This is a MATLAB implementation of the domain segmentation algorithm described in my thesis work, which is available at https://github.com/cao-/Tesi-Magistrale.
The Test.m script gives an example of usage for the function domain_segmentation.m.
The parameters of this function are
X -> the set of data sites
Z -> the set of data values
rf -> the positive definite radial function to use
b -> the global shape parameter for the radial funcion
k -> the number of local points to consider
tol -> the tolerance for the classification
The test functions h1, h2, h3, h4, h5 are the same used in the thesis.
The Reconstruction.m script, if executed after the Test.m script, allows to actually recover the sampled functions by using Support Vector Machines (SVM) and Radial Basis Functions (RBF) interpolation.
The parameters for the SVM can be set inside the function classificating_function.m.
Interpolation is performed globally on each subdomain by the function interpolate.m. This function may be replaced by some partition of unity interpolation method for better performance.
The implementation of the multiclass SVM that is described in the thesis (script Reconstruction.m) may produce bad results when the discontinuity curves of the function have intersections---a better strategy for multiclass SVM should be implemented. One example is the one-vs-all approach implemented in the script Reconstruction_onevsall.m.