梯度下降算法实现感知机模型

对比代码来自GitHub

'''
感知机perception,使用随机梯度下降优化
以iris数据集为例,sepal length和sepal width作为特征,对0和1进行分类
'''

import pandas as pd
import numpy as np
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt


#load data
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'] #原数据集标签带'(cm)'
#print(df)
'''
plt.scatter(df[0:50]['sepal length'],df[0:50]['sepal width'],label='0') #前50行的数据是0
plt.scatter(df[50:100]['sepal length'],df[50:100]['sepal width'],label='1') #前50-100行的数据是1
plt.xlabel('sepal length')
plt.ylabel('sepal width')
plt.legend()
plt.show()
'''

data=np.array(df.iloc[:100,0:5])
X=data[:,[0,1]] #只要第一列和第二列
y=data[:,-1]
y=np.array([1 if i==1 else -1 for i in y]) #感知机分类正类是1,负类是0
#print(X,y)

#model
class MyPerception():
	def __init__(self,feature_dim,data_size):
		self.feature_dim=feature_dim
		self.data_size=data_size
		self.w=np.zeros(feature_dim)
		self.b=0
		self.True_List=np.zeros(data_size) #初始设置为全部误分类,误分类标记为0,正确分类标记为1
		self.alpha=1	#步长
	def train(self,X,y):
		"""
		Loss是所有误分类点到超平面的距离之和,忽略二范数,因为最后优化到分子为零
		注意距离公式的分子有绝对值号,不能直接w@x+b,如果它为负样本,距离应该是-w@x+b
		L(w,b)=-sum{y_i(w@x_i+b)} forall:y_i*(w@x_i+b)<0
		对每一个误分类的样本迭代w和b,直到没有误分类
		"""
		times=0
		while sum(self.True_List)!=self.data_size: #如果不全为1
			times+=1
			for index in range(self.data_size):
				if y[index]*(self.w@X[index]+self.b)<=0: #误分类,注意这里等于零也是误分类:y_i不可能等于0,w@x+b=0说明样点在超平面上,这也是不可能的
					#print("发现误分类:x=[{},{}],y={}".format(X[index][0],X[index][1],y[index]))
					self.True_List[index]=0
					self.w=self.w+self.alpha*y[index]*X[index]
					self.b=self.b+self.alpha*y[index]
				else:
					self.True_List[index]=1
			#print("times={}".format(times))
		print("w={},b={}".format(self.w,self.b))
	def predict(self,data):
		if (self.w@data+self.b<0):
			return -1 #感知机中的-1对应的是负类,即数据集label=0
		elif (self.w@data+self.b>0):

			return 1
#train
'''
train_X,test_X,train_y,test_y=train_test_split(X,y,test_size=0.4)
print(train_X.shape,train_y.shape)
feature_dim=2
data_size=60

model=MyPerception(feature_dim,data_size)
model.train(train_X,train_y)
cnt=0
for i in range(40):
	if test_y[i]==model.predict(test_X[i]):
		cnt+=1
print("Myperception准确率={}".format(cnt/40))
'''


#下面是GitHub的code
data = np.array(df.iloc[:100, [0, 1, -1]])
X, y = data[:,:-1], data[:,-1]
y = np.array([1 if i == 1 else -1 for i in y])

#print(data.shape)
#print(data)
class GitHubCode:
	def __init__(self):
		self.w = np.ones(len(data[0]) - 1, dtype=np.float32) #这里data[0]是第一行数据,而不是取的维度数据
		self.b = 0
		self.l_rate = 0.1
		# self.data = data

	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):
		is_wrong = False
		while not is_wrong:
			wrong_count = 0
			for d in range(len(X_train)):
				X = X_train[d]
				y = y_train[d]
				if y * self.sign(X, self.w, self.b) <= 0:
					self.w = self.w + self.l_rate * np.dot(y, X)
					self.b = self.b + self.l_rate * y
					wrong_count += 1
			if wrong_count == 0:
				is_wrong = True
		return 'Perceptron Model!'

	def score(self):
		pass
'''
#perceptron = Model()
perceptron = MyPerception(2,100)
perceptron.train(X, y)
x_points = np.linspace(4, 7, 10)
y_ = -(perceptron.w[0] * x_points + perceptron.b) / perceptron.w[1]
plt.plot(x_points, y_)

plt.plot(data[:50, 0], data[:50, 1], 'bo', color='blue', label='0')
plt.plot(data[50:100, 0], data[50:100, 1], 'bo', color='orange', label='1')
plt.xlabel('sepal length')
plt.ylabel('sepal width')
plt.legend()
plt.show()
'''

from sklearn.linear_model import Perceptron

clf = Perceptron(fit_intercept=True,
                 max_iter=1000,
                 tol=None,  #这里tol不设置为None可能有被误分类的点
                 shuffle=True)
clf.fit(X, y)

# 画布大小
plt.figure(figsize=(10,10))

# 中文标题
plt.rcParams['font.sans-serif']=['SimHei']
plt.rcParams['axes.unicode_minus'] = False
plt.title('鸢尾花线性数据示例')

plt.scatter(data[:50, 0], data[:50, 1], c='b', label='Iris-setosa',)
plt.scatter(data[50:100, 0], data[50:100, 1], c='orange', label='Iris-versicolor')

# 画感知机的线
x_ponits = np.arange(4, 8)
y_ = -(clf.coef_[0][0]*x_ponits + clf.intercept_)/clf.coef_[0][1]
plt.plot(x_ponits, y_)

# 其他部分
plt.legend()  # 显示图例
plt.grid(False)  # 不显示网格
plt.xlabel('sepal length')
plt.ylabel('sepal width')
plt.legend()
plt.show()