[Support Vector Machine (SVM)]: Gaussian Kernel Matlab Implementation

原创于 2020-08-07 14:36:37 发布 · 512 阅读

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#matlab #支持向量机 #svm

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本文深入解析了支持向量机(SVM)中高斯核函数的原理及MATLAB实现代码，展示了如何通过高斯核函数计算样本之间的相似度，适用于解决非线性分类问题。

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SVM Gaussian Kernel 支持向量机
MATLAB代码

公式
$Kgaussian(x(i),x(j))=exp⁡(−∥x(i)−x(j)∥22σ2)=exp⁡(−∑k=1n(xk(i)−xk(j))22σ2)K_{gaussian}(x^{(i)},x^{(j)}) =\exp\left(-\frac{\left\| x^{(i)}-x^{(j)}\right\|^2}{2\sigma^2}\right) =\exp\left(-\frac{\sum_{k=1}^n{(x_k^{(i)}-x_k^{(j)})^2}}{2\sigma^2}\right)$

function sim = gaussianKernel(x1, x2, sigma)
%RBFKERNEL returns a radial basis function kernel between x1 and x2
%   sim = gaussianKernel(x1, x2) returns a gaussian kernel between x1 and x2
%   and returns the value in sim

% Ensure that x1 and x2 are column vectors x1 = [1 2 1]; x2 = [0 4 -1]; 
x1 = x1(:); x2 = x2(:);

% You need to return the following variables correctly.
sim = 0;

% ===========================================
% Instructions: Fill in this function to return the similarity between x1
%               and x2 computed using a Gaussian kernel with bandwidth
%               sigma

% Simularity function
% 方法一
sim = exp(-((x1-x2)' * (x1-x2)) / (2 * sigma^2));
% 方法二
sim = exp(-sum((x1-x2).^2)/(2*sigma^2));

end