Kernel PCA for Feature Extraction and De-Noising in Nonlinear Regression

In this paper, we propose the application of the Kernel Principal Component Analysis (PCA) technique for feature selection in a high-dimensional feature space, where input variables are mapped by a Gaussian kernel. The extracted features are employed in the regression problems of chaotic Mackey–Glass time-series prediction in a noisy environment and estimating human signal detection performance from brain event-related potentials elicited by task relevant signals. We compared results obtained using either Kernel PCA or linear PCA as data preprocessing steps. On the human signal detection task, we report the superiority of Kernel PCA feature extraction over linear PCA. Similar to linear PCA, we demonstrate de-noising of the original data by the appropriate selection of various nonlinear principal components. The theoretical relation and experimental comparison of Kernel Principal Components Regression, Kernel Ridge Regression and ε-insensitive Support Vector Regression is also provided.     

Roll Waves in High Gradient Channels

Abstract

Vedernikov's number quantifies the allowable capacity that can be sustained as a stable uniform flow in a high gradient channel, but it does not provide any guidance to the design of freeboard when roll waves exist. Without considering roll waves, high gradient channels are undersized using the uniform flow approach and fail to maintain design integrity. This paper presents revised design curves to determine the stability of flow in high gradient channels. When the design condition exceeds the limiting condition, roll waves should be considered in design. This study applies the model of moving hydraulic jump to simulate roll waves. It provides estimations for wave heights when Froude number is greater than 1.50.     

The geometry of flex tangents to a cubic curve and its parameterizations

We show how the study of the geometry of the nine flex tangents to a cubic produces pseudo-parameterizations, including the ones given by Icart, Kammerer, Lercier, Renault and Farashahi, and infinitely many new ones.     

Least eccentric ellipses for geometric Hermite interpolation

We present a rational Bézier solution to the geometric Hermite interpolation problem. Given two points and respective unit tangent vectors, we provide an interpolant that can reproduce a circle if possible. When the tangents permit an ellipse, we produce one that deviates least from a circle. We cast the problem as a theorem and provide its proof, and a method for determining the weights of the control points of a rational curve. Our approach targets ellipses, but we also present a cubic interpolant that can find curves with inflection points and space curves when an ellipse cannot satisfy the tangent constraints.     

四次C-Bézier曲线的拼接技术研究

为了解决造型设计中复杂曲线难以用单一曲线来表示的问题,研究了一种带形状参数的四次C-Bézier曲线的光滑拼接技术.在对四次C-Bézier曲线基函数及其端点性质分析的基础上,给出了两相邻四次C-Bézier曲线间G1、G2和C1、C2的光滑拼接的充要条件,同时还给出了两相邻四次C-Bézier曲线间光滑拼接的基本步骤和几何造型实例.实例结果表明,所提方法简单有效、易实现,极大地增强了四次C-Bézier曲线表达复杂曲线的能力,可广泛地应用于各种CG/CAD/CAID/CAM造型系统中.     

采用主成分分法评价水电开发对人地关系的影响

怒江水电开发将会对当地的经济、生态、环境、旅游、景观等多方面带来较大影响。对此,已开展了大量的研究,以定性研究主,定量研究较少,而且多以单一因素影响为主,综合研究较少。文中对已有人地关系研究成果分析,选取影响人地关系各方面有代表性的4大方面的13个指标,采用主成分分析法,就怒江水电开发对当地人地关系的影响定量地进行了综合评价分析。     

有限封闭环境中基于PCA的水声测距方法

有限空间中多途效应严重影响测距的准确性,针对该问题,提出一种基于主成分分析的水声信号测距方法,对信号协方差矩阵进行降维和特征抽取,在保留协方差矩阵信息量的同时抑制多途干扰信号的影响。实验结果表明,该方法能够提高有限封闭液态场环境中水声测距的准确性和稳健性。     

Reduced order optimization for model predictive control using principal control moves

In order to reduce the computational complexity of model predictive control (MPC) a proper input signal parametrization is proposed in this paper which significantly reduces the number of decision variables. This parametrization can be based on either measured data from closed-loop operation or simulation data. The snapshots of representative time domain data for all manipulated variables are projected on an orthonormal basis by a Karhunen-Loeve transformation. These significant features (termed principal control moves, PCM) can be reduced utilizing an analytic criterion for performance degradation. Furthermore, a stability analysis of the proposed method is given. Considerations on the identification of the PCM are made and another criterion is given for a sufficient selection of PCM. It is shown by an example of an industrial drying process that a strong reduction in the order of the optimization is possible while retaining a high performance level.     

An improved SVD-based watermarking technique for copyright protection

The drawbacks of SVD-based image watermarking are false positive, robust and transparency. The former can be overcome by embedding the principal components of the watermark into the host image, the latter is dependent on how much the quantity (i.e., scaling factor) of the principal components is embedded. For the existing methods, the scaling factor is a fixed value; actually, it is image-dependent. Different watermarks need the different scaling factors, although they are embedded in the same host image. In this paper, two methods are proposed to improve the reliability and robustness. To improve the reliability, for the first method, the principal components of the watermark are embedded into the host image in discrete cosine transform (DCT); and for the second method, those are embedded into the host image in discrete wavelets transform (DWT). To improve the robustness, the particle swarm optimization (PSO) is used for finding the suitable scaling factors. The experimental results demonstrate that the performance of the proposed methods outperforms than those of the existing methods.