A Homomorphic Neural Network for Modeling and Prediction
A Homomorphic Neural Network for Modeling and Prediction
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DOI：
10.1162/neco.2008.12-06-418
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发表时间：
2008-04
影响因子：
2.9
通讯作者：
M. Pedzisz;D. Mandic
中科院分区：
文献类型：
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作者：
M. Pedzisz;D. Mandic
介绍了一种用于非线性自适应滤波的同态前馈网络。这是通过具有指数隐藏层和对数预处理步骤的两层前馈架构来实现的。这样，整个输入-输出关系可以被看作是一个广义的沃尔泰拉模型，或者看作是一组同态滤波器。介绍了这种结构的基于一致性的学习，以及与最佳学习参数的选择和权重初始化相关的一些实际问题。分析和大量的仿真验证了性能和收敛速度。为了严格，模拟进行人工和现实生活中的数据，并对具有相同拓扑结构的S形前馈网络（FFN）所获得的性能进行比较。建议HFFN被证明是一个可行的替代FFN，特别是在关键的情况下，在线学习的中小型数据集。
A homomorphic feedforward network (HFFN) for nonlinear adaptive filtering is introduced. This is achieved by a two-layer feedforward architecture with an exponential hidden layer and logarithmic preprocessing step. This way, the overall input-output relationship can be seen as a generalized Volterra model, or as a bank of homomorphic filters. Gradient-based learning for this architecture is introduced, together with some practical issues related to the choice of optimal learning parameters and weight initialization. The performance and convergence speed are verified by analysis and extensive simulations. For rigor, the simulations are conducted on artificial and real-life data, and the performances are compared against those obtained by a sigmoidal feedforward network (FFN) with identical topology. The proposed HFFN proved to be a viable alternative to FFNs, especially in the critical case of online learning on small- and medium-scale data sets.