It is shown in this paper that if the hidden layer units take a sinusoidalactivation function,the optimum weights of the three-layer feedforward neural networkcan be explicitly solved by relating the layered neural ne...It is shown in this paper that if the hidden layer units take a sinusoidalactivation function,the optimum weights of the three-layer feedforward neural networkcan be explicitly solved by relating the layered neural network with a truncated Fourier se-ries expansion.Based on this result,two approaches are presented of which one is suited tothe case that the detailed statistical information is available or can be easily estimated.An-other is of data-adaptive type,which can be treated as a solution of standardleast-squares.The later is best suited to realtime processing and slowly time-varying ap-plications since it can be straightforwardly implemented by the traditional LMS or RLSadaptive algorithms.It is also shown that for both the approaches,the resulting networksown an ability of forming arbitrary mappings.By using the present approaches,theconventional training procedure,which is usually very time-consuming,can be avoided.展开更多
基金This work was supported by grant 69102007 from the NSF of China the Ph.D Research Foundation of State Educational Commission of China.
文摘It is shown in this paper that if the hidden layer units take a sinusoidalactivation function,the optimum weights of the three-layer feedforward neural networkcan be explicitly solved by relating the layered neural network with a truncated Fourier se-ries expansion.Based on this result,two approaches are presented of which one is suited tothe case that the detailed statistical information is available or can be easily estimated.An-other is of data-adaptive type,which can be treated as a solution of standardleast-squares.The later is best suited to realtime processing and slowly time-varying ap-plications since it can be straightforwardly implemented by the traditional LMS or RLSadaptive algorithms.It is also shown that for both the approaches,the resulting networksown an ability of forming arbitrary mappings.By using the present approaches,theconventional training procedure,which is usually very time-consuming,can be avoided.
