Get locations and sizes of radial basis functions for use in rbf network. Radial basis function are a simple, fast method for universal function approximation / regression. The idea is to find a mapping X->y where X and y are continuous real variables. The mapping is linear over features of X: y=rbfWeight*features(X). The features are of the form: f_j(x) = exp(-||x-mu_j||_2^2 / 2 sig_j^2 ). The number of basis functions controls the complexity of the network. Too many basis functions can lead to overfitting, too few to bad interpolation. Rbf networks are trained in two phases. First, the radial basis functions are found in an unsupervised manner (using only Xtrain), for example by clustering Xtrain. Next, given the basis functions, Xtrain and ytrain, the basis weights are found by solving the system: rbfWeight * features(Xtrain) = ytrain At this point, to interpolate any new points, Xtest, use: ytest = rbfWeight * features(Xtest) The code below achieves all three steps: rbfBasis = rbfComputeBasis( Xtrain, k, cluster, scale, show ); rbfWeight = rbfComputeFtrs(Xtrain,rbfBasis) \ ytrain; ytest = rbfComputeFtrs(Xtest,rbfBasis) * rbfWeight; Note, in the returned rbfBasis struct there are a number of flags that control how the rbf features are computed. These can be altered to achieve the desired effect. For an in depth discussion of rbf networks see: Christopher M. Bishop. "Neural Networks for Pattern Recognition" USAGE rbfBasis = rbfComputeBasis( X, k, [cluster], [scale], [show] ) INPUTS X - [N x d] N points of d dimensions each k - number of basis functions to use cluster - [1]: Computes cluster centers for use as rbf functions. - 0: Evenly centered basis functions (ok for small d) scale - [5] Alter computed value of sigma by given factor set larger for smoother results, too small -> bad interp show - [0] will display results in figure(show) if show<0, assumes X is array Nxs^2 of N sxs patches OUTPUTS rfbBasis .d - feature vector size .k - number of basis functions actually used .mu - [d x k] rbf centers .vars - [1 x k] rbf widths .var - rbf average width .globalVar - [1] if true use single average var for rbfs .constant - [0] if true include extra basis with constant activation .normalize - [0] if true normalize overall rbf response to sum to 1 EXAMPLE See also RBFDEMO, RBFCOMPUTEFTRS Piotr's Computer Vision Matlab Toolbox Version 2.50 Copyright 2014 Piotr Dollar. [pdollar-at-gmail.com] Licensed under the Simplified BSD License [see external/bsd.txt]

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