感知机python实现
文章目录
- 思想：错误驱动
- 模型
- 损失函数
- 梯度下降
- 代码实现
-
- 训练集
- 实验结果
思想：错误驱动
模型
f ( x ) = s i g n ( w T x ) s i g n ( a ) = { 1 , if a > 0 0 , if a < 0 f(x)=sign(w^{T}x)\\ sign(a)= \begin{cases}1,& \text {if $a>0$} \\0, & \text{if $a<0$}\end{cases} f(x)=sign(wTx)sign(a)={1,0,if a>0if a<0
损失函数
L ( w ) = ∑ i = 1 m I { y i w T x i < 0 } L ( w ) = ∑ x i ∈ D − y i w T x i L(w)=\sum_{i=1}^{m}I\{y_{i}w^{T}x_{i}<0\}\\ L(w)=\sum_{x_{i}\in D}-y_{i}w^{T}x_{i}\\ L(w)=i=1∑mI{yiwTxi<0}L(w)=xi∈D∑−yiwTxi
梯度下降
w j = w j − α L ′ ( w ) 即 w j = w j + α ∑ x i ∈ D y i x i w_{j}=w_{j}-\alpha L^{'}(w)\\ 即w_{j}=w_{j}+\alpha \sum_{x_{i}\in D}y_{i}x_{i}\\ wj=wj−αL′(w)即wj=wj+αxi∈D∑yixi
代码实现
import pandas as pd
import numpy as np
from sklearn.datasets import load_iris
import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif']=['SimHei'] #用来正常显示中文标签
plt.rcParams['axes.unicode_minus']=False #用来正常显示负号
#导入数据
iris = load_iris()
df = pd.DataFrame(iris.data, columns=iris.feature_names)
df['label'] = iris.target
#
df.columns = ['sepal length', 'sepal width', 'petal length', 'petal width', 'label']
df.label.value_counts()
data = np.array(df.iloc[:100, [0, 1, -1]])
X, y = data[:,:-1], data[:,-1]
#将标签记作-1和1
y = np.array([1 if i == 1 else -1 for i in y])
# 数据线性可分，二分类数据
# 此处为一元一次线性方程
class Model:
'''
w:权重
b:偏置
l_rate:学习率
'''
def __init__(self):
self.w = np.ones(len(data[0]) - 1, dtype=np.float32)
self.b = 0
self.l_rate = 0.1
# 定义感知机的模型
def sign(self, x, w, b):
y = np.dot(x, w) + b
return y
# 随机梯度下降法
def fit(self, X_train, y_train):
flag = False
while not flag:
flag = True
for i in range(len(X_train)):
if y_train[i] * self.sign(X_train[i], self.w, self.b) < 0:
self.w = self.w + self.l_rate * np.dot(X_train[i], y_train[i])
self.b = self.b + self.l_rate * y_train[i]
flag = False
break
perceptron = Model()
perceptron.fit(X, y)
# 画出分类线及样本点的散状图
plt.rcParams['font.sans-serif']=['SimHei'] #用来正常显示中文标签
plt.rcParams['axes.unicode_minus']=False #用来正常显示负号
fig = plt.figure()
x_points = np.linspace(4, 7, 10)#4-7取10个点
y_ = -(perceptron.b + perceptron.w[0] * x_points) / perceptron.w[1]
plt.plot(x_points, y_,'red')
right = plt.scatter(X[:, 0][y == 1], X[:, 1][y == 1])
false = plt.scatter(X[:, 0][y == -1], X[:, 1][y == -1], marker='^')
plt.xlabel('花萼长度')
plt.ylabel('花萼宽度')
plt.legend([right,false], ['0', '1'])
plt.show()
训练集
实验结果
# b站up主链接