（数据挖掘-入门-6）十折交叉验证和K近邻

主要内容：

1、十折交叉验证

2、混淆矩阵

3、K近邻

4、python实现

一、十折交叉验证

前面提到了数据集分为训练集和测试集，训练集用来训练模型，而测试集用来测试模型的好坏，那么单一的测试是否就能很好的衡量一个模型的性能呢？

答案自然是否定的，单一的测试集具有偶然性和随机性。因此本文介绍一种衡量模型（比如分类器）性能的方法——十折交叉验证(10-fold cross validation)

什么是十折交叉验证？

假设有个数据集，需要建立一个分类器，如何验证分类器的性能呢？

将数据集随机均为为10份，依次选择某1份作为测试集，其他9份作为训练集，训练出来的模型对测试集进行分类，并统计分类结果，就这样，重复10次实验，综合所有分类结果，就可以得到比较稳定的评价结果（当然，由于是随机划分数据集，因此每次运行结果都不一致）。

附：当然也可以选择k折交叉验证，最极端的就是留1交叉验证，每次只留一个样本做测试集，但这样的计算规模太大。

二、混淆矩阵

混淆矩阵：confuse matrix

假设有n个类别，那么分类结果的统计可以通过一个n*n的矩阵来表示，即混淆矩阵。

对角线即为分类正确的样本数。

三、K近邻（KNN）

在协同过滤中已经提到过K近邻，就是选择离某个样本最近的K个样本，根据该K个样本来决定此样本的数值或类别。

如果是连续数值，那么K近邻可以作为回归方法，通过K个样本的矩阵权重来拟合数值；

如果是离散数值，那么K近邻可以作为分类方法，通过K个样本的多数投票策略来决定类别；

四、python实现

数据集：

mpgData.zip

pimaSmall.zip

pima.zip

代码：

1、切分数据

# divide data into 10 buckets
import random

def buckets(filename, bucketName, separator, classColumn):
    """the original data is in the file named filename
    bucketName is the prefix for all the bucket names
    separator is the character that divides the columns
    (for ex., a tab or comma and classColumn is the column
    that indicates the class"""

    # put the data in 10 buckets
    numberOfBuckets = 10
    data = {}
    # first read in the data and divide by category
    with open(filename) as f:
        lines = f.readlines()
    for line in lines:
        if separator != '\t':
            line = line.replace(separator, '\t')
        # first get the category
        category = line.split()[classColumn]
        data.setdefault(category, [])
        data[category].append(line)
    # initialize the buckets
    buckets = []
    for i in range(numberOfBuckets):
        buckets.append([])
    # now for each category put the data into the buckets
    for k in data.keys():
        #randomize order of instances for each class
        random.shuffle(data[k])
        bNum = 0
        # divide into buckets
        for item in data[k]:
            buckets[bNum].append(item)
            bNum = (bNum + 1) % numberOfBuckets

    # write to file
    for bNum in range(numberOfBuckets):
        f = open("%s-%02i" % (bucketName, bNum + 1), 'w')
        for item in buckets[bNum]:
            f.write(item)
        f.close()

# example of how to use this code
buckets("pimaSmall.txt", 'pimaSmall',',',8)

2、十折交叉验证

#
#
#  Nearest Neighbor Classifier for mpg dataset
#

class Classifier:
    def __init__(self, bucketPrefix, testBucketNumber, dataFormat):

        """ a classifier will be built from files with the bucketPrefix
        excluding the file with textBucketNumber. dataFormat is a string that
        describes how to interpret each line of the data files. For example,
        for the mpg data the format is:

        "class    num    num    num    num    num    comment"
        """

        self.medianAndDeviation = []

        # reading the data in from the file

        self.format = dataFormat.strip().split('\t')
        self.data = []
        # for each of the buckets numbered 1 through 10:
        for i in range(1, 11):
            # if it is not the bucket we should ignore, read in the data
            if i != testBucketNumber:
                filename = "%s-%02i" % (bucketPrefix, i)
                f = open(filename)
                lines = f.readlines()
                f.close()
                for line in lines[1:]:
                    fields = line.strip().split('\t')
                    ignore = []
                    vector = []
                    for i in range(len(fields)):
                        if self.format[i] == 'num':
                            vector.append(float(fields[i]))
                        elif self.format[i] == 'comment':
                            ignore.append(fields[i])
                        elif self.format[i] == 'class':
                            classification = fields[i]
                    self.data.append((classification, vector, ignore))
        self.rawData = list(self.data)
        # get length of instance vector
        self.vlen = len(self.data[0][1])
        # now normalize the data
        for i in range(self.vlen):
            self.normalizeColumn(i)

    ##################################################
    ###
    ###  CODE TO COMPUTE THE MODIFIED STANDARD SCORE

    def getMedian(self, alist):
        """return median of alist"""
        if alist == []:
            return []
        blist = sorted(alist)
        length = len(alist)
        if length % 2 == 1:
            # length of list is odd so return middle element
            return blist[int(((length + 1) / 2) -  1)]
        else:
            # length of list is even so compute midpoint
            v1 = blist[int(length / 2)]
            v2 =blist[(int(length / 2) - 1)]
            return (v1 + v2) / 2.0

    def getAbsoluteStandardDeviation(self, alist, median):
        """given alist and median return absolute standard deviation"""
        sum = 0
        for item in alist:
            sum += abs(item - median)
        return sum / len(alist)

    def normalizeColumn(self, columnNumber):
       """given a column number, normalize that column in self.data"""
       # first extract values to list
       col = [v[1][columnNumber] for v in self.data]
       median = self.getMedian(col)
       asd = self.getAbsoluteStandardDeviation(col, median)
       #print("Median: %f   ASD = %f" % (median, asd))
       self.medianAndDeviation.append((median, asd))
       for v in self.data:
           v[1][columnNumber] = (v[1][columnNumber] - median) / asd

    def normalizeVector(self, v):
        """We have stored the median and asd for each column.
        We now use them to normalize vector v"""
        vector = list(v)
        for i in range(len(vector)):
            (median, asd) = self.medianAndDeviation[i]
            vector[i] = (vector[i] - median) / asd
        return vector
    ###
    ### END NORMALIZATION
    ##################################################

    def testBucket(self, bucketPrefix, bucketNumber):
        """Evaluate the classifier with data from the file
        bucketPrefix-bucketNumber"""

        filename = "%s-%02i" % (bucketPrefix, bucketNumber)
        f = open(filename)
        lines = f.readlines()
        totals = {}
        f.close()
        for line in lines:
            data = line.strip().split('\t')
            vector = []
            classInColumn = -1
            for i in range(len(self.format)):
                  if self.format[i] == 'num':
                      vector.append(float(data[i]))
                  elif self.format[i] == 'class':
                      classInColumn = i
            theRealClass = data[classInColumn]
            classifiedAs = self.classify(vector)
            totals.setdefault(theRealClass, {})
            totals[theRealClass].setdefault(classifiedAs, 0)
            totals[theRealClass][classifiedAs] += 1
        return totals

    def manhattan(self, vector1, vector2):
        """Computes the Manhattan distance."""
        return sum(map(lambda v1, v2: abs(v1 - v2), vector1, vector2))

    def nearestNeighbor(self, itemVector):
        """return nearest neighbor to itemVector"""
        return min([ (self.manhattan(itemVector, item[1]), item)
                     for item in self.data])

    def classify(self, itemVector):
        """Return class we think item Vector is in"""
        return(self.nearestNeighbor(self.normalizeVector(itemVector))[1][0])

def tenfold(bucketPrefix, dataFormat):
    results = {}
    for i in range(1, 11):
        c = Classifier(bucketPrefix, i, dataFormat)
        t = c.testBucket(bucketPrefix, i)
        for (key, value) in t.items():
            results.setdefault(key, {})
            for (ckey, cvalue) in value.items():
                results[key].setdefault(ckey, 0)
                results[key][ckey] += cvalue

    # now print results
    categories = list(results.keys())
    categories.sort()
    print(   "\n       Classified as: ")
    header =    "        "
    subheader = "      +"
    for category in categories:
        header += category + "   "
        subheader += "----+"
    print (header)
    print (subheader)
    total = 0.0
    correct = 0.0
    for category in categories:
        row = category + "    |"
        for c2 in categories:
            if c2 in results[category]:
                count = results[category][c2]
            else:
                count = 0
            row += " %2i |" % count
            total += count
            if c2 == category:
                correct += count
        print(row)
    print(subheader)
    print("\n%5.3f percent correct" %((correct * 100) / total))
    print("total of %i instances" % total)

tenfold("mpgData/mpgData/mpgData",        "class    num    num    num    num    num    comment")

3、K近邻

#
#  K Nearest Neighbor Classifier for Pima dataset
#

import heapq
import random

class Classifier:
    def __init__(self, bucketPrefix, testBucketNumber, dataFormat, k):

        """ a classifier will be built from files with the bucketPrefix
        excluding the file with textBucketNumber. dataFormat is a string that
        describes how to interpret each line of the data files. For example,
        for the mpg data the format is:

        "class    num    num    num    num    num    comment"
        """

        self.medianAndDeviation = []
        self.k = k
        # reading the data in from the file

        self.format = dataFormat.strip().split('\t')
        self.data = []
        # for each of the buckets numbered 1 through 10:
        for i in range(1, 11):
            # if it is not the bucket we should ignore, read in the data
            if i != testBucketNumber:
                filename = "%s-%02i" % (bucketPrefix, i)
                f = open(filename)
                lines = f.readlines()
                f.close()
                for line in lines[1:]:
                    fields = line.strip().split('\t')
                    ignore = []
                    vector = []
                    for i in range(len(fields)):
                        if self.format[i] == 'num':
                            vector.append(float(fields[i]))
                        elif self.format[i] == 'comment':
                            ignore.append(fields[i])
                        elif self.format[i] == 'class':
                            classification = fields[i]
                    self.data.append((classification, vector, ignore))
        self.rawData = list(self.data)
        # get length of instance vector
        self.vlen = len(self.data[0][1])
        # now normalize the data
        for i in range(self.vlen):
            self.normalizeColumn(i)

    ##################################################
    ###
    ###  CODE TO COMPUTE THE MODIFIED STANDARD SCORE

    def getMedian(self, alist):
        """return median of alist"""
        if alist == []:
            return []
        blist = sorted(alist)
        length = len(alist)
        if length % 2 == 1:
            # length of list is odd so return middle element
            return blist[int(((length + 1) / 2) -  1)]
        else:
            # length of list is even so compute midpoint
            v1 = blist[int(length / 2)]
            v2 =blist[(int(length / 2) - 1)]
            return (v1 + v2) / 2.0

    def getAbsoluteStandardDeviation(self, alist, median):
        """given alist and median return absolute standard deviation"""
        sum = 0
        for item in alist:
            sum += abs(item - median)
        return sum / len(alist)

    def normalizeColumn(self, columnNumber):
       """given a column number, normalize that column in self.data"""
       # first extract values to list
       col = [v[1][columnNumber] for v in self.data]
       median = self.getMedian(col)
       asd = self.getAbsoluteStandardDeviation(col, median)
       #print("Median: %f   ASD = %f" % (median, asd))
       self.medianAndDeviation.append((median, asd))
       for v in self.data:
           v[1][columnNumber] = (v[1][columnNumber] - median) / asd

    def normalizeVector(self, v):
        """We have stored the median and asd for each column.
        We now use them to normalize vector v"""
        vector = list(v)
        for i in range(len(vector)):
            (median, asd) = self.medianAndDeviation[i]
            vector[i] = (vector[i] - median) / asd
        return vector
    ###
    ### END NORMALIZATION
    ##################################################

    def testBucket(self, bucketPrefix, bucketNumber):
        """Evaluate the classifier with data from the file
        bucketPrefix-bucketNumber"""

        filename = "%s-%02i" % (bucketPrefix, bucketNumber)
        f = open(filename)
        lines = f.readlines()
        totals = {}
        f.close()
        for line in lines:
            data = line.strip().split('\t')
            vector = []
            classInColumn = -1
            for i in range(len(self.format)):
                  if self.format[i] == 'num':
                      vector.append(float(data[i]))
                  elif self.format[i] == 'class':
                      classInColumn = i
            theRealClass = data[classInColumn]
            #print("REAL ", theRealClass)
            classifiedAs = self.classify(vector)
            totals.setdefault(theRealClass, {})
            totals[theRealClass].setdefault(classifiedAs, 0)
            totals[theRealClass][classifiedAs] += 1
        return totals

    def manhattan(self, vector1, vector2):
        """Computes the Manhattan distance."""
        return sum(map(lambda v1, v2: abs(v1 - v2), vector1, vector2))

    def nearestNeighbor(self, itemVector):
        """return nearest neighbor to itemVector"""
        return min([ (self.manhattan(itemVector, item[1]), item)
                     for item in self.data])

    def knn(self, itemVector):
        """returns the predicted class of itemVector using k
        Nearest Neighbors"""
        # changed from min to heapq.nsmallest to get the
        # k closest neighbors
        neighbors = heapq.nsmallest(self.k,
                                   [(self.manhattan(itemVector, item[1]), item)
                     for item in self.data])
        # each neighbor gets a vote
        results = {}
        for neighbor in neighbors:
            theClass = neighbor[1][0]
            results.setdefault(theClass, 0)
            results[theClass] += 1
        resultList = sorted([(i[1], i[0]) for i in results.items()], reverse=True)
        #get all the classes that have the maximum votes
        maxVotes = resultList[0][0]
        possibleAnswers = [i[1] for i in resultList if i[0] == maxVotes]
        # randomly select one of the classes that received the max votes
        answer = random.choice(possibleAnswers)
        return( answer)

    def classify(self, itemVector):
        """Return class we think item Vector is in"""
        # k represents how many nearest neighbors to use
        return(self.knn(self.normalizeVector(itemVector)))                             

def tenfold(bucketPrefix, dataFormat, k):
    results = {}
    for i in range(1, 11):
        c = Classifier(bucketPrefix, i, dataFormat, k)
        t = c.testBucket(bucketPrefix, i)
        for (key, value) in t.items():
            results.setdefault(key, {})
            for (ckey, cvalue) in value.items():
                results[key].setdefault(ckey, 0)
                results[key][ckey] += cvalue

    # now print results
    categories = list(results.keys())
    categories.sort()
    print(   "\n       Classified as: ")
    header =    "        "
    subheader = "      +"
    for category in categories:
        header += "% 2s   " % category
        subheader += "-----+"
    print (header)
    print (subheader)
    total = 0.0
    correct = 0.0
    for category in categories:
        row = " %s    |" % category
        for c2 in categories:
            if c2 in results[category]:
                count = results[category][c2]
            else:
                count = 0
            row += " %3i |" % count
            total += count
            if c2 == category:
                correct += count
        print(row)
    print(subheader)
    print("\n%5.3f percent correct" %((correct * 100) / total))
    print("total of %i instances" % total)

print("SMALL DATA SET")
tenfold("pimaSmall/pimaSmall/pimaSmall",
        "num    num    num    num    num    num    num    num    class", 3)

print("\n\nLARGE DATA SET")
tenfold("pima/pima/pima",
        "num    num    num    num    num    num    num    num    class", 3)