Abstract: The perceptron is a simple linear classifier and is also the cornerstone of SVM and deep neural networks.However,most complex problems are often nonlinear,and the perceptron performs poorly in handling such issues.Therefore,this paper introduces granular computing theory,whereby training samples are granulated into feature granules and feature granular vectors based on reference samples.The paper defines a granular GRAM matrix and proposes a granular perceptron model based on the GRAM matrix.This model optimizes the dual form of the perceptron to construct a new granular perceptron model.To better handle nonlinear classification problems,a kernel function is introduced to construct a kernel GRAM matrix based on granular vectors,and the loss function and learning method of the GRAM granular perceptron are provided.Finally,experiments analyze the model’s convergence,nonlinear processing capability,the number of reference samples,and the classification performance of models.The result shows the effectiveness and correctness of the model of GRAM granular perceptron.

Key words: Granular computing, Perceptron, GRAM matrix, Nonlinear classification, Kernel function