Direct Kernel Perceptron (DKP): ultra-fast kernel ELM-based classification with non-iterative closed-form weight calculation

The Direct Kernel Perceptron (DKP) [1] is a very simple and fast kernel-based classifier, related to the Support Vector Machine (SVM) and to the Extreme Learning Machine (ELM) [2], whose α-coefficients are calculated directly, without any iterative training, using an analytical closed-form expression which involves only the training patterns. The DKP, which is inspired on the Direct Parallel Perceptron [3], uses a Gaussian kernel and a linear classifier (perceptron). The weight vector of this classifier in the feature space minimizes an error measure which combines the training error and the hyperplane margin, without any tunable regularization parameter. This weight vector can be translated, using a variable change, to the α-coefficients, and both are determined without iterative calculations. We calculate solutions using several

keywords: Kernel-based classification, Extreme Learning Machine, Support Vector Machine, Analytical weight calculation, Closed-form solution, Margin maximization, Parallel Delta rule