机器学习_k-近邻算法

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学习教材是《机器学习实战》，书中实现算法所用的语言是Python。第一个算法是k-近邻算法。

先介绍一些算法中使用到的numpy函数和python的语法。

1、python中的元组、列表和numpy中的数组

python没有数组，但是有元组(tuple)和列表(list)。以下是元组和列表的初始化。元组不可改变，列表可以改变。

    testTuple = ((1, 2, 3), (4, 5, 6), (7, 8, 9))   #initialized use ()
    testList = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]    #initialized use []

numpy包含数据结构array。提供了很多很有用的函数。比如shape，tile和sum等等。

1、shape

numpy中的函数，功能是读取矩阵的长度，可以直接调用shape(),并传入矩阵作为参数或者使用array.shape[]。其中array.shape[0]表示返回矩阵第一维的长度。

但是有个前提矩阵必须由array构造。

  arraySample = array([[1, 2 ,3],
                   [5, 3, 7],
                   [4, 9, 6],
                   [5, 9, 0]])
    print(arraySample.shape[0])
    print(arraySample.shape[1])

打印结果是：

4
3

2、tile(arr, rep)

arr为源数组，rep描述了重复数组的方式。举例说明：

Array=[1, 2] ==> tile(Array, 2) == [1, 2, 1, 2]

==> tile(Array, (2, 3)) == [[1, 2, 1, 2, 1, 2], [1, 2, 1, 2, 1, 2]]

==> tile(Array, (2, 2, 3)) ==[ [[1, 2,1 ,2 ,1, 2], [1, 2, 1, 2, 1, 2]] [[1, 2,1 ,2 ,1, 2], [1, 2, 1, 2, 1, 2]] ]

tile(arr, rep)函数的操作中，rep中元组中各元素指定将arr复制到各个维度的次数。

tile(Array, 2)表示将Array在第一个维度中复制2次；

tile(Array, (2, 3))表示将Array在第一个维度中复制3次，在第二个维度中复制2次；

tile(Array, (2, 2, 3)) 表示将Array在第一个维度中复制3次，在第二个维度中复制2次，在第三个维度中复制2次。

3、array.sum(axis=k)

sum(axis=k)的用法有些类似于tile。当k=1或者=0的时候，计算的结果可以认为是列或行的和，但是当k>1的时候，还是用维度的和来区分更合适。

假定矩阵array的维度为5，那么array.sum(axis=4)表示第一维度的和，array.sum(axis=0)表示第五维度的和。举例说明：

 dataTest = array([[[1, 2, 3],
                      [3, 4, 5]],
                     [[5, 6, 7],
                      [8, 9, 10]]])    
    print(dataTest.sum(axis = 0))
    print(" ")
    print(dataTest.sum(axis = 1))
    print(" ")
    print(dataTest.sum(axis = 2))

输出为：

[[ 6  8 10]
 [11 13 15]]
 
[[ 4  6  8]
 [13 15 17]]
 
[[ 6 12]
 [18 27]]

最后的算法如下：

def file2matrix(filename):
    fr = open(filename)
    numberOfLines = len(fr.readlines())         #get the number of lines in the file
    returnMat = zeros((numberOfLines,3))        #prepare matrix to return
    classLabelVector = []                       #prepare labels return   
    fr = open(filename)
    index = 0
    for line in fr.readlines():
        line = line.strip()
        listFromLine = line.split('\t')
        returnMat[index,:] = listFromLine[0:3]
        classLabelVector.append(int(listFromLine[-1]))
        index += 1
    return returnMat,classLabelVector


'''
dataSet = array([[  4.09200000e+04, 8.32697600e+00, 9.53952000e-01]
                 [  1.44880000e+04, 7.15346900e+00, 1.67390400e+00]
                 [  2.60520000e+04, 1.44187100e+00, 8.05124000e-01]
                 [  7.51360000e+04, 1.31473940e+01, 4.28964000e-01]
                 [  3.83440000e+04, 1.66978800e+00, 1.34296000e-01]
                 [  7.29930000e+04, 1.01417400e+01, 1.03295500e+00]
                 [  3.59480000e+04, 6.83079200e+00, 1.21319200e+00]
                 [  4.26660000e+04, 1.32763690e+01, 5.43880000e-01]
                 [  6.74970000e+04, 8.63157700e+00, 7.49278000e-01]
                 [  3.54830000e+04, 1.22731690e+01, 1.50805300e+00]])
inX = array([36661, 11.865402, 0.882810])
labels = [3, 2, 1, 1, 1, 1, 3, 3, 1, 3]
'''
def classify0(inX, dataSet, labels, k):
    dataSetSize = dataSet.shape[0]
# dataSetSize = 10  
    diffMat = tile(inX, (dataSetSize,1)) - dataSet
    '''
    tile(inX, (dataSetSize,1)) = [[  3.66610000e+04   1.18654020e+01   8.82810000e-01]
                                  [  3.66610000e+04   1.18654020e+01   8.82810000e-01]
                                  [  3.66610000e+04   1.18654020e+01   8.82810000e-01]
                                  [  3.66610000e+04   1.18654020e+01   8.82810000e-01]
                                  [  3.66610000e+04   1.18654020e+01   8.82810000e-01]
                                  [  3.66610000e+04   1.18654020e+01   8.82810000e-01]
                                  [  3.66610000e+04   1.18654020e+01   8.82810000e-01]
                                  [  3.66610000e+04   1.18654020e+01   8.82810000e-01]
                                  [  3.66610000e+04   1.18654020e+01   8.82810000e-01]
                                  [  3.66610000e+04   1.18654020e+01   8.82810000e-01]]
    diffMat= [[ -4.25900000e+03   3.53842600e+00  -7.11420000e-02]
              [  2.21730000e+04   4.71193300e+00  -7.91094000e-01]
              [  1.06090000e+04   1.04235310e+01   7.76860000e-02]
              [ -3.84750000e+04  -1.28199200e+00   4.53846000e-01]
              [ -1.68300000e+03   1.01956140e+01   7.48514000e-01]
              [ -3.63320000e+04   1.72366200e+00  -1.50145000e-01]
              [  7.13000000e+02   5.03461000e+00  -3.30382000e-01]
              [ -6.00500000e+03  -1.41096700e+00   3.38930000e-01]
              [ -3.08360000e+04   3.23382500e+00   1.33532000e-01]
              [  1.17800000e+03  -4.07767000e-01  -6.25243000e-01]]

    '''
    sqDiffMat = diffMat**2
   
    '''
    sqDiffMat = [[  1.81390810e+07   1.25204586e+01   5.06118416e-03]
                 [  4.91641929e+08   2.22023126e+01   6.25829717e-01]
                  [  1.12550881e+08   1.08649999e+02   6.03511460e-03]
                  [  1.48032562e+09   1.64350349e+00   2.05976192e-01]
                  [  2.83248900e+06   1.03950545e+02   5.60273208e-01]
                  [  1.32001422e+09   2.97101069e+00   2.25435210e-02]
                  [  5.08369000e+05   2.53472979e+01   1.09152266e-01]
                  [  3.60600250e+07   1.99082788e+00   1.14873545e-01]
                  [  9.50858896e+08   1.04576241e+01   1.78307950e-02]
                  [  1.38768400e+06   1.66273926e-01   3.90928809e-01]]
    '''
    sqDistances = sqDiffMat.sum(axis=1) 
    # sqDistances = [1.81390935e+07 4.91641952e+08 1.12550990e+08 1.48032563e+09 2.83259351e+06 1.32001423e+09 5.08394456e+05 3.60600271e+07 9.50858906e+08 1.38768456e+06]
    distances = sqDistances**0.5
    
    # distances = [4259.00147048 22173.00051477 10609.00512094 38475.00002403 1683.03104868 36332.0000412 713.01785142 6005.00017533 30836.00016986 1178.0002365]
    sortedDistIndicies = distances.argsort()
    print sortedDistIndicies
    # sortedDistIndicies = [6 9 4 0 7 2 1 8 5 3]   distances[6] < distances[9] < distances[4] < distances[0] < distances[7] < distances[2] < distances[1] < distances[8] < distances[5] < distances[3]
    classCount={}  
    # {} indicates classCount is a dictionary        
    for i in range(k):
        voteIlabel = labels[sortedDistIndicies[i]]
        classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1
        # dict.get(key, default=None) return the key value, if the key is not in the dict, return the default value 
        # get(voteIlabel,0) return the key value of voteIlabel ,if voteIlabel is not in classCount return 0 
    sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True)
    # reverse=True means sorted in descending order, reverse=False means in ascending order
    # key=operator.itemgetter(1) means sorted the second item of classCount
    return sortedClassCount[0][0]