基于粒计算的非线性感知机

Non-linear Perceptron Based on Granular Computing

感知机是模式识别领域的二分类判别模型,具有简单、线性和运算效率高的优点,也是众多分类器的基础。然而,感知机无法表达复杂的非线性映射,难以处理非线性可分数据。针对感知机的固有缺陷,结合粒计算特性,本文提出了一种新型的感知机分类模型——粒感知机。通过粒计算理论,样本在单特征上的粒化形成粒子,多特征上的粒化构造成粒向量;进一步定义粒感知机模型,设计粒感知机策略,提出粒感知机学习算法。为了求解粒感知机的优化解,证明了粒感知机损失函数的导数形式,设计了梯度下降算法,并从收敛速度、非线性能力与分类精度多方面进行了实验比较,结果表明所提出的粒感知机模型具有收敛速度快与非线性处理数据的能力。

Perceptron is a binary classification model in the field of pattern recognition,which has the advantages of simplicity,linearity and high computational efficiency,and it is also the basis of many classifiers.However,the perceptron cannot express complex nonlinear mapping and is difficult to process nonlinear data.Aiming at the inherent defects of perceptron and combining the characteristics of granular computing,we propose a new perceptron classification model-Granular perceptron.According to the theory of granular computing,the granulation of samples on single feature forms granules,and the granulation on multiple features constructs a granular vector.Further,the granular perceptron model is defined,the granular perceptron strategy is designed,and the granular perceptron learning algorithm is proposed.In order to solve the optimal solution of the proposed model,the derivative form of the granular loss function is proved,and its gradient descent algorithm is designed.Finally,some experiments are carried out to compare on the convergence speed,nonlinear ability and classification accuracy.The results show that the proposed model has the ability of fast convergence and nonlinear data processing.