and then analyzing it. Received March 31, 1998; revised November 18, 1998.     

Solving Various Weighted Matching Problems with Constraints

This paper studies the resolution of (augmented) weighted matching problems within a constraint programming (CP) framework. The first contribution of the paper is a set of techniques that improves substantially the performance of branch-and-bound algorithms based on constraint propagation and the second contribution is the introduction of weighted matching as a global constraint ( WeightedMatching), that can be propagated using specialized incremental algorithms from Operations Research. We first compare programming techniques that use constraint propagation with specialized algorithms from Operations Research, such as the Busaker and Gowen flow algorithm or the Hungarian method. Although CP is shown not to be competitive with specialized polynomial algorithms for pure matching problems, the situation is different as soon as the problems are modified with additional constraints. Using the previously mentioned set of techniques, a simpler branch-and-bound algorithm based on constraint propagation can outperform a complex specialized algorithm. These techniques have been applied with success to the Traveling Salesman Problems [5], which can be seen as an augmented matching problem. We also show that an incremental version of the Hungarian method can be used to propagate a WeightedMatching constraint. This is an extension to the weighted case of the work of Régin [19], which we show to bring significant improvements on a timetabling example.     

Approximate string matching for music analysis

Approximate pattern matching algorithms have become an important tool in computer assisted music analysis and information retrieval. The number of different problem formulations has greatly expanded in recent years, not least because of the subjective nature of measuring musical similarity. From an algorithmic perspective, the complexity of each problem depends crucially on the exact definition of the difference between two strings. We present an overview of advances in approximate string matching in this field focusing on new measures of approximation.     

Suboptimal solutions using integer approximation techniques forscheduling divisible loads on distributed bus networks

The problem of optimal divisible load distribution in distributed bus networks employing a heterogeneous cluster of processors is addressed. The objective is to minimize the total processing time of the entire load subject to the communication and computation delays. In the mathematical model we adopt, both the granularity of the load fractions and all the associated overheads (also referred to as start-up costs) in the process of communication and computation, are considered explicitly in the problem formulation. We introduce a directed flow graph model for representing the load distribution process. This representation is novel to this literature. With this model, we first derive a closed-form solution for an optimal processing time. We propose an integer approximation algorithm and derive ultimate performance bounds for the class of homogeneous networks. We then extend the problem to a special class of application problems in which the data partitioning is restricted to a finite number of partitions. For this case, we present a recursive procedure to obtain optimal processing time. We then present two different integer approximation algorithms-PIA and IIA that could generate integer load fractions and yield suboptimal solutions. The choice of these algorithms are also analyzed. All the results are extended to a class of homogeneous networks to obtain ultimate performance bounds. Several illustrative examples are provided for ease of explanation     

Approximation models of feed-forward G/G/1/N queueing networks with correlated arrivals

In this paper we develop approximation models for feed-forward networks of G/G/1/N queues. We use Linear Algebra Queueing Theory (LAQT) techniques to create reduced state space representations for the queue departure processes. Reduced state space departure processes are presented where the first three moments and the correlation decay are mapped to a two state process. A three state process is also presented matching the first five moments and the first three lag autocorrelations. Numerical examples of end-to-end performance for high-speed communications networks with correlated arrival traffic are presented. The results are compared with simulation models and other approximation methods.     

A Theoretical and Empirical Study of a Noise-Tolerant Algorithm to Learn Geometric Patterns

Developing the ability to recognize a landmark from a visual image of a robot's current location is a fundamental problem in robotics. We describe a way in which the landmark matching problem can be mapped to that of learning a one-dimensional geometric pattern. The first contribution of our work is an efficient noise-tolerant algorithm (designed using the statistical query model) to PAC learn the class of one-dimensional geometric patterns. The second contribution of our work is an empirical study of our algorithm that provides some evidence that statistical query algorithms may be valuable for use in practice for handling noisy data.     

A dynamical systems approach to weighted graph matching

Graph matching is a fundamental problem that arises frequently in the areas of distributed control, computer vision, and facility allocation. In this paper, we consider the optimal graph matching problem for weighted graphs, which is computationally challenging due the combinatorial nature of the set of permutations. Contrary to optimization-based relaxations to this problem, in this paper we develop a novel relaxation by constructing dynamical systems on the manifold of orthogonal matrices. In particular, since permutation matrices are orthogonal matrices with nonnegative elements, we define two gradient flows in the space of orthogonal matrices. The first minimizes the cost of weighted graph matching over orthogonal matrices, whereas the second minimizes the distance of an orthogonal matrix from the finite set of all permutations. The combination of the two dynamical systems converges to a permutation matrix, which provides a suboptimal solution to the weighted graph matching problem. Finally, our approach is shown to be promising by illustrating it on nontrivial problems.     

CLARO: modeling and processing uncertain data streams

Uncertain data streams, where data are incomplete and imprecise, have been observed in many environments. Feeding such data streams to existing stream systems produces results of unknown quality, which is of paramount concern to monitoring applications. In this paper, we present the claro system that supports stream processing for uncertain data naturally captured using continuous random variables. claro employs a unique data model that is flexible and allows efficient computation. Built on this model, we develop evaluation techniques for relational operators by exploring statistical theory and approximation. We also consider query planning for complex queries given an accuracy requirement. Evaluation results show that our techniques can achieve high performance while satisfying accuracy requirements and outperform state-of-the-art sampling methods.     

一种基于链码的三维心血管图像匹配算法

为了快速准确地进行三维心血管图像匹配，以帮助医生更加准确地进行心血管疾病的治疗，提出一种基于链码理论的三维心血管图像心血管中轴线的匹配方法，即首先将二维的Freeman编码拓展至三维空间，然后将其用于对已获取的三维心血管进行编码，以便于实现对不同时刻的三维心血管图像心血管中轴线的匹配。另外，还对模式识别中链码的串匹配算法作了一个简要介绍，并讨论了其中的编码、代价函数、归一化的链间距离等难点。为了验证该算法的效果，还选择了两种构造替换代价函数的方法对三维心血管进行了实验，并利用标准公式对实验结果进行了评估。实验结果表明，利用两种代价函数都可以实现图像的匹配，但是匹配的程度有较大差异，其中利用第2种代价函数可以得到更加令人满意的匹配结果。     

一种基于部分已验证匹配关系的模式匹配模型

模式匹配是模式集成、语义WEB及电子商务等领域的重点及难点问题. 为了有效利用专家知识提高匹配质量, 提出了一种基于部分已验证匹配关系的模式匹配模型. 在该模型中, 首先,人工验证待匹配模式元素间的少量对应关系, 进而推理出当前任务下部分已知的匹配关系及单独匹配器的缺省权重; 然后,基于上述已收集到的先验知识对多种匹配器所生成的相似度矩阵进行合并及调整, 并在全局范围内进行优化; 最后,对优化矩阵的选择性进行评估, 从而为不同匹配任务推荐最合理的候选匹配生成方案. 实验结果表明, 部分已验证匹配关系的使用有助于模式匹配质量的提高.     

一种评价仿射不变性特征定位误差的新方法

特征点匹配是计算机视觉中的一个基本问题。不同视点图像中相应特征点邻域窗口之间存在几何上的透视畸变,这可用平面单应映射来表示,而目前大多匹配算法将该映射用仿射变换模型来近似,即用具有仿射不变性的特征进行图像的匹配。仿射变换的线性特点不仅能降低算法复杂度,还能保证迭代过程收敛的稳定性,然而并没有人对该近似的可行性及如何减小近似误差给出定量分析。本文首先回顾了各种几何层次上的特征点匹配策略,重点针对具有仿射不变性特征点的定位误差进行研究和定量分析,通过本文提出的椭圆曲线规范化法推导出该近似所造成相应特征点定位误差的解析表达;然后用真实图像的实验结果验证了本文分析方法的必要性和正确性;最后给出相应的分析结果和结论,并指出提高大基线图像特征点匹配精度的相应措施。     

Quasi-finite-rank approximation of compression operators in sampled-data systems and time-delay systems

This article studies an approximation problem of compression operators that play important roles in the operator-theoretic approach to sampled-data systems and time-delay systems. Taking account of the ease in the use of approximated operators in such an approach, we confine ourselves to a special form of approximation that we call quasi-finite-rank approximation. We first introduce a suboptimal method for such approximation by means of what we call the fast-lifting approach, with which the problem can be reduced to a finite-dimensional one in an approximate sense. We further introduce another method that somehow applies the first method in a nested fashion for better overall performance. We also discuss the asymptotic exactness of the suboptimal optimisation methods as the integer parameter M in the fast-lifting approach tends to infinity, as well as the associated monotonic properties as to the reduction of the deviation from the optimal approximation. Numerical examples are given to demonstrate the effectiveness of these approximation techniques.     

Multiple filtration and approximate pattern matching

Given a text of lengthn and a query of lengthq, we present an algorithm for finding all locations ofm-tuples in the text and in the query that differ by at mostk mismatches. This problem is motivated by the dot-matrix constructions for sequence comparison and optimal oligonucleotide probe selection routinely used in molecular biology. In the caseq=m the problem coincides with the classicalapproximate string matching with k mismatches problem. We present a new approach to this problem based on multiple hashing, which may have advantages over some sophisticated and theoretically efficient methods that have been proposed. This paper describes a two-stage process. The first stage (multiple filtration) uses a new technique to preselect roughly similarm-tuples. The second stage compares thesem-tuples using an accurate method. We demonstrate the advantages of multiple filtration in comparison with other techniques for approximate pattern matching.This research was supported in part by the National Science Foundation under Grant No. DMS 90-05833 and the National Institute of Health under Grant No. GM-36230.     

Improved Approximation Bounds for Planar Point Pattern Matching

We analyze the performance of simple algorithms for matching two planar point sets under rigid transformations so as to minimize the directed Hausdorff distance between the sets. This is a well studied problem in computational geometry. Goodrich, Mitchell, and Orletsky presented a very simple approximation algorithm for this problem, which computes transformations based on aligning pairs of points. They showed that their algorithm achieves an approximation ratio of 4. We introduce a modification to their algorithm, which is based on aligning midpoints rather than endpoints. This modification has the same simplicity and running time as theirs, and we show that it achieves a better approximation ratio of roughly 3.14. We also analyze the approximation ratio in terms of a instance-specific parameter that is based on the ratio between diameter of the pattern set to the optimum Hausdorff distance. We show that as this ratio increases (as is common in practical applications) the approximation ratio approaches 3 in the limit. We also investigate the performance of the algorithm by Goodrich et al. as a function of this ratio, and present nearly matching lower bounds on the approximation ratios of both algorithms. This work was supported by the National Science Foundation under grants CCR-0098151 and CCF-0635099.     

基于Hausdorff距离的手势识别

随着先进人机交互技术的提出及发展，手势识别正成为其中一项关键技术，基于视觉的手势识别是当前涉及图象处理，模式识别，计算机视觉等领域的一个比较活跃的课题，由于Hausdorff距离模板匹配的方法具有计算量小，适应性强的特点，因此基于Hausdorff距离，建立了一个手势识别系统，该系统采用边缘特征像素点作为识别特征，并首次利用Hausdorff距离模板匹配的思想，在距离变换空间内，实现了中国手指字母集上的基于单目视觉的30个手指字母的手势识别，为提高系统的鲁棒性，还提出了修正的Hausdorff距离形式，测试集上的平均识别率为96．7％，实验结果表明，基于Hausdorff距离的模板匹配方法用于基于听觉的静态手势识别是可行的。