Data fitting example 3 2 1 0 -2 -1 0 1 2 The result of fitting a set of data points with a quadratic function DATA 17 Copyright 2019 by Xiaoyu Li
Copyright © 2019 by Xiaoyu Li. 17 Data fitting example The result of fitting a set of data points with a quadratic function
Data fitting example 20 15 10 -5 -10 -15 -2020 -15-10-5051015 20 Conic fitting a set of points using least- squares approximation 18 DATA Copyright 2019 by Xiaoyu Li
Copyright © 2019 by Xiaoyu Li. 18 Data fitting example Conic fitting a set of points using leastsquares approximation
1 The least square method-LSM A standard approach in regression analysis to the approximate solution of over determined systems; Widely used to find or estimate the numerical values of the parameters to fit a function to a set of data and to characterize the statistical properties of estimates; Means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation; The most important application is in data fitting 19 Copyright 2019 by Xiaoyu Li
Copyright © 2019 by Xiaoyu Li. 19 1 The least square method-LSM A standard approach in regression analysis to the approximate solution of over determined systems； Widely used to find or estimate the numerical values of the parameters to fit a function to a set of data and to characterize the statistical properties of estimates； Means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation； The most important application is in data fitting
2 Variations of LSM .Ordinary least squares-OLS 。普通最小二乘法 Weighted least squares-WLS ·加权最小二乘法 .Alternating least squares-ALS ·交替最小二乘法 Partial least squares-PLS 。偏最小二乘法 20 DATA Copyright 2019 by Xiaoyu Li
Copyright © 2019 by Xiaoyu Li. 20 2 Variations of LSM Ordinary least squares-OLS 普通最小二乘法 Weighted least squares-WLS 加权最小二乘法 Alternating least squares-ALS 交替最小二乘法 Partial least squares-PLS 偏最小二乘法
3 The principle of LSM (1) a set of N pairs of observations {Yi,Xi} values of an independent variable (X) value of the dependent variable (Y) the prediction is given by the following equation: Y=a+bx. (1) This amounts to minimizing the expression: 8=∑(Y-)2=∑Y-(a+bX2 (2) (where stands for "error"which is the quantity to be minimized) D】ATA 21 Copyright 2019 by Xiaoyu Li
Copyright © 2019 by Xiaoyu Li. 21 3 The principle of LSM (1)