【摘要】 研究了用于分类的投影寻踪学习网络，给出了投影寻踪网络的学习机理，证明了基于Ｌｅｇｅｎｄｒｅ 多项式投影寻踪学习的收敛性，并用投影寻踪学习网络较完满地解决了６４ 维三类目标的分类问题及冰雹云数据的分类问题。更多还原

【Abstract】 ANN (artificial neural network), when applied to classification of high dimensional data, suffers from the following two shortcomings: (1) convergence rate is low, and (2) it is apt to converge to a local minimum. We present a new network——projection pursuit learning network (PPLN) based on Legendre polynomial——to overcome these shortcomings. We propose the criterion function for PPLN as shown in eq.(3), where P m is the m th Lengendre polynomial, E is expectation. Using stochastic approximation method and lagranges′ method of multiplier, we get eq.(5), where the weight vector w is updated by eq.(9). Compared with BPL (backpropagation learning) which estimates all the weights simultaneously at each iteration, PPLN estimates the weights cyclically (neuron by neuron and layer by layer) at each iteration. BPL uses fixed nonlinear activations (usually sigmoidal) for hidden neurons, while PPLN uses Legendre polynomial to approximate the unknown nonlinear activations. At the end of section 1, we give the six steps for learning algorithm of PPLN. In section 2, after a lengthy derivation, we proved that the convergence rate of PPLN is O(n -1/2 ), where n is the number of nodes in the hidden layer of PPLN. Figs.3 through 5 give the classification of the same meteorologic data by Hebb learning method (Fig.3), nonlinear Hebb learning method (Fig.4) and PPLN (Fig.5) respectively. They show that both PPLN and nonlinear Hebb learning can achieve much better results than that of linear Hebb learning. But the computational overhead of PPLN is much smaller than nonlinear Hebb learning. Fig.6 gives the classification result of three targets from hundreds of 64 dimentionnal radar data by PPLN. It shows that PPLN is an effective network for classification.更多还原