A hierarchical fractal net for pattern classification

Hierarchical nets having sparse and localized connectivity with fractal connections within layers have been studied. The performance of the proposed net in classification problems has been compared to that of a fully connected multilayer perceptron and a randomly connected sparse net with an artificially generated fractal data set and a real data set derived from sonar signals for underwater target recognition. A simple version of the backpropagation algorithm has been used to train all the nets. The fractal net seems to be far better than the randomly connected sparse net in fractal pattern recognition. For the second data set the fractally connected net performs well compared to the fully connected net as fractal dimension is increased above 0.75. Moreover the fractal net seems to possess more generalization capability compared to the fully connected net in recognizing patterns other than training patterns