Pair-perturbation influence functions and local influence in PCA

The perturbation theory of an eigenvalue problem provides a useful tool for the sensitivity analysis in principal component analysis (PCA). However, single-perturbation diagnostics can suffer from masking effects. In this paper, we develop the pair-perturbation influence functions for the eigenvalues and eigenvectors of covariance matrices utilized in PCA to uncover the masked influential points. The relationship between the empirical pair-perturbation influence function and local influence in pairs is also investigated. Moreover, we propose an approach for determining cut points for influence function values in PCA, which has not been addressed yet. A simulation study and a specific data example are provided to illustrate the application of these approaches.     

Pair-perturbation influence functions and local influence in PCA

The perturbation theory of an eigenvalue problem provides a useful tool for the sensitivity analysis in principal component analysis (PCA). However, single-perturbation diagnostics can suffer from masking effects. In this paper, we develop the pair-perturbation influence functions for the eigenvalues and eigenvectors of covariance matrices utilized in PCA to uncover the masked influential points. The relationship between the empirical pair-perturbation influence function and local influence in pairs is also investigated. Moreover, we propose an approach for determining cut points for influence function values in PCA, which has not been addressed yet. A simulation study and a specific data example are provided to illustrate the application of these approaches.     

Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows

Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations. In this paper we present a new theoretical result which allows to recast free-form deformations into the general class of perturbation of identity maps, and to guarantee the compactness of the set of admissible shapes. Moreover, we address both a general optimization framework based on the continuous shape gradient and a numerical procedure for solving efficiently three-dimensional optimal design problems. This framework is applied to the optimal design of immersed bodies in Stokes flows, for which we consider the numerical solution of a benchmark case study from literature.     

基于模糊C均值聚类的医学图像分割研究

模糊C均值聚类算法（FCM）在硬C均值聚类的基础上有效地解决了医学图像分割中存在的模糊情况,通过建立表示图像中像素点与聚类中心加权相似度的目标函数,采用迭代优化的方法求解目标函数的极小值来确定最佳聚类。针对FCM算法中存在的对大样本数据分割速度慢、结果易受初始值影响、对噪声敏感、难以适应多种数据分布等缺陷,涌现出了大量的改进算法。对其中的部分改进算法进行综述,主要介绍快速FCM算法、基于初始值选取的FCM算法、基于空间邻域信息的FCM算法以及基于核函数的FCM算法等,并对其优缺点进行概要的总结和介绍。指出该算法进一步的研究方向。     

Semi‐global cooperative output regulation of a class of nonlinear uncertain multi‐agent systems under switching networks

In this paper, we consider the semi‐global cooperative output regulation problem for a class of nonlinear uncertain multi‐agent systems under switching networks. At first, we study the nonadaptive case when the exosystem has no parametric uncertainties and construct a common Lyapunov function to achieve the output regulation for general switching connected networks. Next, we study the case when the exosystem contains some parametric uncertainties. To solve the problem, we establish a stability result for a class of time‐varying system, which is then used in the design of distributed adaptive internal model‐based control. Then we construct multiple Lyapunov functions for the switching signal with its average dwell time lower bounded by a given constant. Throughout the paper, we treat the closed‐loop multi‐agent system from the viewpoint of singular perturbation. In fact, the singular perturbation‐based method provides an effective tool to handle the multi‐agent system under switching networks. Finally, we give numerical simulations based on Duffing systems and flexible manipulator systems to illustrate the effectiveness of our method. Copyright © 2017 John Wiley & Sons, Ltd.     

A size-insensitive integrity-based fuzzy c-means method for data clustering

Fuzzy c-means (FCM) is one of the most popular techniques for data clustering. Since FCM tends to balance the number of data points in each cluster, centers of smaller clusters are forced to drift to larger adjacent clusters. For datasets with unbalanced clusters, the partition results of FCM are usually unsatisfactory. Cluster size insensitive FCM (csiFCM) dealt with “cluster-size sensitivity” problem by dynamically adjusting the condition value for the membership of each data point based on cluster size after the defuzzification step in each iterative cycle. However, the performance of csiFCM is sensitive to both the initial positions of cluster centers and the “distance” between adjacent clusters. In this paper, we present a cluster size insensitive integrity-based FCM method called siibFCM to improve the deficiency of csiFCM. The siibFCM method can determine the membership contribution of every data point to each individual cluster by considering cluster's integrity, which is a combination of compactness and purity. “Compactness” represents the distribution of data points within a cluster while “purity” represents how far a cluster is away from its adjacent cluster. We tested our siibFCM method and compared with the traditional FCM and csiFCM methods extensively by using artificially generated datasets with different shapes and data distributions, synthetic images, real images, and Escherichia coli dataset. Experimental results showed that the performance of siibFCM is superior to both traditional FCM and csiFCM in terms of the tolerance for “distance” between adjacent clusters and the flexibility of selecting initial cluster centers when dealing with datasets with unbalanced clusters.     

Alpha-cut implemented fuzzy clustering algorithms and switching regressions.

In the fuzzy c-means (FCM) clustering algorithm, almost none of the data points have a membership value of 1. Moreover, noise and outliers may cause difficulties in obtaining appropriate clustering results from the FCM algorithm. The embedding of FCM into switching regressions, called the fuzzy c-regressions (FCRs), still has the same drawbacks as FCM. In this paper, we propose the alpha-cut implemented fuzzy clustering algorithms, referred to as FCMalpha, which allow the data points being able to completely belong to one cluster. The proposed FCMalpha algorithms can form a cluster core for each cluster, where data points inside a cluster core will have a membership value of 1 so that it can resolve the drawbacks of FCM. On the other hand, the fuzziness index m plays different roles for FCM and FCMalpha. We find that the clustering results obtained by FCMalpha are more robust to noise and outliers than FCM when a larger m is used. Moreover, the cluster cores generated by FCMalpha are workable for various data shape clusters, so that FCMalpha is very suitable for embedding into switching regressions. The embedding of FCMalpha into switching regressions is called FCRalpha. The proposed FCRalpha provides better results than FCR for environments with noise or outliers. Numerical examples show the robustness and the superiority of our proposed methods.     

Fuzzy logic approaches to structure preserving dimensionalityreduction

Sammon's (1969) nonlinear projection method is computationally prohibitive for large data sets, and it cannot project new data points. We propose a low-cost fuzzy rule-based implementation of Sammon's method for structure preserving dimensionality reduction. This method uses a sample and applies Sammon's method to project it. The input data points are then augmented by the corresponding projected (output) data points. The augmented data set thus obtained is clustered with the fuzzy c-means (FCM) clustering algorithm. Each cluster is then translated into a fuzzy rule to approximate the Sammon's nonlinear projection scheme. We consider both Mamdani-Assilian and Takagi-Sugeno models for this. Different schemes of parameter estimation are considered. The proposed schemes are applied on several data sets and are found to be quite effective to project new points, i.e., such systems have good predictability     

Programming with partially specified aggregates in Java

Various forms of data aggregates, e.g., arrays, lists, sets, etc., are usually provided by programming languages, either as primitive entities or as additional features made available by standard libraries. In conventional programming languages these data structures are usually specified by completely and precisely enumerating all their constituent elements. Conversely, in (constraint) logic programming languages it is common to deal with partially specified aggregates where either some elements or some parts of the aggregate are left unknown. In this paper we consider the case where partially specified aggregates can occur in a conventional O-O programming language. Specifically, we consider partially specified lists and sets as provided by the Java library JSetL. The definition of such data structures is strongly based on the notion of logical (or constrained) variable usually provided by languages and libraries to support constraint programming. We show through simple examples using Java and JSetL how partially specified lists and sets, along with a few basic constraints over them, can be conveniently exploited in a number of common programming problems.     

Modified Kalman filter for networked monitoring systems employing a send-on-delta method

In this paper, we consider a networked estimation problem in which sensor data are transmitted only if their values change more than the specified value. When this send-on-delta method is used, no sensor data transmission implies that the sensor value does not change more than the specified value from the previously transmitted sensor value. Using this implicit information, we propose a modified Kalman filter algorithm. The proposed filter reduces sensor data traffic with relatively small estimation performance degradation. Through experiments, we demonstrate the feasibility of the proposed filter algorithm.     

Optimality test for generalized FCM and its application to parameter selection

In cluster analysis, the fuzzy c-means (FCM) clustering algorithm is the best known and most widely used method. It was proven to converge to either a local minimum or saddle points by Bezdek et al. Wei and Mendel produced efficient optimality tests for FCM fixed points. Recently, a weighting exponent selection for FCM was proposed by Yu et al. Inspired by these results, we unify several alternative FCM algorithms into one model, called the generalized fuzzy c-means (GFCM). This GFCM model presents a wide variation of FCM algorithms and can easily lead to new and interesting clustering algorithms. Moreover, we construct a general optimality test for GFCM fixed points. This is applied to theoretically choose the parameters in the GFCM model. The experimental results demonstrate the precision of the theoretical analysis.     

Constructing G 1 continuous curve on a free-form surface with normal projection

In this paper, we develop a new method for G ¹ continuous interpolation of an arbitrary sequence of points on an implicit or parametric surface with a specified tangent direction at every point. Based on the normal projection method, we design a G ¹ continuous curve in three-dimensional space and then project orthogonally the curves onto the given surface. With the techniques in classical differential geometry, we derive a system of differential equations characterizing the projection curve. The resulting interpolation curve is obtained by numerically solving the initial-value problems for a system of first-order ordinary differential equations in the parametric domain associated to the surface representation for a parametric case or in three-dimensional space for an implicit case. Several shape parameters are introduced into the resulting curve, which can be used in subsequent interactive modification such that the shape of the resulting curve meets our demand. The presented method is independent of the geometry and parameterization of the base surface, and numerical experiments demonstrate that it is effective and potentially useful in surface trim, robot, patterns design on surface and other industrial and research fields.     

Efficiently Querying Large XML Data Repositories: A Survey

Extensible markup language (XML) is emerging as a de facto standard for information exchange among various applications on the World Wide Web. There has been a growing need for developing high-performance techniques to query large XML data repositories efficiently. One important problem in XML query processing is twig pattern matching, that is, finding in an XML data tree D all matches that satisfy a specified twig (or path) query pattern Q. In this survey, we review, classify, and compare major techniques for twig pattern matching. Specifically, we consider two classes of major XML query processing techniques: the relational approach and the native approach. The relational approach directly utilizes existing relational database systems to store and query XML data, which enables the use of all important techniques that have been developed for relational databases, whereas in the native approach, specialized storage and query processing systems tailored for XML data are developed from scratch to further improve XML query performance. As implied by existing work, XML data querying and management are developing in the direction of integrating the relational approach with the native approach, which could result in higher query processing performance and also significantly reduce system reengineering costs.     

Concurrent Viewing of Multiple Attribute‐Specific Subspaces

In this work we present a point classification algorithm for multi‐variate data. Our method is based on the concept of attribute subspaces, which are derived from a set of user specified attribute target values. Our classification approach enables users to visually distinguish regions of saliency through concurrent viewing of these subspaces in single images. We also allow a user to threshold the data according to a specified distance from attribute target values. Based on the degree of thresholding, the remaining data points are assigned radii of influence that are used for the final coloring. This limits the view to only those points that are most relevant, while maintaining a similar visual context.     

Pair-perturbation influence functions of nongaussianity by projection pursuit

The most nongaussian direction to explore the clustering structure of the data is considered to be the interesting linear projection direction by applying projection pursuit. Nongaussianity is often measured by kurtosis, however, kurtosis is well known to be sensitive to influential points/outliers and the projection direction is essentially affected by unusual points. Hence in this paper we focus on developing the influence functions of projection directions to investigate the influence of abnormal observations especially on the pair-perturbation influence functions to uncover the masked unusual observations. A technique is proposed for defining and calculating influence functions for statistical functional of the multivariate distribution. A simulation study and a real data example are provided to illustrate the applications of these approaches.     

Registration based on projective reconstruction technique for augmented reality systems

In AR systems, registration is one of the most difficult problems currently limiting their application. In this paper, we propose a simple registration method using projective reconstruction. This method consists of two steps: embedding and tracking. Embedding involves specifying four points to build the world coordinate system on which a virtual object will be superimposed. In tracking, a projective reconstruction technique is used to track these four specified points to compute the model view transformation for augmentation. This method is simple, as only four points need to be specified at the embedding stage and the virtual object can then be easily augmented onto a real scene from a video sequence. In addition, it can be extended to a scenario using the projective matrix that has been obtained from previous registration results using the same AR system. The proposed method has three advantages: 1) it is fast because the linear least square method can be used to estimate the related matrix in the algorithm and it is not necessary to calculate the fundamental matrix in the extended case. 2) A virtual object can still be superimposed on a related area even if some parts of the specified area are occluded during the whole process. 3) This method is robust because it remains effective even when not all the reference points are detected during the whole process, as long as at least six pairs of related reference points correspondences can be found. Some experiments have been conducted to validate the performance of the proposed method.     

A contribution to convergence theory of fuzzy c-means and derivatives

In this paper, we revisit the convergence and optimization properties of fuzzy clustering algorithms, in general, and the fuzzy c-means (FCM) algorithm, in particular. Our investigation includes probabilistic and (a slightly modified implementation of) possibilistic memberships, which will be discussed under a unified view. We give a convergence proof for the axis-parallel variant of the algorithm by Gustafson and Kessel, that can be generalized to other algorithms more easily than in the usual approach. Using reformulated fuzzy clustering algorithms, we apply Banach's classical contraction principle and establish a relationship between saddle points and attractive fixed points. For the special case of FCM we derive a sufficient condition for fixed points to be attractive, allowing identification of them as (local) minima of the objective function (excluding the possibility of a saddle point).     

A numerical method for quasilinear singular perturbation problems with turning points

In this paper we consider a quasilinear singular perturbation problem with turning points. First derivatives of the exact solution are estimated. Then an approximate problem is constructed. Finally we give an algorithm whose accuracy is good for arbitrary ?>0.     

Analysis of the weighting exponent in the FCM.

The fuzzy c-means (FCM) algorithm is one of the most frequently used clustering algorithms. The weighting exponent m is a parameter that greatly influences the performance of the FCM. But there has been no theoretical basis for selecting the proper weighting exponent in the literature. In this paper, we develop a new theoretical approach to selecting the weighting exponent in the FCM. Based on this approach, we reveal the relation between the stability of the fixed points of the FCM and the data set itself. This relation provides the theoretical basis for selecting the weighting exponent in the FCM. The numerical experiments verify the effectiveness of our theoretical conclusion.     

Influence functions for a linear subspace method

A linear subspace method, which is one of discriminant methods, was proposed as a pattern recognition method and was studied. Because the method and its extensions do not encounter the situation of singular covariance matrix, we need not consider extensions such as generalized ridge discrimination, even when treating a high dimensional and sparse dataset. In addition, classifiers based on a multi-class discrimination method can function faster because of the simple decision procedure. Therefore, they have been widely used for face and speech recognition. However, it seems that sufficient studies have not been conducted about the statistical assessment of training data performance for classifier in terms of prediction accuracy. In statistics, influence functions for statistical discriminant analysis were derived and the assessments for analysis result were performed. These studies indicate that influence functions are useful for detecting large influential observations for analysis results by using discrimination methods and they contribute to enhancing the performance of a target classifier.