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：
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)