Improved fast Gauss transform User manual

In most kernel based machine learning algorithms and non-parametric statistics the key computational task is to compute a linear combination of local kernel functions centered on the training data, i.e., f(x) = ∑N i=1 qik(x, xi), which is the discrete Gauss transform for the Gaussian kernel. f is the regression/classification function in case of regularized least squares, Gaussian process regression, support vector machines, kernel regression, and radial basis function neural networks. For nonparametric density estimation it is the kernel density estimate. Also many kernel methods like kernel principal component analysis and spectral clustering algorithms involve computing the eigen values of the Gram matrix. Training Gaussian process machines involves the solution of a linear system of equations. Solutions to such problems can be obtained using iterative methods, where the dominant computation is evaluation of f(x).