基于蒙特卡罗最小二乘的实验数据拟合方法

采用最小二乘法拟合化工实验数据,相关系数接近于1,精度高,但所得的结果与经验关联式大相径庭。蒙特卡罗方法是一种基于概率模型的非确定性数值方法。蒙特卡罗最小二乘拟合方法处理化工实验数据,应用中更为灵活,适用范围更广。在Excel电子表格中,利用工作表中的数据与VBA混合编程很容易完成蒙特卡罗最小二乘数据拟合,VBA实现与Excel电子表格的数据通讯及并行处理实验数据,读取工作表中的实验数据,计算随机点的大致搜索范围,进行最小二乘统计分析,将结果输出到工作表中。蒙特卡罗最小二乘拟合方法采用与最小二乘法相同的精度标准,在符合大数定理的基础上,精度大幅度提高。蒙特卡罗方法在随机搜索点较小时,误差很大,当随机搜索点达到10000时,其精度与最小二乘法相差无几,却得到与经验关联式十分接近的准数关系方程,取得了实践与理论统一的实验效果。     

一种用于数据校正的最小二乘与准最小二乘组合方法

过程系统的控制与优化要求可靠的过程数据。通过测量得到的过程数据含有随机误差和过失误差,采用数据校正技术可有效地减小过程测量数据的误差,从而提高过程控制与优化的准确性。针对传统基于最小二乘的数据校正方法:和基于准最小二乘的鲁棒数据校正方法:,分析了它们的优缺点,并提出了一种最小二乘与准最小二乘组合方法:。该方法:先采用准最小二乘估计器检测过失误差并剔除,然后再采用最小二乘估计器进行数据校正,可以综合前两种方法:各自的优点,使得数据校正结果:更加准确。将提出最小二乘与准最小二乘组合方法:应用于线性与非线性系统的数据校正中,通过校正结果:的比较说明此方法:的具有较好的过失误差检测能力和较准确的数据校正结果:。最后将此方法:应用于实际过程系统空气分离流程的数据校正中,结果:说明了此方法:的有效性。     

A least squares method in back fitting the data base of a simulation model

This article presents an application of the least squares method in a particular class of inverse problems. Knowing the solution from experimental measurements, what are the corrections we must apply to the data of the problem in order to make the result close as much as possible to it? Normally the data of the problem are state functions known with a given degree of precision and in solving this problem the precision can be enhanced. This kind of problem is felt in many fields of engineering and physics, where an adjustment of a mathematical model on experimental observation is needed. This article shows a method to determine some residual function to be added to the data in order to refine the predictive power of the numerical model. An example is shown in a simple but concrete application.     

面向非匀点云拟合的RSR移动最小二乘法

针对传统的移动最小二乘法在非均匀分布的采样点集拟合中的不足,提出了影响域半径动态调整的移动最小二乘法（RSRMLS）。在传统移动最小二乘法（MLS）的基础上,根据拟合子区域采样点数据稀疏情况,该方法可自动调整MLS的半径区域大小。通过对相同数据点集的拟合比较,提出的RSRMLS拟合效果明显优于传统MLS。     

Hyper least squares fitting of circles and ellipses

This work extends the circle fitting method of Rangarajan and Kanatani (2009) to accommodate ellipse fitting. Our method, which we call HyperLS, relies on algebraic distance minimization with a carefully chosen scale normalization. The normalization is derived using a rigorous error analysis of least squares (LS) estimators so that statistical bias is eliminated up to second order noise terms. Numerical evidence suggests that the proposed HyperLS estimator is far superior to the standard LS and is slightly better than the Taubin estimator. Although suboptimal in comparison to maximum likelihood (ML), our HyperLS does not require iterations. Hence, it does not suffer from convergence issues due to poor initialization, which is inherent in ML estimators. In this sense, the proposed HyperLS is a perfect candidate for initializing the ML iterations.     

Adaptive least squares method for estimation of partial cloud coverage within a pixel

A study of the estimation of partial cloud cover within a pixel has been conducted in order to be able to use pixels partially contaminated with cloud in sea surface temperature determination.

The existing estimation methods based on the least squares method with constraints of minimizing the mixing ratio and observation vector, are theoretically compared and then an adaptive least squares method is proposed. In a comparative study the estimation accuracies for the proposed and other existing methods, including the maximum likelihood method, are compared with simulated and real satellite image data of NOAA AVHRR and MOS-1 VTIR. The results with the simulation data show that the maximum likelihood method is best followed by the adaptive least squares method, the least squares method and the observation vector, while the results with the real VTIR data show that the proposed adaptive least squares method is best followed by the least squares method, the maximum likelihood method and the observation vector but there is no significant differences between all these methods.     

最小二乘曲线拟合在溶液表面张力实验数据处理中的应用

为了优化正丁醇溶液表面张力实验的数据处理方法,本文使用线性和非线性最小二乘曲线拟合方法拟合σ-c关系曲线,并比较了2种拟合方法在溶液表面张力实验数据处理中的应用效果,发现后者能更好地反映正丁醇水溶液表面张力与浓度的函数关系,拟合效果较好,拟合后的计算较简便,计算正丁醇分子截面积结果较准确.继续用后者处理舍弃了2个高浓度数据后的实验数据,拟合效果更好,计算分子截面积结果更准确.在处理正丁醇溶液表面张力实验数据时,应避免使用线性最小二乘曲线拟合方法,应使用非线性最小二乘曲线拟合方法.在正丁醇溶液表面张力实验中,应避免使用高浓度溶液,应使用较低浓度的溶液.     

基于最小二乘拟合的模糊隶属函数构建方法

针对当前模糊隶属函数构造方法中存在的问题,提出一种构造模糊隶属函数方法.采用最小二乘法拟合离散数据来获得隶属函数.为减小拟合误差,采用了3项措施以达到预期目标.所构建的隶属函数,对任意输入物理量可直接得到其对应模糊语言变量的隶属度,从而有效避免专家指定隶属度的主观臆断性及不一致性.该方法简单、求解精度高,具有广泛适用性和较强的应用价值.仿真结果证实了该方法的有效性.     

面向大规模数据流处理的偏最小二乘法

用光谱分析鉴别生物特征,导致数据量大,而实际需要必须实时处理。偏最小二乘法是使用最广泛的鉴别算法,但是对于大规模数据流该算法无法达到实时性。为了解决这个应用矛盾,提出了一种基于NVIDIA CUDA架构下的并行计算策略,利用具有大规模并行计算特征的图形处理器（GPU）作为计算设备,结合GPU存储器的优势实现了偏最小二乘算法。实验的测试结果表明,在GPU上使用CUDA实现的偏最小二乘算法比在CPU上实现该算法快了47倍,性能得到了显著提高,从而使偏最小二乘算法应用于大规模数据流处理成为可能。     

Adaptive pruning algorithm for least squares support vector machine classifier

As a new version of support vector machine (SVM), least squares SVM (LS-SVM) involves equality instead of inequality constraints and works with a least squares cost function. A well-known drawback in the LS-SVM applications is that the sparseness is lost. In this paper, we develop an adaptive pruning algorithm based on the bottom-to-top strategy, which can deal with this drawback. In the proposed algorithm, the incremental and decremental learning procedures are used alternately and a small support vector set, which can cover most of the information in the training set, can be formed adaptively. Using this set, one can construct the final classifier. In general, the number of the elements in the support vector set is much smaller than that in the training set and a sparse solution is obtained. In order to test the efficiency of the proposed algorithm, we apply it to eight UCI datasets and one benchmarking dataset. The experimental results show that the presented algorithm can obtain adaptively the sparse solutions with losing a little generalization performance for the classification problems with no-noises or noises, and its training speed is much faster than sequential minimal optimization algorithm (SMO) for the large-scale classification problems with no-noises.     

Efficient method for lossless LIDAR data compression

Light Detection and Ranging (LIDAR) has become one of the prime technologies for rapid collection of vast spatial data, usually stored in a LAS file format (LIDAR data exchange format standard). In this article, a new method for lossless LIDAR LAS file compression is presented. The method applies three consequent steps: a predictive coding, a variable-length coding and an arithmetic coding. The key to the method is the prediction schema, where four different predictors are used: three predictors for x, y and z coordinates and a predictor for scalar values, associated with each LIDAR point. The method has been compared with the popular general-purpose methods and with a method developed specially for compressing LAS files. The proposed method turns out to be the most efficient in all test cases. On average, the LAS file is losslessly compressed to 12% of its original size.     

A least squares algorithm for fitting an ultrametric tree to a dissimilarity matrix

A least squares algorithm for fitting an ultrametric tree to a dissimilarity matrix is developed. The algorithm is evaluated in a Monte Carlo study in which error-perturbed randomly generated ultrametric distances were analyzed. Finally, an illustrative application is presented.     

A critical comparison of least absolute deviation fitting (robust) and least squares fitting: The importance of error distributions

Non-linear least absolute deviation fitting of data has been shown to be superior to least squares where the data errors are unevenly distributed about the function. The methods give insignificantly different results for evenly-distributed errors. Criteria are given for choosing between least absolute deviation and least squares error minimization. Optical density measurements have non-Gaussian error distributions and are better fitted with minimization of the absolute deviation.     

移动最小二乘法导数近似讨论

在移动最小二乘法（moving least squares method, MLS）构造无网格形函数的数值方法中,通常采用无单元伽辽金法（element-free Galerkin method, EFG）的建议,将系数向量a参与导数运算。为探讨这种导数近似算法在更一般无网格法中的适用性和合理性,针对系数向量a是否应参与运算的问题进行讨论和数值检验。结果表明：单纯从近似意义上讲,这种将系数向量代入导数运算的算法并不具有优势;从数值方法的应用意义上讲,这种导数近似算法对数值求解,特别是强式无网格法,会带来一系列潜在不稳定的问题。建议在MLS导数近似中,系数向量a不应当参与导数运算,并提出采用一种由核基函数代替普通基函数的核近似法。     

Flexible least squares for temporal data mining and statistical arbitrage

A number of recent emerging applications call for studying data streams, potentially infinite flows of information updated in real-time. When multiple co-evolving data streams are observed, an important task is to determine how these streams depend on each other, accounting for dynamic dependence patterns without imposing any restrictive probabilistic law governing this dependence. In this paper we argue that flexible least squares (FLS), a penalized version of ordinary least squares that accommodates for time-varying regression coefficients, can be deployed successfully in this context. Our motivating application is statistical arbitrage, an investment strategy that exploits patterns detected in financial data streams. We demonstrate that FLS is algebraically equivalent to the well-known Kalman filter equations, and take advantage of this equivalence to gain a better understanding of FLS and suggest a more efficient algorithm. Promising experimental results obtained from a FLS-based algorithmic trading system for the S&P 500 Futures Index are reported.     

The posterior selection method for hyperparameters in regularized least squares method

The selection of hyperparameters in regularized least squares plays an important role in large-scale system identification. The traditional methods for selecting hyperparameters are based on experience or marginal likelihood maximization method, which are inaccurate or computationally expensive. In this paper, two posterior methods are proposed to select hyperparameters based on different prior knowledge (constraints), which can obtain the optimal hyperparameters using the optimization theory. Moreover, we also give the theoretical optimal constraints, and verify its effectiveness. Numerical simulation shows that the hyperparameters and parameter vector estimate obtained by the proposed methods are the optimal ones.     

A least squares algorithm for a mixture model for compositional data

The estimation of a model for compositional data is studied where the data are approximated by a mixture of latent compositions. This model is variously known as “endmember analysis” or “latent budget analysis”. Two estimation procedures are available. The first uses a procedure which is incorrect in the sense that, although it claims to be a least squares procedure, it does not always minimize a least squares criterion. The second uses a maximum likelihood procedure starting from assumptions that are often violated for compositional data. In this paper we propose a constrained (weighted) least squares procedure for the estimation of the model.     

一种快速稀疏最小二乘支持向量回归机

将Jiao法直接应用于最小二乘支持向量回归机上的效果并不理想,为此采用不完全抛弃的策略,提出了改进的Jiao法,并将其应用于最小二乘支持向量回归机.数据集测试的结果表明,基于改进Jiao法的稀疏最小二乘支持向量回归机,无论在支持向量个数和训练时间上都取得了一定的优势.与其他剪枝算法相比,在不丧失回归精度的情况下,改进的Jiao法可大大缩短训练时间.另外,改进的Jiao法同样适用于分类问题.