TY - GEN

T1 - Proof of hidden node number in MLP and experiments on well log data inversion

AU - Huang, Kou-Yuan

AU - Shen, Liang Chi

AU - You, Jiun Der

PY - 2015/9/28

Y1 - 2015/9/28

N2 - In the multilayer perceptron (MLP), there was a theorem about the maximum number of separable regions (M) given the number of hidden nodes (H) in the input d-dimensional space. We propose a recurrence relation in the high dimensional space and prove the theorem using the expansion of recurrence relation instead of proof by induction. The MLP model has input layer, one hidden layer, and output layer. We use different MLP models on the well log data inversion to test the number of hidden nodes determined by the theorem. The inputs are the first order, second order, and third order features. Higher order neural network (HONN) has the property of more nonlinear mapping. In the experiments, we have 31 simulated well log data. 25 well log data are used for training, and 6 are for testing. The experimental results can support the number of hidden nodes determined by the theorem.

AB - In the multilayer perceptron (MLP), there was a theorem about the maximum number of separable regions (M) given the number of hidden nodes (H) in the input d-dimensional space. We propose a recurrence relation in the high dimensional space and prove the theorem using the expansion of recurrence relation instead of proof by induction. The MLP model has input layer, one hidden layer, and output layer. We use different MLP models on the well log data inversion to test the number of hidden nodes determined by the theorem. The inputs are the first order, second order, and third order features. Higher order neural network (HONN) has the property of more nonlinear mapping. In the experiments, we have 31 simulated well log data. 25 well log data are used for training, and 6 are for testing. The experimental results can support the number of hidden nodes determined by the theorem.

KW - Multilayer perceptron

KW - hidden node number

KW - higher order neural network

KW - recurrence formula

KW - well log data inversion

UR - http://www.scopus.com/inward/record.url?scp=84951207570&partnerID=8YFLogxK

U2 - 10.1109/IJCNN.2015.7280447

DO - 10.1109/IJCNN.2015.7280447

M3 - Conference contribution

AN - SCOPUS:84951207570

T3 - Proceedings of the International Joint Conference on Neural Networks

BT - 2015 International Joint Conference on Neural Networks, IJCNN 2015

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 12 July 2015 through 17 July 2015

ER -