Using fuzzy clustering with ellipsoidal units in neural networks for robust fault classification.
Computers Chem Eng 1993; 17(8):765-784
A neural network for classification problems and a two stage procedure for network construction and training were proposed. An ellipsoidal activation function was incorporated in the squashing function to give ellipsoidal contours to the constant value of the nodes, in contrast to the hyperplanes formed by linear activation constants. The proposed network consisted of an input layer, a hidden layer which used ellipsoidal activation functions, and an output layer. The ellipsoid formed by the hidden node in the input space was determined by the weights of the connections between the input nodes to each of the hidden nodes. In this network there were two connections from each of the input nodes to each of the hidden nodes. The domain of the classes was defined by the combination of the ellipsoids of the hidden layer. The output layer linearly combined the contributions of the formed ellipsoids to describe the class corresponding to an output node. The weights on the connections from the hidden layer to the output layer were restricted to be positive and the bias weight was restricted to be negative. The advantages of ellipsoidal over linear activation in diagnostic applications were discussed. Use of a fuzzy clustering algorithm allowed the proposal of a set of initial weights and the determination of a minimal number of hidden weights, thus avoiding local minima traps. Gravity effects were also avoided by use of fuzzy membership, eliminating the need for a trial and error approach in the determination of the number of hidden nodes. A modified back propagation algorithm was used to train the network and fine tune the weights. The authors conclude that fuzzy clustering and network decomposition resulted in significantly reduced network training time.
NIOSH-Publication; NIOSH-Grant; Control-technology; Models; Mathematical-models; Monitoring-systems; Information-processing; Analytical-methods
Chemical Engineering Purdue University West Lafayette, IN 47907
Computers in Chemical Engineering
Purdue University West Lafayette, West Lafayette, Indiana