使用Decision Tree对MNIST数据集进行实验

使用的Decision Tree中，对MNIST中的灰度值进行了0/1处理，方便来进行分类和计算熵。

使用较少的测试数据测试了在对灰度值进行多分类的情况下，分类结果的正确率如何。实验结果如下。

#Test change pixel data into more categories than 0/1:
#int(pixel)/50: 37%
#int(pixel)/64: 45.9%
#int(pixel)/96: 52.3%
#int(pixel)/128: 62.48%
#int(pixel)/152: 59.1%
#int(pixel)/176: 57.6%
#int(pixel)/192: 54.0%

可见，在对灰度数据进行二分类，也就是0/1处理时，效果是最好的。

使用0/1处理，最终结果如下：

#Result:
#Train with 10k, test with 60k: 77.79%
#Train with 60k, test with 10k: 87.3%
#Time cost: 3 hours.

最终结果是87.3%的正确率。与SVM和KNN的超过95%相比，差距不小。而且消耗时间更长。

需要注意的是，此次Decision Tree算法中，并未对决策树进行剪枝。因此，还有可以提升的空间。

python代码见最下面。其中：

calcShannonEntropy(dataSet)：是对矩阵的熵进行计算，根据各个数据点的分类情况，使用香农定理计算；

splitDataSet(dataSet, axis, value): 是获取第axis维度上的值为value的所有行所组成的矩阵。对于第axis维度上的数据，分别计算他们的splitDataSet的矩阵的熵，并与该维度上数据的出现概率相乘求和，可以得到使用第axis维度构建决策树后，整体的熵。

chooseBestFeatureToSplit(dataSet): 根据splitDataSet函数，对比得到整体的熵与原矩阵的熵相比，熵的增量最大的维度。根据此维度feature来构建决策树。

createDecisionTree(dataSet, features): 递归构建决策树。若在叶子节点处没法分类，则采用majorityCnt(classList)方法统计出现最多次的class作为分类。

代码如下：

#Decision tree for MNIST dataset by arthur503.
#Data format: 'class    label1:pixel    label2:pixel ...'
#Warning: without fix overfitting!
#
#Test change pixel data into more categories than 0/1:
#int(pixel)/50: 37%
#int(pixel)/64: 45.9%
#int(pixel)/96: 52.3%
#int(pixel)/128: 62.48%
#int(pixel)/152: 59.1%
#int(pixel)/176: 57.6%
#int(pixel)/192: 54.0%
#
#Result:
#Train with 10k, test with 60k: 77.79%
#Train with 60k, test with 10k: 87.3%
#Time cost: 3 hours.

from numpy import *
import operator

def calcShannonEntropy(dataSet):
    numEntries = len(dataSet)
    labelCounts = {}
    for featureVec in dataSet:
        currentLabel = featureVec[0]
        if currentLabel not in labelCounts.keys():
            labelCounts[currentLabel] = 1
        else:
            labelCounts[currentLabel] += 1
    shannonEntropy = 0.0
    for key in labelCounts:
        prob = float(labelCounts[key])/numEntries
        shannonEntropy -= prob  * log2(prob)
    return shannonEntropy

#get all rows whose axis item equals value.
def splitDataSet(dataSet, axis, value):
    subDataSet = []
    for featureVec in dataSet:
        if featureVec[axis] == value:
            reducedFeatureVec = featureVec[:axis]
            reducedFeatureVec.extend(featureVec[axis+1:])   #if axis == -1, this will cause error!
            subDataSet.append(reducedFeatureVec)
    return subDataSet

def chooseBestFeatureToSplit(dataSet):
    #Notice: Actucally, index 0 of numFeatures is not feature(it is class label).
    numFeatures = len(dataSet[0])
    baseEntropy = calcShannonEntropy(dataSet)
    bestInfoGain = 0.0
    bestFeature = numFeatures - 1   #DO NOT use -1! or splitDataSet(dataSet, -1, value) will cause error!
    #feature index start with 1(not 0)!
    for i in range(numFeatures)[1:]:
        featureList = [example[i] for example in dataSet]
        featureSet = set(featureList)
        newEntropy = 0.0
        for value in featureSet:
            subDataSet = splitDataSet(dataSet, i, value)
            prob = len(subDataSet)/float(len(dataSet))
            newEntropy += prob * calcShannonEntropy(subDataSet)
        infoGain = baseEntropy - newEntropy
        if infoGain > bestInfoGain:
            bestInfoGain = infoGain
            bestFeature = i
    return bestFeature

#classify on leaf of decision tree.
def majorityCnt(classList):
    classCount = {}
    for vote in classList:
        if vote not in classCount:
            classCount[vote] = 0
        classCount[vote] += 1
    sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]

#Create Decision Tree.
def createDecisionTree(dataSet, features):
    print 'create decision tree... length of features is:'+str(len(features))
    classList = [example[0] for example in dataSet]
    if classList.count(classList[0]) == len(classList):
        return classList[0]
    if len(dataSet[0]) == 1:
        return majorityCnt(classList)
    bestFeatureIndex = chooseBestFeatureToSplit(dataSet)
    bestFeatureLabel = features[bestFeatureIndex]
    myTree = {bestFeatureLabel:{}}
    del(features[bestFeatureIndex])
    featureValues = [example[bestFeatureIndex] for example in dataSet]
    featureSet = set(featureValues)
    for value in featureSet:
        subFeatures = features[:]
        myTree[bestFeatureLabel][value] = createDecisionTree(splitDataSet(dataSet, bestFeatureIndex, value), subFeatures)
    return myTree

def line2Mat(line):
    mat = line.strip().split(' ')
    for i in range(len(mat)-1):
        pixel = mat[i+1].split(':')[1]
        #change MNIST pixel data into 0/1 format.
        mat[i+1] = int(pixel)/128
    return mat

#return matrix as a list(instead of a matrix).
#features is the 28*28 pixels in MNIST dataset.
def file2Mat(fileName):
    f = open(fileName)
    lines = f.readlines()
    matrix = []
    for line in lines:
        mat = line2Mat(line)
        matrix.append(mat)
    f.close()
    print 'Read file '+str(fileName) + ' to array done! Matrix shape:'+str(shape(matrix))
    return matrix

#Classify test file.
def classify(inputTree, featureLabels, testVec):
    firstStr = inputTree.keys()[0]
    secondDict = inputTree[firstStr]
    featureIndex = featureLabels.index(firstStr)
    predictClass = '-1'
    for key in secondDict.keys():
        if testVec[featureIndex] == key:
            if type(secondDict[key]) == type({}):
                predictClass = classify(secondDict[key], featureLabels, testVec)
            else:
                predictClass = secondDict[key]
    return predictClass

def classifyTestFile(inputTree, featureLabels, testDataSet):
    rightCnt = 0
    for i in range(len(testDataSet)):
        classLabel = testDataSet[i][0]
        predictClassLabel = classify(inputTree, featureLabels, testDataSet[i])
        if classLabel == predictClassLabel:
            rightCnt += 1
        if i % 200 == 0:
            print 'num '+str(i)+'. ratio: ' + str(float(rightCnt)/(i+1))
    return float(rightCnt)/len(testDataSet)

def getFeatureLabels(length):
    strs = []
    for i in range(length):
        strs.append('#'+str(i))
    return strs

#Normal file
trainFile = 'train_60k.txt'
testFile = 'test_10k.txt'
#Scaled file
#trainFile = 'train_60k_scale.txt'
#testFile = 'test_10k_scale.txt'
#Test file
#trainFile = 'test_only_1.txt'
#testFile = 'test_only_2.txt'

#train decision tree.
dataSet = file2Mat(trainFile)
#Actually, the 0 item is class, not feature labels.
featureLabels = getFeatureLabels(len(dataSet[0]))
print 'begin to create decision tree...'
myTree = createDecisionTree(dataSet, featureLabels)
print 'create decision tree done.'

#predict with decision tree.
testDataSet = file2Mat(testFile)
featureLabels = getFeatureLabels(len(testDataSet[0]))
rightRatio = classifyTestFile(myTree, featureLabels, testDataSet)
print 'total right ratio: ' + str(rightRatio)