Quintic spline smooth semi-supervised support vector classification machine

A semi-supervised vector machine is a relatively new learning method using both labeled and unlabeled data in classifi- cation. Since the objective function of the model for an unstrained semi-supervised vector machine is not smooth, many fast opti- mization algorithms cannot be applied to solve the model. In order to overcome the difficulty of dealing with non-smooth objective functions, new methods that can solve the semi-supervised vector machine with desired classification accuracy are in great demand. A quintic spline function with three-times differentiability at the ori- gin is constructed by a general three-moment method, which can be used to approximate the symmetric hinge loss function. The approximate accuracy of the quintic spiine function is estimated. Moreover, a quintic spline smooth semi-support vector machine is obtained and the convergence accuracy of the smooth model to the non-smooth one is analyzed. Three experiments are performed to test the efficiency of the model. The experimental results show that the new model outperforms other smooth models, in terms of classification performance. Furthermore, the new model is not sensitive to the increasing number of the labeled samples, which means that the new model is more efficient.

Denoising of hyperspectral imagery by cubic smoothing spline in the wavelet domain

The acquired hyperspectral images （HSIs） are inherently attected by noise wlm Dano-varylng level, which cannot be removed easily by current approaches. In this study, a new denoising method is proposed for removing such kind of noise by smoothing spectral signals in the transformed multi- scale domain. Specifically, the proposed method includes three procedures： 1 ） applying a discrete wavelet transform （DWT） to each band; 2） performing cubic spline smoothing on each noisy coeffi- cient vector along the spectral axis; 3 ） reconstructing each band by an inverse DWT. In order to adapt to the band-varying noise statistics of HSIs, the noise covariance is estimated to control the smoothing degree at different spectra｜ positions. Generalized cross validation （GCV） is employed to choose the smoothing parameter during the optimization. The experimental results on simulated and real HSIs demonstrate that the proposed method can be well adapted to band-varying noise statistics of noisy HSIs and also can well preserve the spectral and spatial features.

逻辑回归模型的Smooth LASSO及Spline LASSO变量选择

对于逻辑回归模型中的参数估计和变量选择问题,提出了Smooth LASSO以及Spline LASSO.当变量具有连续性,使用Smooth LASSO,可以获得局部恒定的系数.但是在有些情况下,系数可能不同并且缓慢变化,可以使用Spline LASSO来估计参数.本文通过理论证明模型的可靠性,利用坐标下降法对模型进行求解,最后通过模拟验证了模型在变量选择中的准确性以及较好的预测性.

HAZARD REGRESSION WITH PENALIZED SPLINE:THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.

A Study on Precipitation Products with High Resolution in Anhui Province Based on Thin Plate Smoothing Spline

In order to achieve refined precipitation grid data with high accuracy and high spatial resolution,hourly precipitation grid dataset with 1 km spatial resolution in Anhui Province from May to September (in the rainy season) in 2016 and from August 2017 to July 2018 was established based on thin plate smoothing spline (TPS),which meets the needs of climate change research and meteorological disaster risk assessment.The interpolation errors were then analyzed.The grid precipitation product obtained based on thin plate smoothing spline,CLDAS-FAST and CLDAS-FRT were evaluated.The results show that the interpolated values of hourly precipitation by thin plate smoothing spline are close to the observed values in the rainy season of 2016.The errors are generally below 0.9 mm/h.However,the errors of precipitation in the mountainous areas of eastern Huaibei and western Anhui are above 1.2 mm/h.On monthly scale,the errors in June and July are the largest,and the proportion of absolute values of the errors ≥2 mm/h is up to 2.0% in June and 2.2% in July.The errors in September are the smallest,and the proportion of absolute values of the errors ≥2 mm/h is only 0.6%.The root mean square (RMSE) is only 0.37 mm/h,and the correlation coefficient (COR) is 0.93.The interpolation accuracy of CLDAS-FRT is the highest,with the smallest RMSE (0.65 mm/h) and mean error ( ME =0.01 mm/h),and the largest COR (0.81).The accuracy of the precipitation product obtained by thin plate smoothing spline interpolation is close to that of CLDAS-FAST.Its RMSE is up to 0.80 mm/h,and its ME is only -0.01 mm/h.Its COR is 0.73,but its bias (BIAS) is up to 1.06 mm/h.

Automatically Smoothing the Spectroscopic Data by Cubic B-Spline Basis Functions

In the present paper,a new criterion is derived to obtain the optimum fitting curve while using Cubic B-spline basis functions to remove the statistical noise in the spectroscopic data.In this criterion,firstly,smoothed fitting curves using Cubic B-spline basis functions are selected with the increasing knot number.Then,the best fitting curves are selected according to the value of the minimum residual sum of squares(RSS)of two adjacent fitting curves.In the case of more than one best fitting curves,the authors use Reinsch's first condition to find a better one.The minimum residual sum of squares(RSS)of fitting curve with noisy data is not recommended as the criterion to determine the best fitting curve,because this value decreases to zero as the number of selected channels increases and the minimum value gives no smoothing effect.Compared with Reinsch's method,the derived criterion is simple and enables the smoothing conditions to be determined automatically without any initial input parameter.With the derived criterion,the satisfactory result was obtained for the experimental spectroscopic data to remove the statistical noise using Cubic B-spline basis functions.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

基于结点调整B-spline曲面G^1/G^2的光滑拼接

提出了一种构造具有简单结点的B样条曲面G1/G2光滑拼接的方法。该方法根据B样条曲面达到拼接的条件,经过对原曲面和待拼接曲面的偏导曲线进行离散化处理和结点调整,将其转化为Bézier的表示方式。根据Bézier的拼接条件,获得B样条曲面间控制点的关系。最终实现B样条曲面G1/G2的光滑拼接。

二维手绘形状的Spline拟合及角点检测方法

通过二维输入设备采样获得的手绘形状数据为离散的点,这些数据只有当被以某种数学形式表示时有更多的实际意义,Spline即是一种常用的表示形式。本文对手绘形状数据进行了参数化,在此基础上进行了Spline拟合。然而将一个手绘形状中的全部点序列进行Spline拟合时会使尖状角点被平滑,因而使手绘形状的这一重要特征发生了偏离。为此,本文对一次拟合的Spline进行曲率计算,求取曲率的极大值,并将极大值作为角点将采样点进行分段,然后对分段后的采样点进行二次Spline拟合。实验结果表明,这种方法在获得平滑效果较好的手绘形状的同时,保留了重要的角点特征。

A Fast Approach for Time Optimal and Smooth Trajectory Planning of Robot Manipulators

In this paper, a fast approach to generate time optimal and smooth trajectory has been developed and tested. Minimum time is critical for the productivity in industrial applications. Meanwhile, smooth trajectories based on cubic splines are desirable for their ability to limit vibrations and ensure the continuity of position, velocity and acceleration during the robot movement. The main feature of the approach is a satisfactory solution that can be obtained by a local modification process among each intermal between two consecutive via-points. An analytical formulation simplifies the approach to smooth trajectory and few,iterations are enough to determine the correct values. The approach can be applied in many robot manipulators which require high performance on time and smooth. The simulation and application of the approach on a palletizer robot are performed, and the experimental results provide evidence that the approach can realize the robot manipulators more efficiency and high smooth performance.

Estimation of the Piecewise Exponential Model by Bayesian P-Splines via Gibbs Sampling: Robustness and Reliability of Posterior Estimates

In the investigation of disease dynamics, the effect of covariates on the hazard function is a major topic. Some recent smoothed estimation methods have been proposed, both frequentist and Bayesian, based on the relationship between penalized splines and mixed models theory. These approaches are also motivated by the possibility of using automatic procedures for determining the optimal amount of smoothing. However, estimation algorithms involve an analytically intractable hazard function, and thus require ad-hoc software routines. We propose a more user-friendly alternative, consisting in regularized estimation of piecewise exponential models by Bayesian P-splines. A further facilitation is that widespread Bayesian software, such as WinBUGS, can be used. The aim is assessing the robustness of this approach with respect to different prior functions and penalties. A large dataset from breast cancer patients, where results from validated clinical studies are available, is used as a benchmark to evaluate the reliability of the estimates. A second dataset from a small case series of sarcoma patients is used for evaluating the performances of the PE model as a tool for exploratory analysis. Concerning breast cancer data, the estimates are robust with respect to priors and penalties, and consistent with clinical knowledge. Concerning soft tissue sarcoma data, the estimates of the hazard function are sensitive with respect to the prior for the smoothing parameter, whereas the estimates of regression coefficients are robust. In conclusion, Gibbs sampling results an efficient computational strategy. The issue of the sensitivity with respect to the priors concerns only the estimates of the hazard function, and seems more likely to occur when non-large case series are investigated, calling for tailored solutions.

Performance Analysis of Image Smoothing Techniques on a New Fractional Convolution Mask for Image Edge Detection

We present the analysis of three independent and most widely used image smoothing techniques on a new fractional based convolution edge detector originally constructed by same authors for image edge analysis. The implementation was done using only Gaussian function as its smoothing function based on predefined assumptions and therefore did not scale well for some types of edges and noise. The experiments conducted on this mask using known images with realistic geometry suggested the need for image smoothing adaptation to obtain a more optimal performance. In this paper, we use the structural similarity index measure and show that the adaptation technique for choosing smoothing function has significant advantages over a single function implementation. The new adaptive fractional based convolution mask can smoothly find edges of various types in detail quite significantly. The method can now trap both local discontinuities in intensity and its derivatives as well as locating Dirac edges.

改进RRT算法的四旋翼无人机路径规划方法

针对快速扩展随机树(rapidly-exploring random tree,RRT)算法在无人机路径规划过程中采样次数多、生成路径曲折等问题,提出了一种将路径重规划策略和平滑度优化相结合的路径规划算法。首先,通过重新构造采样区域降低RRT算法采样次数,利用目标偏向寻优策略为RRT算法添加导向性;其次,在筛选初始航迹点的同时引入无人机性能约束;然后,利用B样条对重规划路径进行平滑处理;最后,利用Matlab对所提出的算法进行仿真实验。实验结果为平均采样次数为386次,平均运行时间为0.43 s,平均航迹距离为1392.16(无量纲),表明了算法可有效降低采样次数并改善路径平滑性。

基于五次B样条插值的机械臂路径平滑研究

针对机械臂路径规划后的轨迹平滑及角速度和角加速度的突变问题,提出五次B样条插值的机械臂路径平滑方法。通过MATLAB对机械臂建模,并对平滑后的轨迹进行仿真,得到轨迹、角度、角速度及角加速度图。通过与五次多项式和样条曲线对比,证明该算法能够提升机械臂角速度和角加速度的平滑性,保证起、止点速度加速度均为零,过控制点保证路径的有效性。该算法提升了机械臂运动的平顺性,降低运动冲击,为机械臂实物验证提供充分的理论支撑。

MFCDD优化三次样条平滑算法在继电器数据插值中的应用

继电器参数众多,并且对各参数的测量方式和测量间隔不同,释放电压等参数相较于时间参数等实时测量参数,数据量较少,在进行相关分析时会造成结果精度较差的情况。提出一种形态波动一致性偏移距离(MFCDD)优化的平滑指标改进三次样条插值算法。引入平滑指标改进,对数据序列相关点的方差贡献率及单点平滑度进行分析,确定数据序列的平滑点及波动点;采用三次指数平滑对三次样条算法进行改进,确定改进后的插值表达式;引入形态波动一致性偏移距离对插值间隔进行确定,完成数据扩充。采用继电器吸合电压参数和释放电压参数对上述方法进行验证,结果表明上述方法对数据扩充具有较好的准确性。

欠驱动无人船全局轨迹规划方法研究

针对大范围水域内传统全局轨迹规划算法收敛速度慢的问题,提出了基于高效收敛随机树与样条插值的欠驱动无人船全局轨迹规划方法。首先,引入目标区域偏置采样、动态步长扩展以及双向搜索策略,显著缩短渐近最优航路点的规划时间。其次,采用B样条插值技术拟合以上航路点,生成一条参数化路径,再利用期望速度与参数导数得到平滑轨迹,便于无人船跟踪。最后,开展综合的仿真研究,结果表明该方法在收敛速度上明显优于传统轨迹规划方法,且在规划轨迹的引导下,无人船能够安全、稳定地航行。

局部可调的四次Catmull-Rom样条曲面及其形状优化

当控制顶点保持不变时,无法对三次Catmull-Rom样条曲面的形状进行局部调整。为满足实际工程对插值曲面形状设计的要求,给出了一种含局部参数的四次Catmull-Rom样条曲面,并讨论了2种对四次Catmull-Rom样条曲面形状进行优化的方案。结果表明,四次Catmull-Rom样条曲面不仅继承了三次Catmull-Rom样条曲面的插值性与连续性,而且容易利用所含的参数对曲面形状进行局部或整体调整,通过计算所含参数的最优值获得尽可能光顺和尽可能保形的四次Catmull-Rom样条曲面,为插值曲面的构造提供了方法。

B样条与磨光样条在基于矩形格网的DEM内插中的应用

本文研究了 B样条和磨光样条应用在基于矩形格网的 DEM内插中的思想、方法及实现过程。并从逼真性 ,保凸性 ,光滑性 ,运算速度等方面对 B样条、磨光样条与双线性内插算法做了实验比较。理论和实验表明 ,所述方法具有较好的效果。

基于五次B样条的机械手关节空间平滑轨迹规划

为实现机械手作业轨迹平滑,关节轨迹的速度、加速度、加加速度保持连续,起始和停止的速度、加速度和加加速度可以任意配置,采用5次B样条曲线插值方法构造关节轨迹。推导了B样条曲线插值轨迹算法;通过VC++6.0开发平台,基于MFC框架类和OpenGL图形库仿真出机械手的运动过程,并绘制出各关节的位置、速度、加速度时间曲线图。仿真结果表明,该方法使机械手关节调整平滑且运动平稳,运动性能显著优于传统的三次样条轨迹规划。

车轮磨耗分析中平滑方法的选取

为了更好地去除车轮磨耗计算数据中的噪声点,基于数值平滑理论,利用车轮磨耗预测模型得到的车轮磨耗数据,对五点三次平滑法、三次样条平滑法和超光平滑法进行对比研究.结果表明:超光平滑法能在有效抑制噪声的同时,较好地保持磨耗数据的细节信息,更适合处理车轮磨耗数据;将三次样条平滑法与超光平滑法相结合处理磨耗噪声数据,既能保证曲线足够光滑,又能防止数据失真现象.