python中分类的深度学习模型 python分类算法

Logistic回归 分类算法 python实现

Python 机器学习入门之Logistic回归 分类算法

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文章目录

• Logistic回归 分类算法 python实现
• 前言
• 一、Logistic回归是什么？
• 二、Python实现

• 1.引入库
• 2.读入数据

• 实验结果

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前言

随着人工智能的不断发展，机器学习这门技术也越来越重要，很多人都开启了学习机器学习，本文就介绍了机器学习的基础内容。

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一、Logistic回归是什么？

让我们通过一个例子来开始：在分类问题中，我们尝试预测的是结果是否属于某一个类（例如正确或错误）。分类问题的例子有：判断一封电子邮件是否是垃圾邮件；判断一次金融交易是否是欺诈；之前我们也谈到了肿瘤分类问题的例子，区别一个肿瘤是恶性的还是良性的。如果我们要用线性回归算法来解决一个分类问题，对于分类， 取值为 0 或者1，但如果你使用的是线性回归，那么假设函数的输出值可能远大于 1，或者远小于0，即使所有训练样本的标签 都等于 0 或 1。尽管我们知道标签应该取值0 或者1，但是如果算法得到的值远大于1或者远小于0的话，就会感觉很奇怪。所以我们在接下来的要研究的算法就叫做逻辑回归算法，这个算法的性质是：它的输出值永远在0到 1 之间。

二、Python实现

1.引入库

代码如下（示例）：

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import scipy.optimize as opt

2.读入数据

代码如下（示例）：

path = 'ex2data1.txt'
data = pd.read_csv(path, header=None, names=['ExamA', 'ExamB', 'Admitted'])
data.insert(0, 'Ones', 1)
data.head()
print(data)

这个数据集我会在文章末尾给出。

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## 3.具体实现

代码如下（示例）：

"""
函数：sigmoid函数(假设函数)
"""


def sigmoid(z):
    return 1.0 / (1 + np.exp(-z))


"""
代价函数
"""


def cost(theta, X, y):
    theta = np.matrix(theta)  # 转换成为一个矩阵
    X = np.matrix(X)
    y = np.matrix(y)
    first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
    second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
    return np.sum(first - second) / (len(X))


def gradient(theta, X, y):
    theta = np.matrix(theta)
    X = np.matrix(X)
    y = np.matrix(y)

    parameters = int(theta.ravel().shape[1])
    grad = np.zeros(parameters)
    error = sigmoid(X * theta.T) - y
    for i in range(parameters):
        term = np.multiply(error, X[:, i])
        grad[i] = np.sum(term) / len(X)
    return grad


cols = data.shape[1]
X = data.iloc[:, 0:cols - 1]
y = data.iloc[:, cols - 1:cols]
theta = np.zeros(3)
# 转换X，y的类型
X = np.array(X.values)
y = np.array(y.values)
result = opt.fmin_tnc(func=cost, x0=theta, fprime=gradient, args=(X, y))
print(result)
plotting_x1 = np.linspace(30, 100, 100)
plotting_h1 = (- result[0][0] - result[0][1] * plotting_x1) / result[0][2]
positive = data[data['Admitted'].isin([1])]  # 将所有为1的行单独存放在positive
negative = data[data['Admitted'].isin([0])]  # 将所有为0的行单独存放在negative
fig, ax = plt.subplots(figsize=(12, 8))
ax.plot(plotting_x1, plotting_h1, 'y', label='Prediction')
ax.scatter(positive['ExamA'], positive['ExamB'], s=50, c='b', marker='o', label='Admitted')
ax.scatter(negative['ExamA'], negative['ExamB'], s=50, c='r', marker='x', label='Not Admitted')
ax.legend()
ax.set_xlabel('ExamA Score')
ax.set_ylabel('ExamB Score')
plt.show()

这个地方是采用scipy.optimize as opt fmin_tnc这个函数来处理处理theta的值

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实验结果

先将数据可视化

由此可以看出已经找到了分类的参数theta的值带入假设函数

对应的三个theta的值 可以通过这个函数调用我们的梯度下降 自动产生出来 不需要我们进行步数之类的设置

数据集：

34.62365962451697,78.0246928153624,0

30.28671076822607,43.89499752400101,0

35.84740876993872,72.90219802708364,0

60.18259938620976,86.30855209546826,1

79.0327360507101,75.3443764369103,1

45.08327747668339,56.3163717815305,0

61.10666453684766,96.51142588489624,1

75.02474556738889,46.55401354116538,1

76.09878670226257,87.42056971926803,1

84.43281996120035,43.53339331072109,1

95.86155507093572,38.22527805795094,0

75.01365838958247,30.60326323428011,0

82.30705337399482,76.48196330235604,1

69.36458875970939,97.71869196188608,1

39.53833914367223,76.03681085115882,0

53.9710521485623,89.20735013750205,1

69.07014406283025,52.74046973016765,1

67.94685547711617,46.67857410673128,0

70.66150955499435,92.92713789364831,1

76.97878372747498,47.57596364975532,1

67.37202754570876,42.83843832029179,0

89.67677575072079,65.79936592745237,1

50.534788289883,48.85581152764205,0

34.21206097786789,44.20952859866288,0

77.9240914545704,68.9723599933059,1

62.27101367004632,69.95445795447587,1

80.1901807509566,44.82162893218353,1

93.114388797442,38.80067033713209,0

61.83020602312595,50.25610789244621,0

38.78580379679423,64.99568095539578,0

61.379289447425,72.80788731317097,1

85.40451939411645,57.05198397627122,1

52.10797973193984,63.12762376881715,0

52.04540476831827,69.43286012045222,1

40.23689373545111,71.16774802184875,0

54.63510555424817,52.21388588061123,0

33.91550010906887,98.86943574220611,0

64.17698887494485,80.90806058670817,1

74.78925295941542,41.57341522824434,0

34.1836400264419,75.2377203360134,0

83.90239366249155,56.30804621605327,1

51.54772026906181,46.85629026349976,0

94.44336776917852,65.56892160559052,1

82.36875375713919,40.61825515970618,0

51.04775177128865,45.82270145776001,0

62.22267576120188,52.06099194836679,0

77.19303492601364,70.45820000180959,1

97.77159928000232,86.7278223300282,1

62.07306379667647,96.76882412413983,1

91.56497449807442,88.69629254546599,1

79.94481794066932,74.16311935043758,1

99.2725269292572,60.99903099844988,1

90.54671411399852,43.39060180650027,1

34.52451385320009,60.39634245837173,0

50.2864961189907,49.80453881323059,0

49.58667721632031,59.80895099453265,0

97.64563396007767,68.86157272420604,1

32.57720016809309,95.59854761387875,0

74.24869136721598,69.82457122657193,1

71.79646205863379,78.45356224515052,1

75.3956114656803,85.75993667331619,1

35.28611281526193,47.02051394723416,0

56.25381749711624,39.26147251058019,0

30.05882244669796,49.59297386723685,0

44.66826172480893,66.45008614558913,0

66.56089447242954,41.09209807936973,0

40.45755098375164,97.53518548909936,1

49.07256321908844,51.88321182073966,0

80.27957401466998,92.11606081344084,1

66.74671856944039,60.99139402740988,1

32.72283304060323,43.30717306430063,0

64.0393204150601,78.03168802018232,1

72.34649422579923,96.22759296761404,1

60.45788573918959,73.09499809758037,1

58.84095621726802,75.85844831279042,1

99.82785779692128,72.36925193383885,1

47.26426910848174,88.47586499559782,1

50.45815980285988,75.80985952982456,1

60.45555629271532,42.50840943572217,0

82.22666157785568,42.71987853716458,0

88.9138964166533,69.80378889835472,1

94.83450672430196,45.69430680250754,1

67.31925746917527,66.58935317747915,1

57.23870631569862,59.51428198012956,1

80.36675600171273,90.96014789746954,1

68.46852178591112,85.59430710452014,1

42.0754545384731,78.84478600148043,0

75.47770200533905,90.42453899753964,1

78.63542434898018,96.64742716885644,1

52.34800398794107,60.76950525602592,0

94.09433112516793,77.15910509073893,1

90.44855097096364,87.50879176484702,1

55.48216114069585,35.57070347228866,0

74.49269241843041,84.84513684930135,1

89.84580670720979,45.35828361091658,1

83.48916274498238,48.38028579728175,1

42.2617008099817,87.10385094025457,1

99.31500880510394,68.77540947206617,1

55.34001756003703,64.9319380069486,1

74.77589300092767,89.52981289513276,1