李航统计学习方法-感知机python实现
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2022-07-12 12:02:03
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1、理论中原始算法的实现
# 利用Python实现感知机算法的原始形式
# -*- encoding:utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
def createData():
samples = np.array([[3, -3], [4, -3], [1, 1], [1, 2]])
labels = [-1, -1, 1, 1]
return samples, labels
class Perception:
def __init__(self, x, y, a=1):
self.x = x
self.y = y
self.l_rate = a
self.w = np.zeros((x.shape[1], 1))
self.b = 0
self.numSimples = x.shape[0]
self.numFeatures = x.shape[1]
def sign(self, w, b, x):
y = np.dot(x, w) + b # x .w + b
return int(y)
def update(self, label_i, data_i):
tmp = label_i * self.l_rate * data_i # w = w + n yx
tmp = tmp.reshape(self.w.shape)
self.w = tmp + self.w
self.b = self.b + label_i * self.l_rate # b = b + n y
def train(self):
isFind = False
while not isFind:
count = 0
for row in range(self.numSimples):
simY = self.sign(self.w, self.b, self.x[row, :])
if simY * self.y[row] <= 0: # 如果是一个误分类实例点
print('误分类点为:', self.x[row, :], '此时的w和b为:', self.w, self.b)
count += 1
self.update(self.y[row], self.x[row])
if count == 0:
print('最终训练得到的w和b为:', self.w, self.b)
isFind = True
return self.w, self.b
class Picture:
def __init__(self, data, w, b):
self.w = w
self.b = b
plt.figure(1)
plt.title("Perception Learning Algorithm", size=14)
plt.xlabel("x0", size=14)
plt.ylabel("x1", size=14)
xData = np.linspace(0, 5, 100)
yData = self.expression(xData)
plt.plot(xData, yData, color='r', label='data')
plt.scatter(data[0][0], data[0][1], s=50)
plt.scatter(data[1][0], data[1][1], s=50)
plt.scatter(data[2][0], data[2][1], s=50, marker='x')
plt.scatter(data[3][0], data[3][1], s=50, marker='x')
plt.savefig('2d_base.png', dpi=75)
def expression(self, x):
y = (-self.b - self.w[0] * x) / self.w[1]
# 注意在此,把x0,x1当做两个坐标轴,把x1当做自变量,x2为因变量
return y
def show_pic(self):
plt.show()
if __name__ == '__main__':
samples, labels = createData()
myperceptron = Perception(x=samples, y=labels)
weights, bias = myperceptron.train()
Picture = Picture(samples, weights, bias)
Picture.show_pic()
2、理论中对偶形式的实现:
# 利用Python实现感知机算法的对偶形式
# -*- encoding:utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
# 1、 创建数据集
def createdata():
samples = np.array([[3, -3], [4, -3], [1, 1], [1, 2]])
labels = np.array([-1, -1, 1, 1])
return samples, labels
class Perception:
def __init__(self, x, y, a=1):
self.x = x
self.y = y
self.w = np.zeros((1, x.shape[0]))
self.b = 0
self.a = 1 # 学习率
self.numsamples = self.x.shape[0]
self.numfeatures = self.x.shape[1]
self.gMatrix = self.cal_gram(self.x)
def cal_gram(self, x):
gMatrix = np.zeros((self.numsamples, self.numsamples))
for i in range(self.numsamples):
for j in range(self.numsamples):
gMatrix[i][j] = np.dot(self.x[i, :], self.x[j, :])
return gMatrix
def sign(self, w, b, key):
y = np.dot(w * self.y, self.gMatrix[:, key]) + b # αjYjXjXi + b
return int(y)
def update(self, i):
self.w[:, i] = self.w[:, i] + self.a
self.b = self.b + self.y[i] * self.a
def cal_w(self):
w = np.dot(self.w * self.y, self.x)
return w
def train(self):
isFind = False
while not isFind:
count = 0
for i in range(self.numsamples):
tmpY = self.sign(self.w, self.b, i)
if tmpY * self.y[i] <= 0: # 如果是一个误分类实例点
print('误分类点为:', self.x[i, :], '此时的w和b为:', self.cal_w(), ',', self.b)
count += 1
self.update(i)
if count == 0:
print('最终训练得到的w和b为:', self.cal_w(), ',', self.b)
isFind = True
weights = self.cal_w()
return weights, self.b
# 画图描绘
class Picture:
def __init__(self, data, w, b):
self.b = b
self.w = w
plt.figure(1)
plt.title('Perception Learning Algorithm', size=14)
plt.xlabel('x0', size=14)
plt.ylabel('x1', size=14)
xData = np.linspace(0, 5, 100)
yData = self.expression(xData)
plt.plot(xData, yData, color='r', label='data')
plt.scatter(data[0][0], data[0][1], s=50)
plt.scatter(data[1][0], data[1][1], s=50)
plt.scatter(data[2][0], data[2][1], s=50, marker='x')
plt.scatter(data[3][0], data[3][1], s=50, marker='x')
plt.savefig('2d_duio.png', dpi=75)
def expression(self, x):
y = (-self.b - self.w[:, 0] * x) / self.w[:, 1]
return y
def show_pic(self):
plt.show()
if __name__ == '__main__':
samples, labels = createdata()
myperceptron = Perception(x=samples, y=labels)
weights, bias = myperceptron.train()
Picture = Picture(samples, weights, bias)
Picture.show_pic()
3、通过sklearn 中的现象回归的实现
# -*- encoding:utf-8 -*-
"""
利用skLearn中的感知机学习算法进行实验
"""
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import Perceptron
def creatdata():
"""
#创建数据,直接定义数据列表
:return:
"""
samples = np.array([[3, -3], [4, -3], [1, 1], [1, 2]])
labels = np.array([-1, -1, 1, 1])
return samples, labels
def MyPerceptron(samples, labels):
# 定义感知机
clf = Perceptron(fit_intercept=True, n_iter=30, shuffle=False)
# 训练感知机
clf.fit(samples, labels)
# 得到权重矩阵
weigths = clf.coef_
# 得到截距bisa
bias = clf.intercept_
return weigths, bias
# 画图描绘
class Picture:
def __init__(self, data, w, b):
self.b = b
self.w = w
plt.figure(1)
plt.title('Perceptron Learning Algorithm', size=14)
plt.xlabel('x0-axis', size=14)
plt.ylabel('x1-axis', size=14)
xData = np.linspace(0, 5, 100)
yData = self.expression(xData)
plt.plot(xData, yData, color='r', label='sample data')
plt.scatter(data[0][0], data[0][1], s=50)
plt.scatter(data[1][0], data[1][1], s=50)
plt.scatter(data[2][0], data[2][1], s=50, marker='x')
plt.scatter(data[3][0], data[3][1], s=50, marker='x')
plt.savefig('3sk_1.png', dpi=75)
def expression(self, x):
y = (-self.b - self.w[:, 0] * x) / self.w[:, 1]
return y
def show_pic(self):
plt.show()
if __name__ == '__main__':
samples, labels = creatdata()
weights, bias = MyPerceptron(samples, labels)
print('最终训练得到的w和b为:', weights, ',', bias)
Picture = Picture(samples, weights, bias)
Picture.show_pic()
4、基于iris 的分类实现
# -*- encoding:utf-8 -*-
import numpy as np
'''
以scikit-learn 中的perceptron为例介绍分类算法
应用及其学习分类算法的五个步骤
(1)选择特征
(2)选择一个性能指标
(3)选择一个分类器和一个优化算法
(4)评价模型的性能
(5)优化算法
以scikit-learn 中的perceptron为例介绍分类算法
1 读取数据-iris
2 分配训练集和测试集
3 标准化特征值
4 训练感知器模型
5 用训练好的模型进行预测
6 计算性能指标
7 描绘分类界面
'''
from sklearn import datasets
import numpy as np
import matplotlib.pyplot as plt
iris = datasets.load_iris()
X = iris.data[:, [2, 3]]
y = iris.target
# 训练数据和测试数据分为6:4
from sklearn.model_selection import train_test_split
x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=0)
# 标准化数据
from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
sc.fit(x_train)
x_train_std = sc.transform(x_train)
x_test_std = sc.transform(x_test)
# 引入skleran 的Perceptron并进行训练
from sklearn.linear_model import Perceptron
ppn = Perceptron(n_iter=40, eta0=0.01, random_state=0)
ppn.fit(x_train_std, y_train)
y_pred = ppn.predict(x_test_std)
print('错误分类数:%d' % (y_test != y_pred).sum())
from sklearn.metrics import accuracy_score
print('准确率为:%.2f' % accuracy_score(y_test, y_pred))
# 绘制决策边界
from matplotlib.colors import ListedColormap
import warnings
def versiontuple(v):
return tuple(map(int, (v.split('.'))))
def plot_decision_regions(X, y, classifier, test_idx=None, resolution=0.02):
# 设置标记点和颜色
markers = ('s', 'x', 'o', 'b', 'v')
colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')
cmap = ListedColormap(colors[:len(np.unique(y))])
# 绘制决策面
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)
if test_idx:
# 绘制所有数据点
if not versiontuple(np.__version__) >= versiontuple('1.9.0'):
X_test, y_test = X[list(test_idx), :], y[list(test_idx)]
warnings.warn('Please update to NumPy 1.9.0 or newer')
else:
X_test, y_test = X[test_idx, :], y[test_idx]
plt.scatter(X_test[:, 0], X_test[:, 1], c='',
alpha=1.0, linewidth=1, marker='o',
s=55, label='test set')
def plot_result():
X_combined_std = np.vstack((x_train_std, x_test_std))
y_combined = np.hstack((y_train, y_test))
plot_decision_regions(X=X_combined_std, y=y_combined,
classifier=ppn, test_idx=range(105, 150))
plt.xlabel('petal length [standardized]')
plt.ylabel('petal width [standardized]')
plt.legend(loc='upper left')
plt.tight_layout()
plt.show()
plot_result()