▁nature ▁of ▁the ▁non - linear ▁hidden ▁neur ons ▁versus ▁the ▁linear ▁output ▁neur on . ▁ ▁Training ▁the ▁basis ▁function ▁cent ers ▁ ▁Bas is ▁function ▁cent ers ▁can ▁be ▁randomly ▁sample d ▁among ▁the ▁input ▁instances ▁or ▁obtained ▁by ▁Orth ogonal ▁Le ast ▁Square ▁Learning ▁Algorithm ▁or ▁found ▁by ▁clust ering ▁the ▁samples ▁and ▁choosing ▁the ▁cluster ▁means ▁as ▁the ▁cent ers . ▁ ▁The ▁R BF ▁width s ▁are ▁usually ▁all ▁fixed ▁to ▁same ▁value ▁which ▁is ▁proportional ▁to ▁the ▁maximum ▁distance ▁between ▁the ▁chosen ▁cent ers . ▁ ▁Pse udo in verse ▁solution ▁for ▁the ▁linear ▁weights ▁ ▁After ▁the ▁cent ers ▁ ▁have ▁been ▁fixed , ▁the ▁weights ▁that ▁minim ize ▁the ▁error ▁at ▁the ▁output ▁can ▁be ▁computed ▁with ▁a ▁linear ▁pseudo in verse ▁solution : ▁, ▁where ▁the ▁entries ▁of ▁G ▁are ▁the ▁values ▁of ▁the ▁radial ▁basis ▁functions ▁evaluated ▁at ▁the ▁points ▁: ▁. ▁ ▁The ▁existence ▁of ▁this ▁linear ▁solution ▁means ▁that ▁unlike ▁multi - layer ▁per cept ron ▁( ML P ) ▁networks , ▁R BF ▁networks ▁have ▁an ▁explicit ▁minim izer ▁( when ▁the ▁cent ers ▁are ▁fixed ). ▁ ▁Grad ient ▁descent ▁training ▁of ▁the ▁linear ▁weights ▁ ▁Another ▁possible ▁training ▁algorithm ▁is ▁gradient ▁descent . ▁In ▁gradient ▁descent ▁training , ▁the ▁weights ▁are ▁adjust ed ▁at ▁each ▁time ▁step ▁by ▁moving ▁them ▁in ▁a ▁direction ▁opposite ▁from ▁the ▁gradient ▁of ▁the ▁objective ▁function ▁( th us ▁allowing ▁the ▁minimum ▁of ▁the ▁objective ▁function ▁to ▁be ▁found ), ▁ ▁where ▁