感知机原理解析与代码实现

Posted 2021-09-15 Gendan

import numpy as np
from sklearn.datasets import load_iris
import matplotlib.pyplot as plt
import pandas as pd
from matplotlib.colors import ListedColormap
class Perceptron(object):

def __init__(self,lr, n_iter):
    self.lr = lr
    self.n_iter = n_iter
def train(self,X,y):
    #这个向量包含了两重信息，第一w_[0]代表了偏置项b，w_[1:]代表了权重向量
    self.w_ = np.zeros(1+X.shape[1])
    self.errors_ = []
    for _ in range(self.n_iter):
        errors = 0
        for xi, target in zip(X,y):
            #这里的target - self.predict(xi)对应公式（5）中的yi，
            update = self.lr * (target - self.predict(xi))
            self.w_[1:] += update * xi
            self.w_[0] += update
            errors += int(update != 0.0)
        self.errors_.append(errors)
    return self
#这个函数完成了感知机定义里面的w·x+b这个操作
def net_input(self, X):
    return np.dot(X, self.w_[1:])+self.w_[0]
#按照学习算法的第三步，[货币代码](https://www.gendan5.com/currencycode.html)对式子判断其是否小于0
def predict(self, X):
    return np.where(self.net_input(X) >= 0.0, 1, -1)

将bunch格式的数据集转化为pandas的dataframe

def sklearn_to_df(datasets):

df = pd.DataFrame(datasets.data, columns=datasets.feature_names)
df[\'target\'] = pd.Series(datasets.target)
return df

iris = load_iris()
df_iris = sklearn_to_df(iris)
y = df_iris.iloc[0:100,4].values
y = np.where(y == 0,-1,1)
X = df_iris.iloc[0:100,[0,2]].values

鸢尾花数据集的可视化

plt.scatter(X[:50,0],X[:50,1],

color=\'r\',marker=\'o\',label=\'setosa\')

plt.scatter(X[50:100,0],X[50:100,1],

color=\'b\',marker=\'x\',label=\'versicolor\')

plt.xlabel(\'petal length\')

plt.ylabel(\'sepal length\')

plt.legend(loc=\'upper left\')

plt.show()

利用鸢尾花数据集来训练感知机

pn = Perceptron(lr=0.01,n_iter=10)
pn.train(X, y)

plt.plot(range(1,len(pn.errors_)+1),pn.errors_,marker=\'o\')

plt.xlabel(\'Epoch\')

plt.ylabel(\'Number of miscalssifications\')

plt.show()

画出决策边界

def plot_decision_regions(X, y, classifier, resolution=0.02):

markers = (\'s\',\'x\',\'o\',\'^\',\'v\')
colors = (\'red\',\'blue\',\'lightgreen\',\'gray\',\'cyan\')
cmap = ListedColormap(colors[:len(np.unique(y))])
x1_min, x1_max = X[:,0].min() - 1, X[:,0].max() + 1
x2_min, x2_max = X[:,1].min() - 1, X[:,1].max() + 1
xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),
                       np.arange(x2_min, x2_max, resolution))
z = classifier.predict(np.array([xx1.ravel(),xx2.ravel()]).T)
z = z.reshape(xx1.shape)
plt.contourf(xx1,xx2,z,alpha=0.4,cmap=cmap)
plt.xlim(xx1.min(),xx1.max())
plt.ylim(xx2.min(),xx2.max())
for idx, cl in enumerate(np.unique(y)):
    plt.scatter(x = X[y == cl,0], y = X[y == cl,1],
                alpha=0.8, c=cmap(idx),
                marker=markers[idx],label=cl)

plot_decision_regions(X, y, classifier=pn)
plt.xlabel(\'sepal length [cm]\')
plt.ylabel(\'petal length [cm]\')
plt.legend(loc = \'upper left\')
plt.show()