TY - JOUR

T1 - An artificial neural network with partitionable outputs

AU - Guan, Biing T.

AU - Gertner, George Z.

N1 - Funding Information:
This project is partially supported by the U.S. Army Construction Engineering Research Laboratory and by the MC&ire-Stennis MS FOR 55-320. Computer time on the CM-2 computer was granted by the National Center for Supercomputing Applications (NCSA) at University of Illinois at ‘Urbana-Champaign.

PY - 1996/12

Y1 - 1996/12

N2 - In this paper we present a neural network with partitionable outputs. The network is a feedforward network but with special weight connection patterns. Hidden nodes are grouped into subsets with each subset connecting only to one input and no connection between any two subsets. The activation function for the hidden nodes is the arc tangent function (tan-1), and the activation function for the outputs is a linear function (i.e., no squashing). A network of this type can be trained by any available training algorithm. As an example, the proposed network was used to estimate the prediction variances of an ecological model. Two sets of data were generated using a Monte Carlo method; one set for training and the other set for validation. A random optimization procedure was used as the training algorithm. Validation results showed that the network indeed can approximate the unknown variance propagating function. One of the network outputs was then partitioned according to the contribution of each input, and the relative importance of each input was then determined. We believe that the proposed network is a good alternative to certain statistical methods, and it will be a valuable tool for approximation problems that require the partitioning of outputs as part of the results.

AB - In this paper we present a neural network with partitionable outputs. The network is a feedforward network but with special weight connection patterns. Hidden nodes are grouped into subsets with each subset connecting only to one input and no connection between any two subsets. The activation function for the hidden nodes is the arc tangent function (tan-1), and the activation function for the outputs is a linear function (i.e., no squashing). A network of this type can be trained by any available training algorithm. As an example, the proposed network was used to estimate the prediction variances of an ecological model. Two sets of data were generated using a Monte Carlo method; one set for training and the other set for validation. A random optimization procedure was used as the training algorithm. Validation results showed that the network indeed can approximate the unknown variance propagating function. One of the network outputs was then partitioned according to the contribution of each input, and the relative importance of each input was then determined. We believe that the proposed network is a good alternative to certain statistical methods, and it will be a valuable tool for approximation problems that require the partitioning of outputs as part of the results.

KW - Ecological model

KW - Error budget

KW - Mechanistic forest growth model

KW - Neural network

KW - Partitionable output

KW - Uncertainty assessment

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U2 - 10.1016/S0168-1699(96)00025-7

DO - 10.1016/S0168-1699(96)00025-7

M3 - Article

AN - SCOPUS:0030417945

VL - 16

SP - 39

EP - 46

JO - Computers and Electronics in Agriculture

JF - Computers and Electronics in Agriculture

SN - 0168-1699

IS - 1

ER -