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N-dimension geometrical approach to the design of an automatic feature extraction scheme in a noniterative neural network

To continue the study we reported last year in this conference, we would like to present here the theoretical origin of our design of this super-fast learning, neural network pattern recognition system. As we published in the last few years, a one-layered, hard-limited perceptron can be used to classify analog pattern vectors if the latter satisfy the PLI condition. For most pattern recognition applications, this condition should be satisfied. When this condition is satisfied, then an automatic feature extraction scheme can be derived using some N-dimension Euclidean geometry theories. This automatic scheme will automatically extract the most distinguished parts of the N-vectors used in the training. It selects the feature vectors automatically according to the descending order of the volumes of the parallelepiped spanned by these sub-vectors. Theoretical derivation and numerical examples revealing the physical nature of this process and its effect in optimizing the robustness of this novel pattern recognition system will be reported in detail.