算法描述

最原始的神经网络模型，类似于神经网络中的单个神经元，该算法局限性也很大，只适用于解决线性可分的问题和异或问题，对于线性不可分的问题则无法解决。但作为神经网络的基本单元，学习和理解单层感知器，对后续的学习是很有帮助的。

python实现

# ************************** Perception ****************** import numpy as np import pandas as pd import matplotlib.pyplot as plt class CyrusPerception(object):     def __init__(self,**kargs):         self.X = None         self.Y = None         self.W = None         self.output = None         if "epoch" in kargs.keys():             self.epoch = kargs["epoch"] else:             self.epoch = 1000 if "lr" in kargs.keys():             self.lr = kargs["lr"] else:             self.lr = 0.1     def fit(self,X,Y,**kargs):         self.X = np.hstack((np.ones((np.array(X).shape[0],1)),np.array(X)))         self.Y = np.array(Y).reshape(-1,1)         # 1、初始化权值         if "W" in kargs.keys():             self.W = kargs["W"] else:             self.W = (np.random.random([self.X.shape[1],1])-0.5)*2         # 2、更新权值         for i in range(self.epoch):             self.update_w() print("*"*20) print("epoch:",i+1) print("w:",self.W) if (self.Y == self.output).all(): print("*"*20) print("Finihed") print("epoch",self.epoch) break     def update_w(self):         self.output = np.sign(self.X.dot(self.W)).reshape(-1,1)         self.W += self.lr*(self.X.T.dot(self.Y - self.output))/int(self.X.shape[0]) if __name__ == "__main__":     model = CyrusPerception()     x = [[3,3],[4,3],[1,1],[0,2]]     y = [1,1,-1,-1]     model.fit(x,y)     # 绘图     k = -model.W[1]/model.W[2]     b = -model.W[0]/model.W[2]     x_lineal = np.array([0,5])     y_lineal = k*x_lineal + b     plt.figure()     colors = "rgb" [plt.scatter(x[i][0],x[i][1],color = colors[y[i]]) for i in range(len(x))]     plt.plot(x_lineal,y_lineal,color = "r")     plt.show() 

示例运行结果

******************** epoch: 1 w: [[-0.31672519] [-0.16285498] [ 0.19094236]] ******************** epoch: 2 w: [[-0.26672519] [ 0.18714502] [ 0.39094236]] ******************** epoch: 3 w: [[-0.36672519] [ 0.13714502] [ 0.24094236]] ******************** epoch: 4 w: [[-0.46672519] [ 0.08714502] [ 0.09094236]] ******************** epoch: 5 w: [[-0.46672519] [ 0.08714502] [ 0.09094236]] ******************** Finihed epoch 1000 

可视化

by CyrusMay 2020 05 05

当烟雾随晨光飘散
枕畔的湖已风干
期待已退化成等待
而我告别了突然

——五月天（后青春期的诗）——