核函数-KernelFunction的讲义.pdfVIP

核函数 -Kernel Function Kernel Functions Below is a list of some kernel functions available from the existing literature. As was the case with previous articles, every LaTeX notation for the formulas below are readily available from their alternate text html tag . I can not guarantee all of them are perfectly correct, thus use them at your own risk. Most of them have links to articles where they have been originally used or proposed. 1. Linear Kernel The Linear kernel is the simplest kernel function. It is given by the inner product x,y plus an optional constant c. Kernel algorithms using a linear kernel are often equivalent to their non-kernel counterparts, i.e. KPCA with linear kernel is the same as standard PCA . 2. Polynomial Kernel The Polynomial kernel is a non-stationary kernel. Polynomial kernels are well suited for problems where all the training data is normalized. Adjustable parameters are the slope alpha, the constant term c and the polynomial degree d. 3. Gaussian Kernel The Gaussian kernel is an example of radial basis function kernel. Alternatively, it could also be implemented using The adjustable parameter sigma plays a major role in the performance of the kernel, and should be carefully tuned to the problem at hand. If overestimated, the exponential will behave almost linearly and the higher-dimensional projection will start to lose its non-linear power. In the other hand, if underestimated, the function will lack regularization and the decision boundary will be highly sensitive to noise in training data. 4. Exponential Kernel The exponential kernel is closely related to the Gaussian kernel, with only the square of the norm left out. It is also a radial basis function kernel. 5. Laplacian Kernel The Laplace Kernel is completely equivalent to the exponential kernel, except for being less sensitive for changes in the sigma