Geometry of decision boundaries of neural networks

Chulhee Lee; Ohjae Kwon; Eunsuk Jung

doi:10.1117/12.449334

13 November 2001 Geometry of decision boundaries of neural networks

Chulhee Lee, Ohjae Kwon, Eunsuk Jung

Proceedings Volume 4471, Algorithms and Systems for Optical Information Processing V; (2001) https://doi.org/10.1117/12.449334
Event: International Symposium on Optical Science and Technology, 2001, San Diego, CA, United States

Abstract

In this paper, we provide a thorough analysis of decision boundaries of neural networks when they are used as a classifier. It has been shown that the classifying mechanism of the neural network can be divided into two parts: dimension expansion by hidden neurons and linear decision boundary formation by output neurons. In this paradigm, the input data is first warped into a higher dimensional space by the hidden neurons and the output neurons draw linear decision boundaries in the expanded space (hidden neuron space). We also note that the decision boundaries in the hidden neuron space are not completely independent. This dependency of decision boundaries is extended to multiclass problems, providing a valuable insight into formation of decision boundaries in the hidden neuron space. This analysis provides a new understanding of how neural networks construct complex decision boundaries and explains how different sets of weights may prove similar results.

Citation Download Citation

Chulhee Lee, Ohjae Kwon, and Eunsuk Jung "Geometry of decision boundaries of neural networks", Proc. SPIE 4471, Algorithms and Systems for Optical Information Processing V, (13 November 2001); https://doi.org/10.1117/12.449334

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