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[ML]逻辑分类入门：两类

2024-10-29 01:50:39   210人阅读

注明：本文仅作为记录本人的日常学习历程而存在。

 

这次要实现的功能是 使用已经划分为两类的数据进行训练参数theta，得到theta后，任意给出一组数据，与theta相乘，得到一个0－1之间的小数，分别对应了1st类和2nd类。

1.使用的训练数据集如下

技术分享 
Id,SepalLengthCm,SepalWidthCm,PetalLengthCm,PetalWidthCm,Species
1,5.1,3.5,1.4,0.2,Iris-setosa
2,4.9,3.0,1.4,0.2,Iris-setosa
3,4.7,3.2,1.3,0.2,Iris-setosa
4,4.6,3.1,1.5,0.2,Iris-setosa
5,5.0,3.6,1.4,0.2,Iris-setosa
6,5.4,3.9,1.7,0.4,Iris-setosa
7,4.6,3.4,1.4,0.3,Iris-setosa
8,5.0,3.4,1.5,0.2,Iris-setosa
9,4.4,2.9,1.4,0.2,Iris-setosa
10,4.9,3.1,1.5,0.1,Iris-setosa
11,5.4,3.7,1.5,0.2,Iris-setosa
12,4.8,3.4,1.6,0.2,Iris-setosa
13,4.8,3.0,1.4,0.1,Iris-setosa
14,4.3,3.0,1.1,0.1,Iris-setosa
15,5.8,4.0,1.2,0.2,Iris-setosa
16,5.7,4.4,1.5,0.4,Iris-setosa
17,5.4,3.9,1.3,0.4,Iris-setosa
18,5.1,3.5,1.4,0.3,Iris-setosa
19,5.7,3.8,1.7,0.3,Iris-setosa
20,5.1,3.8,1.5,0.3,Iris-setosa
21,5.4,3.4,1.7,0.2,Iris-setosa
22,5.1,3.7,1.5,0.4,Iris-setosa
23,4.6,3.6,1.0,0.2,Iris-setosa
24,5.1,3.3,1.7,0.5,Iris-setosa
25,4.8,3.4,1.9,0.2,Iris-setosa
26,5.0,3.0,1.6,0.2,Iris-setosa
27,5.0,3.4,1.6,0.4,Iris-setosa
28,5.2,3.5,1.5,0.2,Iris-setosa
29,5.2,3.4,1.4,0.2,Iris-setosa
30,4.7,3.2,1.6,0.2,Iris-setosa
31,4.8,3.1,1.6,0.2,Iris-setosa
32,5.4,3.4,1.5,0.4,Iris-setosa
33,5.2,4.1,1.5,0.1,Iris-setosa
34,5.5,4.2,1.4,0.2,Iris-setosa
35,4.9,3.1,1.5,0.1,Iris-setosa
36,5.0,3.2,1.2,0.2,Iris-setosa
37,5.5,3.5,1.3,0.2,Iris-setosa
38,4.9,3.1,1.5,0.1,Iris-setosa
39,4.4,3.0,1.3,0.2,Iris-setosa
40,5.1,3.4,1.5,0.2,Iris-setosa
41,5.0,3.5,1.3,0.3,Iris-setosa
42,4.5,2.3,1.3,0.3,Iris-setosa
43,4.4,3.2,1.3,0.2,Iris-setosa
44,5.0,3.5,1.6,0.6,Iris-setosa
45,5.1,3.8,1.9,0.4,Iris-setosa
46,4.8,3.0,1.4,0.3,Iris-setosa
47,5.1,3.8,1.6,0.2,Iris-setosa
48,4.6,3.2,1.4,0.2,Iris-setosa
49,5.3,3.7,1.5,0.2,Iris-setosa
50,5.0,3.3,1.4,0.2,Iris-setosa
51,7.0,3.2,4.7,1.4,Iris-versicolor
52,6.4,3.2,4.5,1.5,Iris-versicolor
53,6.9,3.1,4.9,1.5,Iris-versicolor
54,5.5,2.3,4.0,1.3,Iris-versicolor
55,6.5,2.8,4.6,1.5,Iris-versicolor
56,5.7,2.8,4.5,1.3,Iris-versicolor
57,6.3,3.3,4.7,1.6,Iris-versicolor
58,4.9,2.4,3.3,1.0,Iris-versicolor
59,6.6,2.9,4.6,1.3,Iris-versicolor
60,5.2,2.7,3.9,1.4,Iris-versicolor
61,5.0,2.0,3.5,1.0,Iris-versicolor
62,5.9,3.0,4.2,1.5,Iris-versicolor
63,6.0,2.2,4.0,1.0,Iris-versicolor
64,6.1,2.9,4.7,1.4,Iris-versicolor
65,5.6,2.9,3.6,1.3,Iris-versicolor
66,6.7,3.1,4.4,1.4,Iris-versicolor
67,5.6,3.0,4.5,1.5,Iris-versicolor
68,5.8,2.7,4.1,1.0,Iris-versicolor
69,6.2,2.2,4.5,1.5,Iris-versicolor
70,5.6,2.5,3.9,1.1,Iris-versicolor
71,5.9,3.2,4.8,1.8,Iris-versicolor
72,6.1,2.8,4.0,1.3,Iris-versicolor
73,6.3,2.5,4.9,1.5,Iris-versicolor
74,6.1,2.8,4.7,1.2,Iris-versicolor
75,6.4,2.9,4.3,1.3,Iris-versicolor
76,6.6,3.0,4.4,1.4,Iris-versicolor
77,6.8,2.8,4.8,1.4,Iris-versicolor
78,6.7,3.0,5.0,1.7,Iris-versicolor
79,6.0,2.9,4.5,1.5,Iris-versicolor
80,5.7,2.6,3.5,1.0,Iris-versicolor
81,5.5,2.4,3.8,1.1,Iris-versicolor
82,5.5,2.4,3.7,1.0,Iris-versicolor
83,5.8,2.7,3.9,1.2,Iris-versicolor
84,6.0,2.7,5.1,1.6,Iris-versicolor
85,5.4,3.0,4.5,1.5,Iris-versicolor
86,6.0,3.4,4.5,1.6,Iris-versicolor
87,6.7,3.1,4.7,1.5,Iris-versicolor
88,6.3,2.3,4.4,1.3,Iris-versicolor
89,5.6,3.0,4.1,1.3,Iris-versicolor
90,5.5,2.5,4.0,1.3,Iris-versicolor
91,5.5,2.6,4.4,1.2,Iris-versicolor
92,6.1,3.0,4.6,1.4,Iris-versicolor
93,5.8,2.6,4.0,1.2,Iris-versicolor
94,5.0,2.3,3.3,1.0,Iris-versicolor
95,5.6,2.7,4.2,1.3,Iris-versicolor
96,5.7,3.0,4.2,1.2,Iris-versicolor
97,5.7,2.9,4.2,1.3,Iris-versicolor
98,6.2,2.9,4.3,1.3,Iris-versicolor
99,5.1,2.5,3.0,1.1,Iris-versicolor
100,5.7,2.8,4.1,1.3,Iris-versicolor
101,6.3,3.3,6.0,2.5,Iris-virginica
102,5.8,2.7,5.1,1.9,Iris-virginica
103,7.1,3.0,5.9,2.1,Iris-virginica
104,6.3,2.9,5.6,1.8,Iris-virginica
105,6.5,3.0,5.8,2.2,Iris-virginica
106,7.6,3.0,6.6,2.1,Iris-virginica
107,4.9,2.5,4.5,1.7,Iris-virginica
108,7.3,2.9,6.3,1.8,Iris-virginica
109,6.7,2.5,5.8,1.8,Iris-virginica
110,7.2,3.6,6.1,2.5,Iris-virginica
111,6.5,3.2,5.1,2.0,Iris-virginica
112,6.4,2.7,5.3,1.9,Iris-virginica
113,6.8,3.0,5.5,2.1,Iris-virginica
114,5.7,2.5,5.0,2.0,Iris-virginica
115,5.8,2.8,5.1,2.4,Iris-virginica
116,6.4,3.2,5.3,2.3,Iris-virginica
117,6.5,3.0,5.5,1.8,Iris-virginica
118,7.7,3.8,6.7,2.2,Iris-virginica
119,7.7,2.6,6.9,2.3,Iris-virginica
120,6.0,2.2,5.0,1.5,Iris-virginica
121,6.9,3.2,5.7,2.3,Iris-virginica
122,5.6,2.8,4.9,2.0,Iris-virginica
123,7.7,2.8,6.7,2.0,Iris-virginica
124,6.3,2.7,4.9,1.8,Iris-virginica
125,6.7,3.3,5.7,2.1,Iris-virginica
126,7.2,3.2,6.0,1.8,Iris-virginica
127,6.2,2.8,4.8,1.8,Iris-virginica
128,6.1,3.0,4.9,1.8,Iris-virginica
129,6.4,2.8,5.6,2.1,Iris-virginica
130,7.2,3.0,5.8,1.6,Iris-virginica
131,7.4,2.8,6.1,1.9,Iris-virginica
132,7.9,3.8,6.4,2.0,Iris-virginica
133,6.4,2.8,5.6,2.2,Iris-virginica
134,6.3,2.8,5.1,1.5,Iris-virginica
135,6.1,2.6,5.6,1.4,Iris-virginica
136,7.7,3.0,6.1,2.3,Iris-virginica
137,6.3,3.4,5.6,2.4,Iris-virginica
138,6.4,3.1,5.5,1.8,Iris-virginica
139,6.0,3.0,4.8,1.8,Iris-virginica
140,6.9,3.1,5.4,2.1,Iris-virginica
141,6.7,3.1,5.6,2.4,Iris-virginica
142,6.9,3.1,5.1,2.3,Iris-virginica
143,5.8,2.7,5.1,1.9,Iris-virginica
144,6.8,3.2,5.9,2.3,Iris-virginica
145,6.7,3.3,5.7,2.5,Iris-virginica
146,6.7,3.0,5.2,2.3,Iris-virginica
147,6.3,2.5,5.0,1.9,Iris-virginica
148,6.5,3.0,5.2,2.0,Iris-virginica
149,6.2,3.4,5.4,2.3,Iris-virginica
150,5.9,3.0,5.1,1.8,Iris-virginica
View Code

2.引入库，定义相关sigmoid、cost、gradient函数，并对数据进行整理：将第一列的序号去除、将两种分类类别改为0和1等等。

程序将在gradient函数中计算出最终的theta。

import csv
import numpy as np
import matplotlib.pyplot as plt
def sigmoid(z):
    g = 1/(1+np.exp(-z))
    return g
def cost_function(X,Y,theta):
    pred = sigmoid(X.dot(theta))
    J = (1/len(Y))*np.sum(-Y*np.log(pred)-(1-Y)*np.log(1-pred))
    return J
def gradient(X,Y,theta,max_iter,alpha):
    cost = []
    for i in range(max_iter):
        Y_pred = sigmoid(X.dot(theta))
        diff = Y_pred - Y
        grad = (1/len(Y)) * X.T.dot(diff)
        theta -= alpha * grad
        cost.append(cost_function(X,Y,theta))
    return (theta,cost)
with open(‘Iris.csv‘) as f:
    reader = csv.reader(f)
    data = [row for row in reader]
data = np.array(data)
header = data[0,:]
data = data[1:,:]
for i in range(data.shape[0]):
    data[i,0] = 1
    if data[i,5] == ‘Iris-setosa‘:
        data[i,5] = 1
    else:
        data[i,5] = 0
data = data.astype(‘float‘)

3.定义theta，利用gradient函数，计算theta

theta = np.zeros((5,1))
(theta,cost) = gradient(data[:,:5],data[:,5:6],theta,300,0.1)

4.可视化处理

class_1 = data[:50,:]
class_2 = data[51:,:]

plt.subplot(2,1,1)
plt.plot(class_1[:,1],class_1[:,2],‘ro‘)
plt.plot(class_2[:,1],class_2[:,2],‘bx‘)
plt.plot()
print(theta)
plt.subplot(212)
plt.plot(cost)
ex =np.array([ 1,  5.1,  3.5,  1.4,  0.2])
print(sigmoid(ex.dot(theta)))

5.总结

两类的分类比较简单，就是利用递度下降，得到theta值，结合sigmoid函数将X*theta，得到一个0~1的数字，便可据此是接近0还是接近1来推断该X的类别。

 

今天也尝试了多类别（>2）的分类，由于暂时找不到coursera中介绍的fmincg()在python中的替代函数而作废。

后来考虑能不能纯用递度下降法来做，虽然吃力，但也许会有个结果呢？

[ML]逻辑分类入门：两类


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