感知器算法

**感知器算法:

线性判别函数 或者说广义的线性判别曲面 进行二分类或者多分类的代码实现

以及使用iris_data 的感知机测试代码

不断地迭代赏罚 为后面的梯度下降方式做铺垫**

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github：https://github.com/cuixuage/Machine_Learning

参考资料 https://ljalphabeta.gitbooks.io/python-/content/ch2section3.html

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1.模型二分类问题 得到一个判别函数

例如: W1 W2 分别为二类模式

用感知器算法求下列模式分类的解向量w:

ω1: {(0 0 0)T, (1 0 0)T, (1 0 1)T, (1 1 0)T}

ω2: {(0 0 1)T, (0 1 1)T, (0 1 0)T, (1 1 1)T}

编写求解上述问题的感知器算法程序

#coding:utf-8
二分类问题   假设线性可分
用感知器算法求下列模式分类的解向量w:
ω1: {(0 0 0)T, (1 0 0)T, (1 0 1)T, (1 1 0)T}
ω2: {(0 0 1)T, (0 1 1)T, (0 1 0)T, (1 1 1)T}

编写求解上述问题的感知器算法程序

import numpy as np
x1 = np.mat([0,0,0,1])
x2 = np.mat([1,0,0,1])
x3 = np.mat([1,0,1,1])
x4 = np.mat([1,1,0,1])
#w2区域的全部乘以 -1 作为分类的区分
x5 = np.mat([0,0,-1,-1])
x6 = np.mat([0,-1,-1,-1])
x7 = np.mat([0,-1,0,-1])
x8 = np.mat([-1,-1,-1,-1])
x = [x1.T,x2.T,x3.T,x4.T,x5.T,x6.T,x7.T,x8.T]
#print(x)
w = np.mat([0,0,0,0])         #初始化取C=1，w(1)= (0 0 0)
w = w.T
#print(w)
bool = True
while bool:
bool = False
for i in range(len(x)):
d= w.T * x[i]       #得到1*1矩阵
print(d.sum())
if d <= 0:
w = w + x[i]      #惩罚
bool = True       #存在惩罚 继续迭代
print("***********")
print(w)

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2.多分类问题 得到广义的线性判别曲面

用多类感知器算法求下列模式的判别函数：

ω1: (-1 -1)T

ω2: (0 0)T

ω3: (1 1)T

import numpy as np
多分类问题 广义的线性可分 三维空间中判别面
用多类感知器算法求下列模式的判别函数：
ω1: (-1 -1)T
ω2: (0 0)T
ω3: (1 1)T

x1 = np.mat([-1,-1,1])
x2 = np.mat([0,0,1])
x3 = np.mat([1,1,1])
x = [x1.T,x2.T,x3.T]
w1 = np.mat([0,0,0])
w2 = np.mat([0,0,0])
w3 = np.mat([0,0,0])
w = [w1.T,w2.T,w3.T]
w2 = [w1,w2,w3]
f = True
count = 0
while f:
f = False
for i in range(len(x)):
count += 1
d = []
for j in range(len(w)):
d.append(w[j].T * x[i])
print(d)
print(w2)
if (count % 3 == 1):
if d[0] <= d[1] or d[0] <= d[2]:
w[0] += x[0]
w[1] -= x[0]
w[2] -= x[0]
f = True
# d = np.array(d)
if(count%3==2):
if d[1] <= d[0] or d[1] <= d[2]:
w[0] -= x[1]
w[1] += x[1]
w[2] -= x[1]
f = True
if(count%3==0):
if  d[2] <= d[1] or d[2] <= d[1]:
w[0] -= x[2]
w[1] -= x[2]
w[2] += x[2]
f = True
print count,"**********"
print w
print w2

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**

3.IRIS_DATA数据集上的感知器计算

**

感知器算法类如下

参考来源 python_machine_learning :

https://ljalphabeta.gitbooks.io/python-/content/ch2section3.html

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import numpy as np
class Perceptron(object):
"""Perceptron classifier.

Parameters
------------
eta:float
Learning rate (between 0.0 and 1.0)
n_iter:int
Passes over the training dataset.

Attributes
-------------
w_: 1d-array
Weights after fitting.
errors_: list
Numebr of misclassifications in every epoch.

"""

def __init__(self, eta=0.01, n_iter=10):
self.eta = eta
self.n_iter = n_iter

def fit(self, X, y):
"""Fit training data.

Parameters
------------
X: {array-like}, shape=[n_samples, n_features]
Training vectors, where n_samples is the number of samples
and n_featuers is the number of features.
y: array-like, shape=[n_smaples]
Target values.

Returns
----------
self: object
"""

self.w_ = np.zeros(1 + X.shape[1]) # Add w_0
self.errors_ = []

for _ in range(self.n_iter):
errors = 0
for xi, target in zip(X, y):
update = self.eta * (target - self.predict(xi))
self.w_[1:] += update * xi
self.w_[0] += update
errors += int(update != 0.0)
self.errors_.append(errors)
return self

def net_input(self, X):
"""Calculate net input"""
return np.dot(X, self.w_[1:]) + self.w_[0]

def predict(self, X):
"""Return class label after unit step"""
return np.where(self.net_input(X) >= 0.0, 1, -1) #analoge ? : in C++

#coding:utf-8
#**********************************https://ljalphabeta.gitbooks.io/python-/content/ch2section3.html
#pərˈsepträn
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from matplotlib.colors import ListedColormap
import Perceptron as perceptron_class
df = pd.read_csv('D:\Pycharm\Projects\Perceptron_1\iris.data', header=None)
#print df.tail()

#抽取出前100条样本，这正好是Setosa和Versicolor对应的样本，我们将Versicolor对应的数据作为类别1，Setosa对应的作为-1。
# 对于特征，我们抽取出sepal length和petal length两维度特征，然后用散点图对数据进行可视化

y = df.iloc[0:100, 4].values
y = np.where(y == 'Iris-setosa', -1, 1)
X = df.iloc[0:100, [0, 2]].values
# plt.scatter(X[:50, 0], X[:50, 1],color='red', marker='o', label='setosa')
# plt.scatter(X[50:100, 0], X[50:100, 1],color='blue', marker='x', label='versicolor')
# plt.xlabel('sepal length')
# plt.ylabel('petal length')
# plt.legend(loc='upper left')
# plt.show()

#这里是对于感知机模型进行训练
ppn = perceptron_class.Perceptron(eta=0.1, n_iter=10)
ppn.fit(X, y)

#画出分界线
def plot_decision_regions(X, y, classifier, resolution=0.02):
# setup marker generator and color map
markers = ('s', 'x', 'o', '^', 'v')
colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')
cmap = ListedColormap(colors[:len(np.unique(y))])
# plot the decision surface
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())
# plot class samples
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=ppn)
plt.xlabel('sepal length [cm]')
plt.ylabel('petal length [cm]')
plt.legend(loc='upper left')
plt.show()