A comparison of second-order neural networks to transform-based method for translation- and orientation-invariant object recognition

Neural networks can use second-order neurons to obtain invariance to translations in the input pattern. Alternatively transform methods can be used to obtain translation invariance before classification by a neural network. The authors compare the use of second-order neurons to various translation-invariant transforms. The mapping properties of second-order neurons are compared to those of the general class of fast translation-invariant transforms introduced by Wagh and Kanetkar (1977) and to the power spectra of the Walsh-Hadamard and discrete Fourier transforms. A fast transformation based on the use of higher-order correlations is introduced. Three theorems are proven concerning the ability of various methods to discriminate between similar patterns. Second-order neurons are shown to have several advantages over the transform methods. Experimental results are presented that corroborate the theory