Research On Algorithm Complexity And Application Of First Class Orthogonal (Tensor) Weight Function Neural Network

Traditional neural network algorithms such as Back Propogation and Radical Basis Functionalgorithm is easy to fall into local minimum point and have slow training convergence, literature [1]propose the concept of spline weight function neural network, give the learning algorithm. Splineweight function neural network has a simple structure, fast training speed and would not fall intolocal minimum point. The literatures also give the simulation experiment which shows that thespline weight function neural network has a good approximation and generalization abilitycompared with traditional neural networks.This article which bases on spline weight function neural network theory combines the weightfunction neural network with the orthogonal polynomials fitting functions, give the concept of firstcategory orthogonal weight function neural network that weight functions are polynomialsfunctions with orthogonal polynomials fitting. Simulation result shows that compared withtraditional neural network algorithm, first category orthogonal weight function neural network havea certain advantage both on training time and recognition accuracy.To solve the singular samples issue in traditional weight function neural network trainingsamples, this paper also proposes a method that use tensor invariant mathematical property to docoordinate transformation to singular samples that solve the singular issue in traditional sampleswhich extract after feature extraction.This paper finally applies first category orthogonal weight function neural network in facerecognition technology, extrace features from face images in AT&T face database and YaleB facedatabase and use the sample to train first category orthogonal weight function neural networkclassifier. Experiment results show that compared with the traditional neural network classifier anddistance-based classifier, the first category orthogonal weight function neural network has a greatlyimproved overall performance in both training time and recognition rate.