Properties of predictor based on relative neighborhood graph localized FIR filters

A time signal prediction algorithm based on relative neighborhood graph (RNG) localized FIR filters is defined. The RNG connects two nodes, of input space dimension D, if their lune does not contain any other node. The FIR filters associated with the nodes, are used for local approximation of the training vectors belonging to the lunes formed by the nodes. The predictor training is carried out by iteration through 3 stages: initialization of the RNG of the training signal by vector quantization, LS estimation of the FIR filters localized in the input space by RNG nodes and adaptation of the RNG nodes by equalizing the LS approximation error among the lunes formed by the nodes of the RNG. The training properties of the predictor is exemplified on a burst signal and characterized by the normalized mean square error (NMSE) and the mean valence of the RNG nodes through the adaptation.