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Clustering Irregular Shapes Using High-Order Neurons

Mechanical Engineering Department, Technion—Israel Institute of Technology, Haifa 32000, Israel

H. T. Siegelmann

Industrial Engineering and Management Department, Technion—Israel Institute of Technology, Haifa 32000, Israel

This article introduces a method for clustering irregularly shaped data arrangements using high-order neurons. Complex analytical shapes are modeled by replacing the classic synaptic weight of the neuron by high-order tensors in homogeneous coordinates. In the first- and second-order cases, this neuron corresponds to a classic neuron and to an ellipsoidal-metric neuron. We show how high-order shapes can be formulated to follow the maximum-correlation activation principle and permit simple local Hebbian learning. We also demonstrate decomposition of spatial arrangements of data clusters, including very close and partially overlapping clusters, which are difficult to distinguish using classic neurons. Superior results are obtained for the Iris data.

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				K. Ramanathan and S.-U. Guan Multiorder neurons for evolutionary higher-order clustering and growth. Neural Comput., December 1, 2007; 19(12): 3369 - 3391. [Abstract] [Full Text] [PDF]