KNN分类算法原理

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# kNN: k Nearest Neighbors

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# 输入:      newInput:  (1xN)的待分类向量

#             dataSet:   (NxM)的训练数据集

#             labels: 训练数据集的类别标签向量

#             k: 近邻数 

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# 输出:     可能性最大的分类标签

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from numpy import *

import operator

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#创建一个数据集，包含2个类别共4个样本

def createDataSet():

# 生成一个矩阵，每行表示一个样本

group = array([[1.0, 0.9], [1.0, 1.0], [0.1, 0.2], [0.0, 0.1]])

# 4个样本分别所属的类别

labels = ['A', 'A', 'B', 'B']

return group, labels

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# KNN分类算法函数定义

def kNNClassify(newInput, dataSet, labels, k):

numSamples = dataSet.shape[0]   # shape[0]表示行数

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## step 1: 计算距离

# tile(A, reps): 构造一个矩阵，通过A重复reps次得到

# the following copy numSamples rows for dataSet

diff = tile(newInput, (numSamples, 1)) - dataSet  # 按元素求差值

squaredDiff = diff ** 2  #将差值平方

squaredDist = sum(squaredDiff, axis = 1)   # 按行累加

distance = squaredDist ** 0.5  #将差值平方和求开方，即得距离

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## step 2: 对距离排序

# argsort() 返回排序后的索引值

sortedDistIndices = argsort(distance)

classCount = {} # define a dictionary (can be append element)

for i in xrange(k):

## step 3: 选择k个最近邻

voteLabel = labels[sortedDistIndices[i]]

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## step 4: 计算k个最近邻中各类别出现的次数

# when the key voteLabel is not in dictionary classCount, get()

# will return 0

classCount[voteLabel] = classCount.get(voteLabel, 0) + 1

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## step 5: 返回出现次数最多的类别标签

maxCount = 0

for key, value in classCount.items():

if value > maxCount:

maxCount = value

maxIndex = key

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return maxIndex

import kNN

from numpy import *

#生成数据集和类别标签

dataSet, labels = kNN.createDataSet()

#定义一个未知类别的数据

testX = array([1.2, 1.0])

k = 3

#调用分类函数对未知数据分类

outputLabel = kNN.kNNClassify(testX, dataSet, labels, 3)

print "Your input is:", testX, "and classified to class: ", outputLabel

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testX = array([0.1, 0.3])

outputLabel = kNN.kNNClassify(testX, dataSet, labels, 3)

print "Your input is:", testX, "and classified to class: ", outputLabel

Your input is: [ 1.2  1.0] and classified to class:  A

Your input is: [ 0.1  0.3] and classified to class:  B

#########################################

# kNN: k Nearest Neighbors

​

# 参数:        inX: vector to compare to existing dataset (1xN)

#             dataSet: size m data set of known vectors (NxM)

#             labels: data set labels (1xM vector)

#             k: number of neighbors to use for comparison

​

# 输出:     多数类

#########################################

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from numpy import *

import operator

import os

​

​

# KNN分类核心方法

def kNNClassify(newInput, dataSet, labels, k):

numSamples = dataSet.shape[0]  # shape[0]代表行数

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## step 1: 计算欧式距离

# tile(A, reps): 将A重复reps次来构造一个矩阵

# the following copy numSamples rows for dataSet

diff = tile(newInput, (numSamples, 1)) - dataSet  # Subtract element-wise

squaredDiff = diff ** 2 # squared for the subtract

squaredDist = sum(squaredDiff, axis = 1)  # sum is performed by row

distance = squaredDist ** 0.5

​

## step 2: 对距离排序

# argsort()返回排序后的索引

sortedDistIndices = argsort(distance)

​

classCount = {}  # 定义一个空的字典

for i in xrange(k):

## step 3: 选择k个最小距离

voteLabel = labels[sortedDistIndices[i]]

​

## step 4: 计算类别的出现次数

# when the key voteLabel is not in dictionary classCount, get()

# will return 0

classCount[voteLabel] = classCount.get(voteLabel, 0) + 1

​

## step 5: 返回出现次数最多的类别作为分类结果

maxCount = 0

for key, value in classCount.items():

if value > maxCount:

maxCount = value

maxIndex = key

​

return maxIndex

​

# 将图片转换为向量

def  img2vector(filename):

  rows = 32

  cols = 32

  imgVector = zeros((1, rows * cols))

  fileIn = open(filename)

  for row in xrange(rows):

  lineStr = fileIn.readline()

  for col in xrange(cols):

  imgVector[0, row * 32 + col] = int(lineStr[col])

​

  return imgVector

​

# 加载数据集

def loadDataSet():

## step 1: 读取训练数据集

print "---Getting training set..."

dataSetDir = 'E:/Python/ml/knn/'

trainingFileList = os.listdir(dataSetDir + 'trainingDigits')  # 加载测试数据

numSamples = len(trainingFileList)

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train_x = zeros((numSamples, 1024))

train_y = []

for i in xrange(numSamples):

filename = trainingFileList[i]

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# get train_x

train_x[i, :] = img2vector(dataSetDir + 'trainingDigits/%s' % filename)

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# get label from file name such as "1_18.txt"

label = int(filename.split('_')[0]) # return 1

train_y.append(label)

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## step 2:读取测试数据集

print "---Getting testing set..."

testingFileList = os.listdir(dataSetDir + 'testDigits') # load the testing set

numSamples = len(testingFileList)

test_x = zeros((numSamples, 1024))

test_y = []

for i in xrange(numSamples):

filename = testingFileList[i]

​

# get train_x

test_x[i, :] = img2vector(dataSetDir + 'testDigits/%s' % filename)

​

# get label from file name such as "1_18.txt"

label = int(filename.split('_')[0]) # return 1

test_y.append(label)

​

return train_x, train_y, test_x, test_y

​

# 手写识别主流程

def testHandWritingClass():

## step 1: 加载数据

print "step 1: load data..."

train_x, train_y, test_x, test_y = loadDataSet()

​

## step 2: 模型训练.

print "step 2: training..."

pass

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## step 3: 测试

print "step 3: testing..."

numTestSamples = test_x.shape[0]

matchCount = 0

for i in xrange(numTestSamples):

predict = kNNClassify(test_x[i], train_x, train_y, 3)

if predict == test_y[i]:

matchCount += 1

accuracy = float(matchCount) / numTestSamples

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## step 4: 输出结果

print "step 4: show the result..."

print 'The classify accuracy is: %.2f%%' % (accuracy * 100)

import kNN

kNN.testHandWritingClass()

step 1: load data...

---Getting training set...

---Getting testing set...

step 2: training...

step 3: testing...

step 4: show the result...

The classify accuracy is: 98.84%