機器學習——邏輯回歸

通過散點圖，觀察一下數據點的空間分布情況，代碼如下：

1
2
3from numpy import *
4import matplotlib.pyplot as plt  
5
6def loadData():  
7    train_x = []  
8    train_y = []  
9    fileIn = open('testSet.txt')
10    for line in fileIn.readlines():  
11        lineArr = line.strip().split()  
12        train_x.append([1.0, float(lineArr[0]), float(lineArr[1])])  
13        train_y.append(float(lineArr[2]))
14    return mat(train_x), mat(train_y).transpose()  
15
16train_x,train_y= loadData()
17for i in xrange(100):  
18    if int(train_y[i, 0]) == 0:  
19        plt.plot(train_x[i, 1], train_x[i, 2], 'or')  
20    elif int(train_y[i, 0]) == 1:  
21        plt.plot(train_x[i, 1], train_x[i, 2], 'ob')
22min_x = min(train_x[:, 1])[0, 0]  
23max_x = max(train_x[:, 1])[0, 0]
24plt.xlabel('X1'); plt.ylabel('X2')  
25plt.show()

運行python腳本畫出來的測試數據的散點圖如圖3所示：

圖3 測試數據散點圖

從圖3中，可以看出測試數據基本可以通過一條直線進行分隔，下邊筆者的邏輯回歸python代碼將通過用一條直線將數據分成兩部分，代碼中的優化算法可以選擇梯度下降法、隨機梯度下降和平滑梯度下降三種方法。模型的代碼如下（讀者可將模型代碼複製入logic.py文件中）：

1from numpy import *  
2import matplotlib.pyplot as plt  
3import time  
4
5
6def sigmoid(inX):  
7    return 1.0 / (1 + exp(-inX))  
8
9
10
11
12
13
14def trainLogRegres(train_x, train_y, opts):  
15    
16    startTime = time.time()  
17
18    numSamples, numFeatures = shape(train_x)  
19    alpha = opts['alpha']; maxIter = opts['maxIter']  
20    weights = ones((numFeatures, 1))  
21
22    
23    for k in range(maxIter):                          
24        if opts['optimizeType'] == 'gradDescent':
25            output = sigmoid(train_x * weights)
26            error = train_y - output  
27            weights = weights + alpha * train_x.transpose() * error  
28        elif opts['optimizeType'] == 'stocGradDescent':
29            for i in range(numSamples):  
30                output = sigmoid(train_x[i, :] * weights)  
31                error = train_y[i, 0] - output  
32                weights = weights + alpha * train_x[i, :].transpose() * error  
33        elif opts['optimizeType'] == 'smoothStocGradDescent':
34          
36            for i in range(numSamples):  
37                alpha = 4.0 / (1.0 + k + i) + 0.01  
38                randIndex = int(random.uniform(0, len(dataIndex)))  
39                output = sigmoid(train_x[randIndex, :] * weights)  
40                error = train_y[randIndex, 0] - output  
41                weights = weights + alpha * train_x[randIndex, :].transpose() * error  
42                del(dataIndex[randIndex])
43        else:  
44            raise NameError('Not support optimize method type!')  
45
46
47    print 'Congratulations, training complete! Took %fs!' % (time.time() - startTime)  
48    return weights  
49
50
51
52
53def testLogRegres(weights, test_x, test_y):  
54    numSamples, numFeatures = shape(test_x)  
55    matchCount = 0  
56    for i in xrange(numSamples):  
57        predict = sigmoid(test_x[i, :] * weights)[0, 0] > 0.5  
58        if predict == bool(test_y[i, 0]):  
59            matchCount += 1  
60    accuracy = float(matchCount) / numSamples  
61    return accuracy  
62
63
64
65
66def showLogRegres(weights, train_x, train_y):  
67    
68    numSamples, numFeatures = shape(train_x)  
69    if numFeatures != 3:  
70        print "Sorry! I can not dra 
71        return 1  
72
73    
74    for i in xrange(numSamples):  
75        if int(train_y[i, 0]) == 0:  
76            plt.plot(train_x[i, 1], train_x[i, 2], 'or')  
77        elif int(train_y[i, 0]) == 1:  
78            plt.plot(train_x[i, 1], train_x[i, 2], 'ob')  
79
80    
81    min_x = min(train_x[:, 1])[0, 0]  
82    max_x = max(train_x[:, 1])[0, 0]  
83    weights = weights.getA()  
84    y_min_x = float(-weights[0] - weights[1] * min_x) / weights[2]  
85    y_max_x = float(-weights[0] - weights[1] * max_x) / weights[2]  
86    plt.plot([min_x, max_x], [y_min_x, y_max_x], '-g')  
87    plt.xlabel('X1'); plt.ylabel('X2')  
88plt.show()

對代碼的分類效果進行測試，測試代碼如下（讀者可將測試代碼複製入test_logic.py文件中）：

1from numpy import *  
2import matplotlib.pyplot as plt  
3import time  
4import logic as logic
5
6def loadData():  
7    train_x = []  
8    train_y = []  
9    
10    fileIn = open('testSet.txt')  
11    for line in fileIn.readlines():  
12        lineArr = line.strip().split()  
13        train_x.append([1.0, float(lineArr[0]), float(lineArr[1])])  
14        train_y.append(float(lineArr[2]))  
15    return mat(train_x), mat(train_y).transpose()  
16  
17
18print "step 1: load data..."  
19train_x, train_y = loadData()  
20
21
22test_x = train_x; test_y = train_y  
23
24print "step 2: training..."  
25opts = {'alpha': 0.01, 'maxIter': 5, 'optimizeType': 'smoothStocGradDescent'}
26
27optimalWeights = logic.trainLogRegres(train_x, train_y, opts)  
28
29print optimalWeights
30
31print "step 3: testing..."  
32accuracy = logic.testLogRegres(optimalWeights, test_x, test_y)  
33
34print "step 4: show the result..."    
35print 'The classify accuracy is: %.3f%%' % (accuracy * 100)  
36logic.showLogRegres(optimalWeights, train_x, train_y)

運行測試代碼test_logic.py，測試結果如圖4所示：

圖4 邏輯回歸線性分類效果

筆者統計了一下，在迭代5次的情況下，線性分類的正確率為96%。讀者可以通過複製代碼，自行的進行測試，也可以將線性分類改變成曲線形式，去測一下分類效果。在這篇文章中筆者簡單介紹了一下邏輯回歸的原理，並且給出了實現的代碼以供讀者直觀學習體驗。在下一篇，本公眾號中關於機器學習文章中，筆者將詳細的介紹支持向量機SVM的原理，並附上python實現的代碼。

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