Multi-aggregation Process Neural Networks

• Published in: Process Neural Networks pp. 143 - 160
• Main Authors: He, Xingui, Xu, Shaohua
• Format: Book Chapter
• Language: English
• Published: Germany Springer Berlin / Heidelberg 2009; Springer Berlin Heidelberg
• Series: Advanced Topics in Science and Technology in China
• Subjects: Artificial intelligence; General Regression Neural Network; Input Function; Multivariate Process; Pattern recognition; Reservoir Pressure; Well Bore
• ISBN: 9783540737612; 3540737618
• ISSN: 1995-6819
• DOI: 10.1007/978-3-540-73762-9_7

The inputs to the process neural networks introduced in previous chapters are only time-dependent unary functions. In fact, the input/output functions of the process neural networks need not always depend on time or one variable, they may depend on other multiple process factors, i.e. they may be arbitrary multivariate functions. For example, the output of a practical system whose inputs are relative to both a space position (x,y,z) and time t is the joint action result of several inputs depending on these process factors, such as debris flow formation[1], crop growth prediction[2], earthquake magnitude prediction[3], chemical action in a chemical reaction tower[4], etc. The forms of the input functions (such as rainfall, the degree of erosion, pressure, temperature, etc.) of these systems are ut(x,y,z,t) (i=l,2,...,n) which are all multivariate functions (or processes). If neural networks are used to simulate and build models for these dynamic systems, then multi-factor aggregation and accumulation must be considered when the neurons process the input information. Therefore, process neural networks with only a time dimension can be extended into multi-aggregation process neural networks that can process several multivariate functions (or processes). In this chapter, we will give several models of multi-aggregation process neural networks and derive a gradient descent learning algorithm based on the expansion of a multivariate function.