机器学习|机器学习_感知机机器学习|python

感知机是二分类的线性分类模型，输入为特征向量，输出为类别(1,-1)。感知机目的是求能够将输入的线性数据进行划分的超平面。对误分类样本求损失函数，使其最小从而得到超平面。
感知机分为原始形式以及对偶形式。模型:
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sign（）为符号函数，小于零输出-1，大于等于0输出1
原始形式:
(1) 选取初始w，b
(2) 在训练集中选取数据(x，y)
(3)如果y(w*x +b)<=0，更新权重（分类正确的时候不更新）
更新方法：

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(4) 转（2）直到没有误分类点，求出来的w，,b带入模型
对偶形式:
(1)初始alpha=[0,0....] n个,n=样本个数,b=0学习率
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(2)计算gram矩阵https://zhuanlan.zhihu.com/p/105470826
(3)如果
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更新权重
更新方法:

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(4)计算得到
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, b
带入到
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x+b=0求出w
代码如下，如有错误请告知谢谢

import numpy as npclass percePtron: def __init__(self, data): self.weight = np.array([0.0, 0.0]) self.bias = 0.0 self.data = https://www.it610.com/article/datadef train(self, learning_rate = 1.): num_change = 0 for epoch in range(10): print('训练第{0}次'.format(epoch+1)) for input in data: pre = input[2]*(input[0]*self.weight[0] + input[1]*self.weight[1] + self.bias) if pre <= 0: num_change += 1 print('误差为:', pre)self.weight[0] = self.weight[0] + input[2] *input[0] *learning_rate self.weight[1] = self.weight[1] + input[2] *input[1] * learning_rate self.bias = self.bias + input[2] * learning_rate print('-------第{0}次更新权重'.format(num_change)) print("weight : ", self.weight) print("bias : ", self.bias)def predict(self, input): out =input[0]*self.weight[0] + input[1]*self.weight[1] + self.bias if out >=0 : return 1 else: return -1class percePtron_Dual: def __init__(self, data): self.weight = np.array([0.0, 0.0]) self.bias = 0.0 self.data = https://www.it610.com/article/datadef train(self, learning_rate = 1.): train_data = self.data[:,:-1] train_label = self.data[:,-1:] m = train_data.shape[0] alpha = np.zeros(m) gram = np.zeros((m, m)) for i in range(m): for j in range(m): gram[i][j] = train_data[i] * np.mat(train_data[j]).transpose()# print(gram) for i in range(100): for idx in range(m): tmp = 0 for j in range(m): tmp += alpha[j] * train_label[j] * gram[j, idx] tmp += self.bias if (train_label[idx] * tmp <= 0): alpha[idx] = alpha[idx] + learning_rate self.bias = self.bias + learning_rate * train_label[idx] # print(alpha, self.bias)for num in range(m): self.weight += alpha[num]*train_data[num]*train_label[num]def predict(self, input): out =self.weight[0]*input[0]+self.weight[1]*input[1] -3 if out>=0 : return 1 else: return -1if __name__ == "__main__": data = https://www.it610.com/article/np.array([[3, 3, 1], [4, 3, 1], [1, 1, -1]])per = percePtron(data) per.train() result_ = per.predict(input=[1, 0]) print(result_)per_d = percePtron_Dual(data) per_d.train() result = per_d.predict(input=[1, 0]) print(result)

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