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 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.     

Influence functions and local influence in linear discriminant analysis

The perturbation theory provides a useful tool for the sensitivity analysis in linear discriminant analysis (LDA). Though some influence functions by single perturbation and local influence in LDA have been discussed in literature, we propose yet another influence function inspired by Critchley [1985. Influence in principal component analysis. Biometrika 72, 627-636], called the deleted empirical influence function, as an alternative approach for the influence analysis in LDA. It is well-known that single-perturbation diagnostics can suffer from the masking effect. Hence in this paper we also develop the pair-perturbation influence functions to detect the masked influential points. The comparisons between pair-perturbation influence functions and local influences in pairs in LDA are also investigated. Finally, two examples are provided to illustrate the results of these approaches.     

Global and local clustering with kNN and local PCA

Multimedia Tools and Applications - This paper proposes a new clustering method that combines the k Near Neighbor (k NN) method and the local Principal Component Analysis (PCA) to consider the...     

Robust local tangent space alignment via iterative weighted PCA

Recently manifold learning has attracted extensive interest in machine learning and related communities. This paper investigates the noise manifold learning problem, which is a key issue in applying manifold learning algorithm to practical problems. We propose a robust version of LTSA algorithm called RLTSA. The proposed RLTSA algorithm makes LTSA more robust from three aspects: firstly robust PCA algorithm based on iterative weighted PCA is employed instead of the standard SVD to reduce the influence of noise on local tangent space coordinates; secondly RLTSA chooses neighborhoods that are well approximated by the local coordinates to align with the global coordinates; thirdly in the alignment step, the influence of noise on embedding result is further reduced by endowing clean data points and noise data points with different weights into the local alignment errors. Experiments on both synthetic data sets and real data sets demonstrate the effectiveness of our RLTSA when dealing with noise manifold.     

Smooth functions and local extreme values

The problem of specifying a smooth and simple function that approximates noisy data is considered. A new automatic method is described that is based on solving a constrained optimisation problem. The target functional to be minimised is the sum of the squared residuals penalised by the curve length of the approximation. Multiresolution and monotonicity constraints provide a good approximation to the data with a small number of local extreme values. The new method can also be applied to density estimation.     

An unsupervised approach to learn the kernel functions: from global influence to local similarity

Recently there has been a steep growth in the development of kernel-based learning algorithms. The intrinsic problem in such algorithms is the selection of the optimal kernel for the learning task of interest. In this paper, we propose an unsupervised approach to learn a linear combination of kernel functions, such that the resulting kernel best serves the objectives of the learning task. This is achieved through measuring the influence of each point on the structure of the dataset. This measure is calculated by constructing a weighted graph on which a random walk is performed. The measure of influence in the feature space is probabilistically related to the input space that yields an optimization problem to be solved. The optimization problem is formulated in two different convex settings, namely linear and semidefinite programming, dependent on the type of kernel combination considered. The contributions of this paper are twofold: first, a novel unsupervised approach to learn the kernel function, and second, a method to infer the local similarity represented by the kernel function by measuring the global influence of each point toward the structure of the dataset. The proposed approach focuses on the kernel selection which is independent of the kernel-based learning algorithm. The empirical evaluation of the proposed approach with various datasets shows the effectiveness of the algorithm in practice.     

Stepwise local influence analysis

A new method called stepwise local influence analysis is proposed to detect influential observations and to identify masking effects in a dataset. Influential observations are detected step-by-step such that any highly influential observations identified in a previous step are removed from the perturbation in the next step. The process iterates until no further influential observations can be found. It is shown that this new method is very effective to identify the influential observations and has the power to uncover the masking effects. Additionally, the issues of constraints on perturbation vectors and bench-mark determination are discussed. Several examples with regression models and linear mixed models are illustrated for the proposed methodology.     

Inverse mapping of continuous functions using local and globalinformation

This paper presents a method for solving inverse mapping of a continuous function learned by a multilayer feedforward mapping network. The method is based on the iterative update of input vector toward a solution, while escaping from local minima. The input vector update is determined by the pseudo-inverse of the gradient of Lyapunov function, and, should an optimal solution be searched for, the projection of the gradient of a performance index on the null space of the gradient of Lyapunov function. The update rule is allowed to detect an input vector approaching local minima through a phenomenon called "update explosion". At or near local minima, the input vector is guided by an escape trajectory generated based on "global information", where global information is referred to here as predefined or known information on forward mapping; or the input vector is relocated to a new position based on the probability density function (PDF) constructed over the input vector space by Parzen estimate. The constructed PDF reflects the history of local minima detected during the search process, and represents the probability that a particular input vector can lead to a solution based on the update rule. The proposed method has a substantial advantage in computational complexity as well as convergence property over the conventional methods based on Jacobian pseudo-inverse or Jacobian transpose.     

局部PCA参数约束的Hough多椭圆分层检测算法

针对随机Hough变换(RHT)在复杂图像中检测圆及椭圆时随机采样所造成的大量无效采样、无效累积以及运算时间长等问题,提出基于局部PCA感兴趣参数约束Hough多椭圆分层检测思路。首先利用边缘检测算子获得边缘信息并去除边缘交叉点,在边缘图像中标记并提取出满足一定长度的连续曲线段;其次利用线段PCA方向分析确定是否属于有效曲线段;然后,对所有感兴趣曲线段按照标记顺序依次利用椭圆拟合办法初步得到感兴趣椭圆粗略参数,根据拟合结果进而模糊约束Hough变换参数搜索范围,得到精确椭圆参数;最后利用检测结果更新图像空间,删除已经检测到的椭圆,依次进行,直到所有椭圆检测完毕。实验结果表明,该算法在计算、存储消耗上均大大减少。     

Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

The key in applying energy-based control approach is to be able to express the system under consideration as a dissipative Hamiltonian system, i.e., to obtain Dissipative Hamiltonian Realization (DHR) for the system. In general, the precise DHR form is hard to obtain for nonlinear dynamic systems. When a precise DHR does not exist for a dynamic system or such a precise realization is difficulty to obtain, it is necessary to consider its approximate realization. This paper investigates approximate DHR and construction of local Lyapunov functions for time-invariant nonlinear systems. It is shown that every nonlinear affine system has an approximate DHR if linearization of the system is controllable. Based on the diagonal normal form of nonlinear dynamic systems, a new algorithm is established for the approximate DHR. Finally, we present the concept of kth degree approximate Lyapunov function, and provide a method to construct such a Lyapunov function. Example studies show that the methodology presented in this paper is very effective.     

Towards multiscale functions: enriching finite element spaces with local but not bubble-like functions

In this paper we propose a novel way, via finite elements to treat problems that can be singular perturbed, a reaction–diffusion equation in our case. We enrich the usual piecewise linear or bilinear finite element trial spaces with local solutions of the original problem, as in the residual free bubble (RFB) setting, but do not require these functions to vanish on each element edge, a departure from the RFB paradigm. Such multiscale functions have an analytic expression, for triangles and rectangles. Bubbles are the choice for the test functions allowing static condensation, thus our method is of Petrov–Galerkin type. We perform several numerical validations which confirm the good performance of the method.     

Maximal local classes of partial functions of infinite-valued logic

The language of invariant relations is applied to describe all the maximal local classes (local clones of partial operations) of partial functions defined on arbitrary infinite sets.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 45–56, September–October, 1992.     

Spatial conditioning of transfer functions using local material distributions

In many applications of Direct Volume Rendering (DVR) the importance of a certain material or feature is highly dependent on its relative spatial location. For instance, in the medical diagnostic procedure, the patient's symptoms often lead to specification of features, tissues and organs of particular interest. One such example is pockets of gas which, if found inside the body at abnormal locations, are a crucial part of a diagnostic visualization. This paper presents an approach that enhances DVR transfer function design with spatial localization based on user specified material dependencies. Semantic expressions are used to define conditions based on relations between different materials, such as only render iodine uptake when close to liver. The underlying methods rely on estimations of material distributions which are acquired by weighing local neighborhoods of the data against approximations of material likelihood functions. This information is encoded and used to influence rendering according to the user's specifications. The result is improved focus on important features by allowing the user to suppress spatially less-important data. In line with requirements from actual clinical DVR practice, the methods do not require explicit material segmentation that would be impossible or prohibitively time-consuming to achieve in most real cases. The scheme scales well to higher dimensions which accounts for multi-dimensional transfer functions and multivariate data. Dual-Energy Computed Tomography, an important new modality in radiology, is used to demonstrate this scalability. In several examples we show significantly improved focus on clinically important aspects in the rendered images.     

Learning local objective functions for robust face model fitting

Model-based techniques have proven to be successful in interpreting the large amount of information contained in images. Associated fitting algorithms search for the global optimum of an objective function, which should correspond to the best model fit in a given image. Although fitting algorithms have been the subject of intensive research and evaluation, the objective function is usually designed ad hoc, based on implicit and domain-dependent knowledge. In this article, we address the root of the problem by learning more robust objective functions. First, we formulate a set of desirable properties for objective functions and give a concrete example function that has these properties. Then, we propose a novel approach that learns an objective function from training data generated by manual image annotations and this ideal objective function. In this approach, critical decisions such as feature selection are automated, and the remaining manual steps hardly require domain-dependent knowledge. Furthermore, an extensive empirical evaluation demonstrates that the obtained objective functions yield more robustness. Learned objective functions enable fitting algorithms to determine the best model fit more accurately than with designed objective functions.     

PCA在语音检测中的应用研究

提出主元分析PCA(Principal Component Analysis)用于语音检测的方法研究.用主元分析法在多维空间中建立坐标轴,将待处理信号投影到该坐标轴中,通过分析投影结果判断是否为语音信号.通过将语音和非语音分别建立子空间,来区分语音和非语音信号.该方法不同于常规的语音时域、频域处理方法,而是在多维空间中对信号进行分析.实验结果表明,该方法准确率高、简单、容易实现,而且能区分多种非语音信号.     

Accessibility of local government websites: influence of financial resources,county characteristics and local demographics

Universal Access in the Information Society - Although many studies have investigated how well government websites have implemented website accessibility standards, such as Section 508 and...     

Highly nonlinear balanced Boolean functions with good local and global avalanche characteristics

Here we deal with an interesting subset of n-variable balanced Boolean functions which satisfy strict avalanche criteria. These functions achieve the sum-of-square indicator value (a measure for global avalanche criteria) strictly less than 2²ⁿ⁺¹ and nonlinearity strictly greater than 2ⁿ⁻¹−2^⌊n/2⌋. These parameters are currently best known. Moreover, these functions do not possess any nonzero linear structure. The technique involves a well-known simple construction coupled with very good initial functions obtained by computer search, which were not known earlier.     

A multilayered microfluidic system with functions for local electrical and thermal measurements

Microfluidic systems have been extensively applied in research of chemistry, biology and fluidic dynamics. In these applications, local and precise measurements are often crucial for reliable results. We demonstrate here a multilayered, multifunctional microfluidic platform with embedded electrodes open to the microchannel and thermocouple sensors underneath the microchannel that are suitable for local electrical and thermal measurements, respectively. We demonstrate that precise transport measurements with ac excitation frequency up to 1 MHz can be performed for electrolytes in centimeter-long microchannels. Local temperature sensing of the fluids in the microchannels can also be performed on this system. Such system can be either used to characterize local electrical and thermal properties of fluids, or applied to the study of thermal related electrokinetic phenomena, such as joule heat generation in dc conductance or temperature dependence of electrical transport.