機械学習アルゴリズムとPython実践の論理回帰(Logistic Regression)

機械学習アルゴリズムとPython実践このシリーズは主に「機械学習実戦」という本を参考にしている.大神のコードを参考に自分でテストします.

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# logRegression: Logistic Regression
# Author : cai
# Date   : 2018-09-13
# HomePage : http://blog.csdn.net/
#################################################
 
from numpy import *
import matplotlib.pyplot as plt
import time
 
 
# calculate the sigmoid function
def sigmoid(inX):
	return 1.0 / (1 + exp(-inX))
 
 
# train a logistic regression model using some optional optimize algorithm
# input: train_x is a mat datatype, each row stands for one sample
#		 train_y is mat datatype too, each row is the corresponding label
#		 opts is optimize option include step and maximum number of iterations   opts        ，           
def trainLogRegres(train_x, train_y, opts):
	#          
	startTime = time.time()
 
	numSamples, numFeatures = shape(train_x)#train_x   (XL,XL)     
	alpha = opts['alpha']
	maxIter = opts['maxIter'] #    
	weights = ones((numFeatures, 1))
	#print 'weights',weights
	print 'train_y:',train_y
	
	print '    maxIter：',maxIter
	# optimize through gradient descent algorilthm           
	for k in range(maxIter):
		if opts['optimizeType'] == 'gradDescent': # gradient descent algorilthm     (gradient descent)
			output = sigmoid(train_x * weights)
			error = train_y - output
			print 'error:',error
			print 'output:',output
			weights = weights + alpha * train_x.transpose() * error
		elif opts['optimizeType'] == 'stocGradDescent': #       SGD (stochastic gradient descent)
			for i in range(numSamples):
				output = sigmoid(train_x[i, :] * weights)
				error = train_y[i, 0] - output
				weights = weights + alpha * train_x[i, :].transpose() * error
		elif opts['optimizeType'] == 'smoothStocGradDescent': # smooth stochastic gradient descent          
			# randomly select samples to optimize for reducing cycle fluctuations                 
			dataIndex = range(numSamples)
			for i in range(numSamples):
				alpha = 4.0 / (1.0 + k + i) + 0.01
				randIndex = int(random.uniform(0, len(dataIndex)))
				output = sigmoid(train_x[randIndex, :] * weights)
				error = train_y[randIndex, 0] - output
				weights = weights + alpha * train_x[randIndex, :].transpose() * error
				del(dataIndex[randIndex]) # during one interation, delete the optimized sample
		else:
			raise NameError('Not support optimize method type!')
	
 
	print 'Congratulations, training complete! Took %fs!' % (time.time() - startTime)
	return weights
 
 
# test your trained Logistic Regression model given test set
def testLogRegres(weights, test_x, test_y):
	numSamples, numFeatures = shape(test_x)
	matchCount = 0
	for i in xrange(numSamples):
		predict = sigmoid(test_x[i, :] * weights)[0, 0] > 0.5
		if predict == bool(test_y[i, 0]):
			matchCount += 1
	accuracy = float(matchCount) / numSamples
	return accuracy
 
 
# show your trained logistic regression model only available with 2-D data
def showLogRegres(weights, train_x, train_y):
	# notice: train_x and train_y is mat datatype
	numSamples, numFeatures = shape(train_x)
	if numFeatures != 3:
		print "Sorry! I can not draw because the dimension of your data is not 2!"
		return 1
 
	# draw all samples
	for i in xrange(numSamples):
		if int(train_y[i, 0]) == 0:
			plt.plot(train_x[i, 1], train_x[i, 2], 'or')
		elif int(train_y[i, 0]) == 1:
			plt.plot(train_x[i, 1], train_x[i, 2], 'ob')
 
	# draw the classify line
	min_x = min(train_x[:, 1])[0, 0]
	max_x = max(train_x[:, 1])[0, 0]
	weights = weights.getA()  # convert mat to array
	y_min_x = float(-weights[0] - weights[1] * min_x) / weights[2]
	y_max_x = float(-weights[0] - weights[1] * max_x) / weights[2]
	plt.plot([min_x, max_x], [y_min_x, y_max_x], '-g')
	plt.xlabel('X1'); plt.ylabel('X2')
	plt.show()
	
from numpy import *
import matplotlib.pyplot as plt
import time
 
def loadData():
	train_x = []
	train_y = []
	fileIn = open('C:\\Users\\root\\Desktopng\\machinelearninginaction-master\\machinelearninginaction-master\\Ch05\\testSet1.txt')
	for line in fileIn.readlines():
		lineArr = line.strip().split()
		train_x.append([1.0, float(lineArr[0]), float(lineArr[1])])
		train_y.append(float(lineArr[2]))
	return mat(train_x), mat(train_y).transpose()  #.transpose()   
 
 
## step 1: load data     
print "step 1: load data..."
train_x, train_y = loadData()
test_x = train_x; test_y = train_y
 
## step 2: training...   
print "step 2: training..."
opts = {'alpha': 0.01, 'maxIter': 330, 'optimizeType': 'gradDescent'}
print '      maxIter:',opts['maxIter'],'
','      ：optimizeType',opts['optimizeType']
optimalWeights = trainLogRegres(train_x, train_y, opts)
 
## step 3: testing   
print "step 3: testing..."
accuracy = testLogRegres(optimalWeights, test_x, test_y)
 
## step 4: show the result     
print "step 4: show the result..."	
print 'The classify accuracy is: %.3f%%' % (accuracy * 100)
showLogRegres(optimalWeights, train_x, train_y) 

反復330回を選択し、3つの方法の正解率を比較します.
左図選択反復数maxIter:330選択方法:勾配降下algorilthm
正解率:The classify accuracy is:95.000%
右図選択反復数maxIter:330選択方法:ランダム勾配降下
正解率:The classify accuracy is:97.000%
左二図選択反復数maxIter:330選択方法は、定常ランダム勾配降下
The classify accuracy is: 95.000%
結論:ランダム勾配降下の正解率は最高97%に達し、このシーンでのデータマイニングに適している.