作业:
一:感知机算法原始形式实现
（一）伪代码
（二）实现感知机算法
class MyPerceptron:
def __init__(self): # 属性初始化
self.w = None
self.b = 0
self.l_rate = 1
def fit(self, X_train, y_train):
global history_w, history_b #保持w,b信息，方便一会绘制图像
# 根据X形状,设置w
self.w = np.zeros(X_train.shape[1])
i = 0
while i < X_train.shape[0]: # 注意我们按顺序查看误分类点
X = X_train[i]
y = y_train[i]
# 如果y*(wX+b)<=0,则是误分类点,我们就要更新一次w,b,我们每更新一次w,b,我们就要从新查找整个数据集
if y * (np.dot(self.w, X) + self.b) <= 0:
self.w = self.w + self.l_rate * np.dot(y, X)
self.b = self.b + self.l_rate * y
i = 0
history_w.append(self.w)
history_b.append(self.b)
else:
i += 1
（三）设置数据，进行训练
if __name__ == "__main__":
# 构建数据集和标签值
X_train = np.array([[3, 3], [4, 3], [1, 1]])
y = np.array([1, 1, -1])
history_w = []
history_b = []
perc = MyPerceptron()
perc.fit(X_train, y) # 进行训练 获取w,b信息
（四）数据可视化
# 数据集可视化
fig = plt.figure()
ax = plt.axes()
line, = ax.plot([], [], 'g', lw=2)
def init():
line.set_data([], [])
plt.scatter(X_train[np.where(y == 1), 0], X_train[np.where(y == 1), 1], marker="o", c="b")
plt.scatter(X_train[np.where(y == -1), 0], X_train[np.where(y == -1), 1], marker="x", c="r")
return line,
def update(i):
global history_w, history_b, ax, line
w = history_w[i]
b = history_b[i]
if w[1] == 0:
return line,
x1 = -1
y1 = -(b + w[0] * x1) / w[1]
x2 = 6
y2 = -(b + w[0] * x2) / w[1]
line.set_data([x1, x2], [y1, y2])
return line,
plt.xlim(-1, 6)
plt.ylim(-1, 4)
print(history_w)
print(history_b)
#[[[3, 3], 1], [[2, 2], 0], [[1, 1], -1], [[0, 0], -2], [[3, 3], -1], [[2, 2], -2], [[1, 1], -3]]
ani = anim.FuncAnimation(fig=fig, func=update,init_func=init, frames=len(history_b), interval=1000, repeat=True, blit=True)
plt.show()
参数详解：
fig 进行动画绘制的figurefunc 自定义动画函数，即传入刚定义的函数animateframes 动画长度，一次循环包含的帧数init_func 自定义开始帧，即传入刚定义的函数initinterval 更新频率，以ms计blit 选择更新所有点，还是仅更新产生变化的点。应选择True，但mac用户请选择False，否则无法显示动画
注意：我们要实现Animation动画，需要设置pycharm中(File->Settings->Tools->Python Scientific）的Show plots in tool window选项（disable不使用）
（五）结果显示
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as anim
class MyPerceptron:
def __init__(self): # 属性初始化
self.w = None
self.b = 0
self.l_rate = 1
def fit(self, X_train, y_train):
global history_w, history_b
# 根据X形状,设置w
self.w = np.zeros(X_train.shape[1])
i = 0
while i < X_train.shape[0]: # 注意我们按顺序查看误分类点
X = X_train[i]
y = y_train[i]
# 如果y*(wX+b)<=0,则是误分类点,我们就要更新一次w,b,我们每更新一次w,b,我们就要从新查找整个数据集
if y * (np.dot(self.w, X) + self.b) <= 0:
self.w = self.w + self.l_rate * np.dot(y, X)
self.b = self.b + self.l_rate * y
i = 0
history_w.append(self.w)
history_b.append(self.b)
else:
i += 1
if __name__ == "__main__":
# 构建数据集和标签值
X_train = np.array([[3, 3], [4, 3], [1, 1]])
y = np.array([1, 1, -1])
history_w = []
history_b = []
perc = MyPerceptron()
perc.fit(X_train, y) # 进行训练 获取w,b信息
# 数据集可视化
fig = plt.figure()
ax = plt.axes()
line, = ax.plot([], [], 'g', lw=2)
def init():
line.set_data([], [])
plt.scatter(X_train[np.where(y == 1), 0], X_train[np.where(y == 1), 1], marker="o", c="b")
plt.scatter(X_train[np.where(y == -1), 0], X_train[np.where(y == -1), 1], marker="x", c="r")
return line,
def update(i):
global history_w, history_b, ax, line
w = history_w[i]
b = history_b[i]
if w[1] == 0:
return line,
x1 = -1
y1 = -(b + w[0] * x1) / w[1]
x2 = 6
y2 = -(b + w[0] * x2) / w[1]
line.set_data([x1, x2], [y1, y2])
return line,
plt.xlim(-1, 6)
plt.ylim(-1, 4)
print(history_w)
print(history_b)
#[[[3, 3], 1], [[2, 2], 0], [[1, 1], -1], [[0, 0], -2], [[3, 3], -1], [[2, 2], -2], [[1, 1], -3]]
ani = anim.FuncAnimation(fig=fig, func=update,init_func=init, frames=len(history_b), interval=1000, repeat=True, blit=True)
plt.show()
全部代码
二：感知机算法对偶形式实现
（一）伪代码
（二）实现感知机对偶算法
class MyPerceptron:
def __init__(self): # 属性初始化
self.a = None
self.b = 0
self.l_rate = 1
self.gram = None
self.gram_diag = None
def cal_gram(self,X_train):
self.gram = np.zeros((X_train.shape[0],X_train.shape[0]))
self.gram = np.dot(X_train,X_train.T)
def fit(self, X_train, y_train):
global history_a, history_b
self.cal_gram(X_train)
# 根据X形状,设置a 对于每一个样本，都有一个a
self.a = np.zeros(X_train.shape[0])
i = 0
while i < X_train.shape[0]: # 注意我们按顺序查看误分类点
y = y_train[i]
sigma_gram = np.sum(self.gram[i]*self.a*y_train) #使用了gram矩阵，减少计算量
# 如果y*(wX+b)<=0,则是误分类点,我们就要更新一次w,b,我们每更新一次w,b,我们就要从新查找整个数据集
if y * (sigma_gram + self.b) <= 0:
self.a[i] = self.a[i]+ self.l_rate
self.b = self.b + self.l_rate * y
i = 0
history_a.append(self.a.copy())
history_b.append(self.b)
else:
i += 1
（三）训练数据
if __name__ == "__main__":
# 构建数据集和标签值
X_train = np.array([[3, 3], [4, 3], [1, 1]])
y_train = np.array([1, 1, -1])
history_a = []
history_b = []
perc = MyPerceptron()
perc.fit(X_train, y_train) # 进行训练 获取w,b信息
# 数据集可视化
fig = plt.figure()
ax = plt.axes()
line, = ax.plot([], [], 'g', lw=2)
print(history_a)
print(history_b)
（四）数据可视化
if __name__ == "__main__":
# 构建数据集和标签值
X_train = np.array([[3, 3], [4, 3], [1, 1]])
y_train = np.array([1, 1, -1])
history_a = []
history_b = []
perc = MyPerceptron()
perc.fit(X_train, y_train) # 进行训练 获取w,b信息
# 数据集可视化
fig = plt.figure()
ax = plt.axes()
line, = ax.plot([], [], 'g', lw=2)
print(history_a)
print(history_b)
def init():
line.set_data([], [])
plt.scatter(X_train[np.where(y_train == 1), 0], X_train[np.where(y_train == 1), 1], marker="o", c="b")
plt.scatter(X_train[np.where(y_train == -1), 0], X_train[np.where(y_train == -1), 1], marker="x", c="r")
return line,
def update(i):
global history_a, history_b, line,X_train,y_train
a = history_a[i]
b = history_b[i]
w = np.sum(X_train*np.array([a]).T*np.array([y_train]).T,0) #这一步实现获取w
if w[1] == 0:
return line,
x1 = -1
y1 = -(b + w[0] * x1) / w[1]
x2 = 6
y2 = -(b + w[0] * x2) / w[1]
line.set_data([x1, x2], [y1, y2])
return line,
plt.xlim(-1, 6)
plt.ylim(-1, 4)
ani = anim.FuncAnimation(fig=fig, func=update,init_func=init, frames=len(history_b), interval=1000, repeat=True, blit=True)
plt.show()
（五）结果显示
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as anim
class MyPerceptron:
def __init__(self): # 属性初始化
self.a = None
self.b = 0
self.l_rate = 1
self.gram = None
self.gram_diag = None
def cal_gram(self,X_train):
self.gram = np.zeros((X_train.shape[0],X_train.shape[0]))
self.gram = np.dot(X_train,X_train.T)
def fit(self, X_train, y_train):
global history_a, history_b
self.cal_gram(X_train)
# 根据X形状,设置a 对于每一个样本，都有一个a
self.a = np.zeros(X_train.shape[0])
i = 0
while i < X_train.shape[0]: # 注意我们按顺序查看误分类点
y = y_train[i]
sigma_gram = np.sum(self.gram[i]*self.a*y_train) #使用了gram矩阵，减少计算量
# 如果y*(wX+b)<=0,则是误分类点,我们就要更新一次w,b,我们每更新一次w,b,我们就要从新查找整个数据集
if y * (sigma_gram + self.b) <= 0:
self.a[i] = self.a[i]+ self.l_rate
self.b = self.b + self.l_rate * y
i = 0
history_a.append(self.a.copy())
history_b.append(self.b)
else:
i += 1
if __name__ == "__main__":
# 构建数据集和标签值
X_train = np.array([[3, 3], [4, 3], [1, 1]])
y_train = np.array([1, 1, -1])
history_a = []
history_b = []
perc = MyPerceptron()
perc.fit(X_train, y_train) # 进行训练 获取w,b信息
# 数据集可视化
fig = plt.figure()
ax = plt.axes()
line, = ax.plot([], [], 'g', lw=2)
print(history_a)
print(history_b)
def init():
line.set_data([], [])
plt.scatter(X_train[np.where(y_train == 1), 0], X_train[np.where(y_train == 1), 1], marker="o", c="b")
plt.scatter(X_train[np.where(y_train == -1), 0], X_train[np.where(y_train == -1), 1], marker="x", c="r")
return line,
def update(i):
global history_a, history_b, line,X_train,y_train
a = history_a[i]
b = history_b[i]
w = np.sum(X_train*np.array([a]).T*np.array([y_train]).T,0)
print(w,b)
if w[1] == 0:
return line,
x1 = -1
y1 = -(b + w[0] * x1) / w[1]
x2 = 6
y2 = -(b + w[0] * x2) / w[1]
line.set_data([x1, x2], [y1, y2])
return line,
plt.xlim(-1, 6)
plt.ylim(-1, 4)
ani = anim.FuncAnimation(fig=fig, func=update,init_func=init, frames=len(history_b), interval=1000, repeat=True, blit=True)
plt.show()
全部代码
（六）原始算法对比对偶算法
三：Sklearn实现感知机
（一）代码实现
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import Perceptron
if __name__ == "__main__":
# 构建数据集和标签值
X_train = np.array([[3, 3], [4, 3], [1, 1]])
y_train = np.array([1, 1, -1])
#构建Perceptron对象，训练数据并输出结果
perc = Perceptron()
perc.fit(X_train,y_train)
print("w:",perc.coef_,"\n","b:",perc.intercept_,"\n","n_iter:",perc.n_iter_,"\n")
#获取模型预测的准确率
res = perc.score(X_train,y_train)
print("Correct rate:{}".format(res))
（二）方法参数说明
