模糊最小二乘支持向量机回归研究及应用

针对传统支持向量机对训练样本内的噪声和孤立点比较敏感,导致建模精度不高的问题,将模糊集理论引入到最小二乘支持向量机回归中,建立一种基于数据域描述的模糊最小二乘支持向量机回归的数学模型,该方法将样本映射到高维空间,在高维空间中寻找最小包含超球,然后根据样本到超球心的距离确定模糊隶属度的大小,通过仿真实验验证,该算法提高了支持向量机回归的训练精度,将此模型应用于谷氨酸发酵过程菌体浓度预测,结果表明此方法的有效性。     

Orthogonal vs. uncorrelated least squares discriminant analysis for feature extraction

In this paper, a new discriminant analysis for feature extraction is derived from the perspective of least squares regression. To obtain great discriminative power between classes, all the data points in each class are expected to be regressed to a single vector, and the basic task is to find a transformation matrix such that the squared regression error is minimized. To this end, two least squares discriminant analysis methods are developed under the orthogonal or the uncorrelated constraint. We show that the orthogonal least squares discriminant analysis is an extension to the null space linear discriminant analysis, and the uncorrelated least squares discriminant analysis is exactly equivalent to the traditional linear discriminant analysis. Comparative experiments show that the orthogonal one is more preferable for real world applications.     

一种在三个医学解剖面上任意切面图像提取的有效方法

针对在三个正交医学图像切面上任意斜切面的提取问题,通过空间几何知识,把抽象的切面空间位置关系进行描述,对不同的正交面上的提取切面采用相应的插值方式以获取较高质量的图片结果,从而为医生的临床提供更多和有效的图像视角。通过提取结果对采用的方法和原理进行了验证。     

基于多分割和口袋方法的最小二乘分类算法

提出了一种改进的最小二乘分类算法,该算法首先利用最小二乘算法对两类数据分类,然后计算每类的中心点,过中心点作已得到的分类线(面)的平行线(面),保留所作平行线(面)之间及线(面)上的数据,剔除其余数据,对剩余数据重新利用最小二乘算法分类,如此循环.在循环过程中利用口袋方法记录下具有最好的分类效果的分类线(面),循环结束后口袋中即为最佳分类线(面).实验结果表明,该算法有效的解决了原有最小二乘分类算法的缺陷,有着良好的分类效果.     

Fuzzy linear regression model based on fuzzy scalar product

The new concept and method of imposing imprecise (fuzzy) input and output data upon the conventional linear regression model is proposed in this paper. We introduce the fuzzy scalar (inner) product to formulate the fuzzy linear regression model. In order to invoke the conventional approach of linear regression analysis for real-valued data, we transact the α-level linear regression models of the fuzzy linear regression model. We construct the membership functions of fuzzy least squares estimators via the form of “Resolution Identity” which is a well-known formula in fuzzy sets theory. In order to obtain the membership value of any given least squares estimate taken from the fuzzy least squares estimator, we transform the original problem into the optimization problems. We also provide two computational procedures to solve the optimization problems.     

未标定单幅结构场景图像的三维重构

提出了一种单视三维重构方法，该方法是利用用户提供图像点及其对应的三维点之间几何信息。由于结构场景是由大量平面构成的，存在大量的平行性、正交性约束，因此该方法主要应用于结构场景的三维重构。首先，相机定标和计算每个平面的度量信息，即先基于3组互相垂直方向的影灭点，对方形像素相机标定，再利用影灭线和圆环点像，对每个平面度量校正；然后考虑每个校正平面的尺度因子和非正交平面间的相对面向，从而将所有校正后的平面缝合起来。采用真实图像进行实验，实验结果表明，该方法简单易用。     

基于测地回归模型的颅面复原

颅面复原是指根据一个未知颅骨的特征预测出对应的面貌,在考古研究、医学整容、刑事案件调查等领域有重要应用.为解决颅面复原过程中存在着数据量大、需要大量标定特征点的手工工作及颅面特征点定义困难的问题,针对三角网格表示的三维颅骨和面皮模型,将颅面模型用从鼻尖出发的一组测地线表示,提出了基于测地回归的颅面复原方法.该方法首先从...     

网点印刷呈色平面规律产生机理的初步探讨

寻找相对简便而又高效的颜色空间转换方法是色彩管理的一项关键内容,网点呈色平面规律作为一种客观现象为研究颜色空间转换提供了较新颖的思路。采用ECI2002标准色靶数据,利用数理统计的二元线性回归方法,验证了平面理论的正确性,并首次通过CIE1931Yxy色度系统,分析平面理论的产生机理。     

Kernel continuum regression

The continuum regression technique provides an appealing regression framework connecting ordinary least squares, partial least squares and principal component regression in one family. It offers some insight on the underlying regression model for a given application. Moreover, it helps to provide deep understanding of various regression techniques. Despite the useful framework, however, the current development on continuum regression is only for linear regression. In many applications, nonlinear regression is necessary. The extension of continuum regression from linear models to nonlinear models using kernel learning is considered. The proposed kernel continuum regression technique is quite general and can handle very flexible regression model estimation. An efficient algorithm is developed for fast implementation. Numerical examples have demonstrated the usefulness of the proposed technique.     

A Hough Transform with projection for velocity estimation

An extended Hough Transform is proposed to estimate the velocity of Regions Of Interest (ROI). Each ROI is first characterized by a spatio-temporal point (centroids for example). The velocity of each point is then computed by searching the line that passes through this point and fits at best the other ones. In order to avoid high dimension problems (a three-dimensional (3D) spatio-temporal line is defined by four parameters), the data are projected on several planes. The velocities are deduced by combining the results obtained on each plane using weighted least squares. The robustness of this method called “Hough Transform with Projection (HTP)”, compared to the Standard Hough Transform (applied on 3D spatio-temporal data) is demonstrated. Finally, experimental results on synthetic and real sequences validate the approach.     

两种基于等式约束支持向量回归机比较研究

为了减小支持向量回归机(SVR)的计算复杂度、缩短训练时间,将应用于分类问题的近似支持向量机(PSVM)扩展到回归问题中,针对其原始优化问题采用直接法求取最优解,而不是转换为对偶问题求解,给出了近似支持向量回归机(PSVR)线性和非线性回归算法.并与同样基于等式约束的最小二乘支持向量回归机(LSSVR)进行了比较,在一维、二维函数回归以及不同规模通用数据集上的测试结果表明,PSVR算法简单,训练速度快,尤其在大规模数据集处理上更具优势.     

基于协同最小二乘支持向量机的Q学习

针对强化学习系统收敛速度慢的问题, 提出一种适用于连续状态、离散动作空间的基于协同最小二乘支持向量机的Q学习. 该Q学习系统由一个最小二乘支持向量回归机(Least squares support vector regression machine, LS-SVRM)和一个最小二乘支持向量分类机(Least squares support vector classification machine, LS-SVCM)构成. LS-SVRM用于逼近状态--动作对到值函数的映射, LS-SVCM则用于逼近连续状态空间到离散动作空间的映射, 并为LS-SVRM提供实时、动态的知识或建议(建议动作值)以促进值函数的学习. 小车爬山最短时间控制仿真结果表明, 与基于单一LS-SVRM的Q学习系统相比, 该方法加快了系统的学习收敛速度, 具有较好的学习性能.     

PLS在状态检测多元线性回归中的应用

系统的状态检测过程中,各影响因子之闻往往存在着多重相关性,给回归建模分析带来许多负面影响,采用偏最小二乘(PLS)回归建模分析可以很好地解决这个问题.在简述PLS原理的基础上,结合系统状态检测仿真数据,建立系统的状态检测的PLS模型,分别验证PLS回归预测模型用于多个自变量对单个因变量和多个自变量对多个因变量的回归模型...     

Transformation-based estimation

To alleviate the computational burden of making the relevant estimation algorithms stable for nonlinear and semiparametric regression models with, particularly, high-dimensional data, a transformation-based method combining sufficient dimension reduction approach is proposed. To this end, model-independent transformations are introduced to models under study. This generic methodology can be applied to transformation models; generalized linear models; and their corresponding quantile regression variants. The constructed estimates almost have closed forms in certain sense such that the above goals can be achieved. Simulation results show that, in finite sample cases with high-dimensional predictors and long-tailed distributions of error, the new estimates often exhibit a smaller degree of variance, and have much less computational burden than the classical methods such as the classical least squares and quantile regression estimation.     

基于支持向量回归的光谱反射率重建方法

提出了一种基于支持向量回归和小框架核的光谱反射率重建方法。光谱反射率重建是光学研究的一个重要问题,其目的是通过各种成像设备所获取的与设备相关的RGB三色值重建出物体本身固有的与设备和光照都无关的光谱反射率。回归方法已经在这一领域取得了广泛应用,如基于多项式模型的正则化最小二乘方法、基于核的正则化最小二乘方法等。提出了一种新的光谱反射率重建方法,这种方法采用了一种可以减弱样本不规则噪音影响的小框架核函数,并将其用于支持向量回归来重建光谱反射率函数。实验表明,新方法可以提高光谱反射率重建的精度和稳定性。     

局部惩罚加权核偏最小二乘算法及其应用

为改善软测量模型精度,提出了一种局部惩罚加权核偏最小二乘算法.该方法通过核映射将原始输入映射到高维特征空间实现对非线性问题的线性化处理,并通过偏最小二乘算法进行主成分提取,降低数据维数;对由主成分构成的新数据集,依据局部学习思想构建局部惩罚加权最小二采回归模型,降低模型对异常数据的敏感度、优化模型参数.鉴于多模型可以改...     

虚平面映射:深度图像内部视点的绘制技术

首先推导与归纳了图像三维变换中像素深度场的变换规律,同时提出了基于深度场和极线原则的像素可见性别方法,根据上述理论和方法,提出一种基于深度图像的建模与绘制(image-based modeling and rendering,简称IBMR)技术,称为虚平面映射.该技术可以基于图像空间内任意视点对场景进行绘制.绘制时,先在场景中根据视线建立若干虚拟平面,将源深度图像中的像素转换到虚平面上,然后通过对虚平面上像素的中间变换,将虚平面转换成平面纹理,再利用虚平面的相互拼接,将视点的成像以平面纹理映射的方式完成.新方法还能在深度图像内侧,基于当前视点快速获得该视点的全景图,从而实现视点的实时漫游.新方法视点运动空间大、存储需求小,且可以发挥图形硬件的纹理映射功能,并能表现物体表面的三维凹凸细节和成像视差效果,克服了此前类似算法的局限和不足.     

基于粒子群优化的最小二乘支持向量机税收预测模型研究

针对税收收入预测存在着非线性、不稳定性和多经济因素影响的复杂性,提出用最小二乘支持向量回归机的方法对广东省从化市的税收收入进行预测,并建立数学模型。由于模型中的参数C和σ²直接影响支持向量机的预测效果,因此巧妙地融合了粒子群优化算法的思想,采用粒子群算法对参数进行寻优来确保预测模型的精确性和稳定性。仿真实验结果表明,相对于各参比模型,用粒子群算法对参数进行寻优的最小二乘支持向量回归机的预测精度有了显著提高,从而说明了该模型的有效性和实用性。     

基于特征指数加权的最小二乘支持向量机算法

根据支持向量回归机原理,针对样本特征对回归预测重要性的差异,采用最小二乘支持向量回归机(LS-SVR)算法,减少参数数量,针对参数对预测效果的影响,并考虑到特征加权的意义,采用特征指数进行加权,其权重系数由灰色关联度确定,提出了基于特征指数加权的最小二乘支持向量回归机算法。为验证该算法的有效性,对实际股票价格进行预测,结果表明该算法较传统最小二乘支持向量回归机算法,其回归估计函数的预测能力明显提高,具有一定的实用价值。     

A random sampling strategy for piecewise planar scene segmentation

We investigate the problem of automatically creating 3D models of man-made environments that we represent as collections of textured planes. A typical approach is to automatically reconstruct a sparse 3D model made of points, and to manually indicate their plane membership, as well as the delineation of the planes: this is the piecewise planar segmentation phase. Texture images are then extracted by merging perspectively corrected input images. We propose an automatic approach to the piecewise planar segmentation phase, that detects the number of planes to approximate the scene surface to some extent, and the parameters of these planes, from a sparse 3D model made of points. Our segmentation method is inspired from the robust estimator ransac. It generates and scores plane hypotheses by random sampling of the 3D points. Our plane scoring function and our plane comparison function, required to prevent detecting the same plane twice, are designed to detect planes with large or small support. The plane scoring function recovers the plane delineation and quantifies the saliency of the plane hypothesis based on approximate photoconsistency. We finally refine all the 3D model parameters, i.e., the planes and the points on these planes, as well as camera pose, by minimizing the reprojection error with respect to the measured image points, using bundle adjustment. The approach is validated on simulated and real data.