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Abstract : |
This paper introduces a novel feedforward network called the pi-sigma network. This network utilizes product cells as the output units to indirectly incorporate the capabilities of higher-order networks while using a fewer number of weights and processing units. The network has a regular structure, exhibits much faster learning, and is amenable to the incremental addition of units to attain a desired level of complexity. Simluation results show good convergence properties and accuracy for function approximation. Comparative results using the DARPA acoustic transient data set are also provided to highlight the classification abilities of pi-sigma networks. I. Higher-order feedforward networks Multi-layered perceptron (MLP) networks using the backpropagation learning rule or its variants have been successfully applied to applications involving pattern classification and function approximation. Unfortunately, the training speeds for multilayered networks are extremely slower than those for feedforward networks comprising of a single layer of threshold logic units, and using the perceptron, ADALINE or Hebbian type learning rules [1,2]. Moreover, these networks converge very slowly in typical situations dealing with complex and nonlinear problems, and do not scale well with problem size [2,3]. Higher-order correlations among the input components can be used to construct a higher-order network to yield a nonlinear discriminant function using only a single layer of cells [4]. The building block of such networks in the higher-order processing unit (HPU), defined as a neural processing unit that includes higher-order input correlations, and whose output, y, is given by [5,6]: y = s j, |
