Design of the Codewords for Performing the Pattern Recognitions via a Set of Perceptrons with the Domains of These Activation Functions Have More Than Two Pieces
Ziyin N. Huang, Bingo Wing‐Kuen Ling · 2019
This paper proposes a method for designing the codewords for performing the pattern recognitions via a set of perceptrons with the domains of these activation functions have more than two pieces. First, perform a clustering algorithm on a set of input feature vectors. Second, initialize the total number of the perceptrons as the dimensions of the input feature vectors. Third, for each perceptron and each cluster obtained in the above, estimate the weight vector as well as both the upper and the lower projection boundaries for all the input feature vectors in this particular cluster via an optimization approach. Fourth, determine the total number of the regions generated by the activation functions such that it is larger than or equal to the total number of the clusters. Fifth, for each perceptron, perform a clustering algorithm on the sets of both the upper and the lower projection boundaries obtained in the above. Sixth, for each perceptron and each piece of the activation function, find the weight vector and both the upper and the lower projection boundaries for all the input feature vectors in this piece of the activation function via a linear programming approach. Seventh, assign the codewords to the regions generated by the perceptrons. Eighth, if any two different regions generated by the perceptrons with the same codewords correspond to different classes of objects, then increment the total number of the perceptrons. Repeat these procedures until any two different regions generated by the perceptrons with the same codewords correspond to the same classes of objects. Finally, employ these perceptrons for performing the pattern recognitions.