1.试用感知机学习算法的原始形式求感知机模型f(x)=sign(w·x+b),训练数据包括，正实例点x1=(3,4)T,x2=(4,4)T：；负实例点：x3=(1,2)T,x4=(0,1)T。要求画出分离超平面。

2.试用scikit-learn求感知机模型f(x)=sign(w·x+b),训练数据包括，正实例点x1=(3,4)T,x2=(4,4)T：；负实例点：x3=(1,2)T,x4=(0,1)T。要求画出分离超平面。

参考以下算法

import pandas as pd
import numpy as np
from sklearn.datasets import load_iris
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'
]
df.label.value_counts()

plt.scatter(df[:50]['sepal length'], df[:50]['sepal width'], label='0')
plt.scatter(df[50:100]['sepal length'], df[50:100]['sepal width'], label='1')
plt.xlabel('sepal length')
plt.ylabel('sepal width')
plt.legend()
plt.show()

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])

数据线性可分，二分类数据

此处为一元一次线性方程

class Model:
def init(self):
self.w = np.ones(len(data[0]) - 1, dtype=np.float32)
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.fit(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()

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

import sklearn
from sklearn.linear_model import Perceptron

load data

iris = load_iris()
df = pd.DataFrame(iris.data, columns=iris.feature_names) #四个特征：花萼长度、花萼宽度、花瓣长度、花瓣宽度
df['label'] = iris.target

df.columns = [
'sepal length', 'sepal width', 'petal length', 'petal width', 'label'
]
df.label.value_counts()

plt.scatter(df[:50]['sepal length'], df[:50]['sepal width'], label='0')
plt.scatter(df[50:100]['sepal length'], df[50:100]['sepal width'], label='1')
plt.xlabel('sepal length')
plt.ylabel('sepal width')
plt.legend()
plt.show()

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])

clf = Perceptron(fit_intercept=True, #拦截
max_iter=1000, #最大训练次数
tol=None,
shuffle=True) #每次训练后重新洗牌数据
clf.fit(X, y)

print(clf.coef_)
print(clf.intercept_)

画布大小

plt.figure(figsize=(10,10))

中文标题

plt.rcParams['font.sans-serif']=['SimHei'] #设置字体
plt.rcParams['axes.unicode_minus'] = False #字符显示
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()