正交最小二乘拟合matlab代码
时间: 2025-02-26 14:21:40 浏览: 41
### 正交最小二乘拟合的MATLAB实现
对于正交最小二乘(OLS)拟合,在计算机视觉和图像分析领域内,虽然提供的参考资料未直接提及OLS的具体实现[^3],可以基于一般的线性回归原理并考虑误差项的方向来构建该方法。下面提供一段用于执行二维数据点集上正交最小二乘直线拟合的MATLAB代码示例:
```matlab
function [a, b] = orthogonalLeastSquaresFitting(xdata, ydata)
% ORTHOGONALEASTSQUARESFITTING Performs Orthogonal Least Squares Fitting.
%
% Input:
% xdata - Independent variable data points as a column vector.
% ydata - Dependent variable data points as a column vector.
%
% Output:
% a - Intercept parameter of the fitted line (y=ax+b).
% b - Slope parameter of the fitted line.
n = length(xdata);
centroidX = mean(xdata);
centroidY = mean(ydata);
% Construct matrix A and B according to OLS formulation
A = zeros(n, 2);
for i=1:n
dx = xdata(i)-centroidX;
dy = ydata(i)-centroidY;
A(i,:) = [dx,dy];
end
B = -(xdata.*xdata + ydata.*ydata)/2;
% Solve for parameters using SVD decomposition
[U,S,V] = svd(A,'econ');
V = V(:,end); % Last column corresponds to smallest singular value
params = V ./ norm(V);
a = params(2)/params(1);
b = centroidY-a*centroidX;
disp(['Estimated slope: ', num2str(a)]);
disp(['Estimated intercept:', num2str(b)]);
end
```
此函数接收两组对应的数据点作为输入参数`xdata` 和 `ydata` ,并通过奇异值分解(SVD)求解最优拟合直线方程中的斜率(`a`)与截距(`b`)。
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