A Discrete Data Fitting Models Fusing Genetic Algorithm

2011 ◽  
Vol 267 ◽  
pp. 427-432
Author(s):  
Tong Rang Fan ◽  
Yong Bin Zhao ◽  
Lan Wang
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Discrete Distribution ◽  
Data Fitting ◽  
Small Sample ◽  
Load Testing ◽  
Accurate Data ◽  
Sample Data ◽  
Testing Data ◽  
Dynamic Measuring

To address problems of Least squares method (LSM) fitting curves in application domains, the essay attempts to build a new model by using LMS (Least Median Squares) to analyze the error points, and pretreating the dynamic measuring errors and then getting the fitting curves of testing data. This model is used for electromotor parameters testing which includes load testing and unload testing. Experiments show that the model can erase the influence of outline points, while improving the effects of data curve fitting and reflecting the characteristic of the motor, provide more accurate data fitting curve with small sample data that is in discrete distribution compared with Least squares method.

scholarly journals Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

2008 ◽  
Vol 8 (2) ◽  
pp. 6409-6436 ◽  
Author(s):  
C. A. Cantrell
Keyword(s):  
Least Squares ◽  
Atmospheric Chemistry ◽  
Least Squares Method ◽  
Technical Note ◽  
Routine Practice ◽  
Data Sets ◽  
Straight Line ◽  
Sample Data ◽  
Straight Lines ◽  
Best Fit

Abstract. The representation of data, whether geophysical observations, numerical model output or laboratory results, by a best fit straight line is a routine practice in the geosciences and other fields. While the literature is full of detailed analyses of procedures for fitting straight lines to values with uncertainties, a surprising number of scientists blindly use the standard least squares method, such as found on calculators and in spreadsheet programs, that assumes no uncertainties in the x values. Here, the available procedures for estimating the best fit straight line to data, including those applicable to situations for uncertainties present in both the x and y variables, are reviewed. Representative methods that are presented in the literature for bivariate weighted fits are compared using several sample data sets, and guidance is presented as to when the somewhat more involved iterative methods are required, or when the standard least-squares procedure would be expected to be satisfactory. A spreadsheet-based template is made available that employs one method for bivariate fitting.

scholarly journals Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

2008 ◽  
Vol 8 (17) ◽  
pp. 5477-5487 ◽  
Author(s):  
C. A. Cantrell
Keyword(s):  
Least Squares ◽  
Atmospheric Chemistry ◽  
Least Squares Method ◽  
Technical Note ◽  
Routine Practice ◽  
Data Sets ◽  
Straight Line ◽  
Sample Data ◽  
Straight Lines ◽  
Best Fit

Abstract. The representation of data, whether geophysical observations, numerical model output or laboratory results, by a best fit straight line is a routine practice in the geosciences and other fields. While the literature is full of detailed analyses of procedures for fitting straight lines to values with uncertainties, a surprising number of scientists blindly use the standard least-squares method, such as found on calculators and in spreadsheet programs, that assumes no uncertainties in the x values. Here, the available procedures for estimating the best fit straight line to data, including those applicable to situations for uncertainties present in both the x and y variables, are reviewed. Representative methods that are presented in the literature for bivariate weighted fits are compared using several sample data sets, and guidance is presented as to when the somewhat more involved iterative methods are required, or when the standard least-squares procedure would be expected to be satisfactory. A spreadsheet-based template is made available that employs one method for bivariate fitting.

A Comparison of Different Methods for LAD Regression

2010 ◽  
Vol 143-144 ◽  
pp. 1328-1331
Author(s):  
Hai Jun Chen ◽  
Xiao Ling Liu ◽  
Ling Hui Liu
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Least Squares Method ◽  
Small Sample ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
Simple Alternative ◽  
Dual Forms

The least squares method is very sensitive to outliers, one of the simple alternative is the least absolute deviation, i.e. L1 regression, which is less sensitive to outliers, so which is more suitable the small sample and much noise situation. In this paper, the L1 problem of linear model is discussed, the previous work is reviewed systematically, different algorithms is compared, it is proved that the dual forms of different algorithms are the same.

Study on Forecasting the OD Volume of Railway Luggage and Parcel

2011 ◽  
Vol 105-107 ◽  
pp. 1280-1283
Author(s):  
Xue Fei Li ◽  
Mao Xiang Lang
Keyword(s):  
Least Squares ◽  
Gravity Model ◽  
Statistical Data ◽  
Least Squares Method ◽  
High Accuracy ◽  
Gray Model ◽  
Sample Data

The OD volume of railway luggage and parcel on Beijing-Guangzhou Corridor is forecasted by using the gray model and the gravity model. According to the historical statistical data, firstly the sending and arrival volume of railway luggage and parcel of the major cities on Beijing-Guangzhou Corridor is forecasted by applying the gray model and it takes the Beijing volume of railway luggage and parcel for example to show the calculative process. Secondly, by using the least squares method to calibrate the sample data, obtain the value of each coefficient to be determined, get the calibrated gravity model and then the OD volume of railway luggage and parcel is forecasted by adopting the gravity model. Finally the rationality of the forecasting results is analyzed and the forecasting results which can be used in the railway luggage and parcel organization work have a high accuracy and meet the actual needs.

The Application of Total Least Squares Method in Data Fitting of Speed Radar

2012 ◽  
Vol 203 ◽  
pp. 69-75 ◽  
Author(s):  
Cheng Chen ◽  
Chang Jin Liu
Keyword(s):  
Least Squares ◽  
Initial Velocity ◽  
High Speed ◽  
Least Squares Method ◽  
Data Fitting ◽  
Total Least Squares ◽  
Measure Data ◽  
Observation Data ◽  
Unknown Parameters ◽  
Observation Matrix

For acquiring the initial velocity of high-speed object, it needs data fitting to get the unknown parameters. Least squares method(LS) is usually uses to complete this work, but LS method takes no account of the errors in the observation matrix, not only may makes error in unknown parameters' fitting, but also do harm to the further analysis. Therefore, this paper lead total least squares method(TLS) into data fitting, it can at the same time in consideration of observation data and its error margin, and at last in actually measure data analysis to prove TLS compare to LS enjoy higher accuracy.

Application of the Least Squares Support Vector Machine Based on Quantum Particle Swarm Optimization for Data Fitting of Small Samples

2014 ◽  
Vol 472 ◽  
pp. 485-489 ◽  
Author(s):  
Hong Kai Wang ◽  
Ji Sheng Ma ◽  
Li Qing Fang ◽  
Yan Feng Yang ◽  
Hai Ping Liu
Keyword(s):  
Support Vector Machine ◽  
Particle Swarm Optimization ◽  
Least Squares ◽  
Quantum Particle ◽  
Particle Swarm ◽  
Data Fitting ◽  
Small Sample ◽  
Support Vector ◽  
Swarm Optimization ◽  
Quantum Particle Swarm Optimization

In order to better observe the trend of small sample data, this paper based on that the least squares support vector machine (LS-SVM) algorithm has an outstanding performance in the data processing of small sample, presents a data fitting method for small sample. The quantum particle swarm optimization (QPSO) that has better global search ability is used to optimize the parameters of the least squares support vector machine, and establish the curve fitting model. According to error analysis, show that the method presented in this paper has a good application value.

scholarly journals Measurement Data Fitting Based on Moving Least Squares Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Huaiqing Zhang ◽  
Chunxian Guo ◽  
Xiangfeng Su ◽  
Chuanbao Zhu
Keyword(s):  
Data Processing ◽  
Least Squares ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Data Fitting ◽  
Local Approximation ◽  
Least Square ◽  
Superior Performance ◽  
Moving Least Squares

In the electromagnetic field measurement data postprocessing, this paper introduced the moving least squares (MLS) approximation method. The MLS combines the concept of moving window and compact support weighting functions. It can be regarded as a combination of weighted least squares and segmented least square. The MLS not only can acquire higher precision even with low order basis functions, but also has good stability due to its local approximation scheme. An attractive property of MLS is its flexible adjustment ability. Therefore, the data fitting can be easily adjusted by tuning weighting function’s parameters. Numerical examples and measurement data processing reveal its superior performance in curves fitting and surface construction. So the MLS is a promising method for measurement data processing.

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