收集数据

数据来源：http://archive.ics.uci.edu/ml/datasets/Haberman%27s+Survival
文本数据如下图所示：

31,65,4,1
33,58,10,1
33,60,0,1
34,59,0,2
34,66,9,2

这是关于乳腺癌已手术患者存活时间(寿命)的样本集，文本文件中共包含306个样本，样本包含的属性有：
1. 患者做手术时的年龄 opAge
2. 患者做手术的年份-1900 opYear，比如1970年做的手术，则opYear属性的值为70
3. 阳性腋窝淋巴结的数目 cellNum
4. 存活时间 status，其中，status等于1表示该患者存活了5年以上，status等于2表示该患者在5年之内死亡。
使用pandas读取文本文件，将数据转换为DataFrame对象：

data = http://www.mamicode.com/pd.read_table(r"C:\data\Haberman‘s Survival Data.txt", sep=",", header=None, names=[‘opAge‘, ‘opYear‘, ‘cellNum‘, ‘status‘], engine="python")
data1 = data[data[‘status‘] == 1]  # status为1的数据
data2 = data[data[‘status‘] == 2]  # status为2的数据

查看data.shape为(306, 4)

数据散点图

fig = plt.figure(figsize=(16, 12))
ax = fig.gca(projection="3d") #get current axis
ax.scatter(data1[‘opAge‘], data1[‘opYear‘], data1[‘cellNum‘], c=‘r‘, s=100, marker="*", label="survived 5 years or longer") #status为1的样本的散点图
ax.scatter(data2[‘opAge‘], data2[‘opYear‘], data2[‘cellNum‘], c=‘b‘, s=100, marker="^", label="died within 5 year") #status为2的样本的散点图
ax.set_xlabel("operation age", size=15)
ax.set_ylabel("operation year", size=15)
ax.set_zlabel("cell number", size=15)
ax.set_title(‘Haberman\‘s Survival Scatter Plot‘, size=15, weight=‘bold‘)
ax.set_zlim(0, 30)
ax.legend(loc="lower right", fontsize=15)
plt.show()

得到的3D散点图如下所示：

准备数据

KNN算法的原则是：找到距离目标样本距离最近的K个样本，这K个样本中类别出现次数最多的那个类，作为目标样本的类别。这里采用的距离是欧式距离，那么数值较大的属性在衡量距离的时候起的作用较大，这会导致样本距离衡量出现偏差，为了屏蔽这种影响，需要对数据进行归一化：

# 归一化 (x-min)/(max-min)∈[0,1]
def autoNorm(dataSet):
    minVals = samples.min(axis=0) # 按列求最小值，即求每个属性的最小值
    maxVals = samples.max(axis=0) # 求每个属性的最大值
    factors = maxVals - minVals # 归一化因子
    sNum = dataSet.shape[0]  # 数据集的行数，即样本数
    normDataSet = (dataSet - np.tile(minVals, (sNum, 1))) / np.tile(factors, (sNum, 1))  # 先将minVals和归一化因子转换成与dataSet相同的shape，再做减法和除法运算，最终归一化后的数据都介于[0,1]
    return normDataSet

训练算法

划分数据集

采用K折交叉验证的方法来评估分类器的性能，从样本集中随机抽取10%作为测试集testing data，其余的90%用来做10 fold cross validation

testIdxs = random.sample(range(0, len(samples), 1), len(samples) * 1 / 10)  # 随机选取testing data的索引
testingSet = samples.ix[testIdxs]  # 根据索引从样本集中获取testing data
idxs = range(0, len(samples), 1)  # 总的数据索引序列
#以下for循环是从总的数据索引序列中将testing data的索引去除
for i in range(0, len(testIdxs)):
    idxs.remove(testIdxs[i])
trainData = http://www.mamicode.com/samples.ix[idxs]  # 获取用作训练的数据集

对trainData使用10折交叉验证，首先随机打乱trainData的索引序列random.shuffle(idxs) idxs是引用类型，在执行完remove操作后，idxs已只剩trainData的索引。

k nearest neighbor

采用欧氏距离作为距离评价准则：

#inX: 目标样本
#dataSet: 用来找k nearest neighbor的数据集，labels是该数据集对应的类别标签，dataSet和labels的索引是一一对应的
def classifyKNN(inX, dataSet, labels, k):
    #以下代码是为了防止出现这种情况：dataSet和labels的索引不是从0开始的有序自然数，导致在argsort排序的时候出现错乱，因为argsort排序结果是从0开始的自然数，因此首先需要重置dataSet和labels的索引，使其索引变为依次从0开始自然数。
    nDataSet = zeros((dataSet.shape[0], dataSet.shape[1])) #与dataSet同型的0矩阵
    j = 0
    for i in dataSet.index:
        nDataSet[j] = dataSet.ix[i]
        j += 1
    nDataSet = pd.DataFrame(nDataSet)

    nLabels = zeros(labels.shape[0]) #与labels同型的0向量
    h = 0
    for i in labels.index:
        nLabels[h] = labels.ix[i]
        h += 1

    dataSetNum = nDataSet.shape[0]  # 样本数(DataFrame行数)
    diffMat = tile(inX, (dataSetNum, 1)) - nDataSet #目标样本与参照样本集的差，对应属性相减，结果为与nDataSet同型的矩阵
    sqDiffMat = diffMat ** 2  #平方
    sqDistances = sqDiffMat.sum(axis=1) #矩阵sqDiffMat的列之和，即目标样本与样本集中每个样本对应属性的差值的平方和
    distances = sqDistances ** 0.5 #平方根，欧氏距离，即目标样本与每个样本点的距离
    sortedDistanceIdx = distances.argsort()  # 距离从小到大的索引值，sortedDistanceIdx的索引是从0开始的自然数，sortedDistanceIdx的值表示对应的distance的索引，比如sortedDistanceIdx[0]是150，表示最小的距离在distances中的索引是150
    classCount = {}
    for i in range(k):
        #找出distance最小的k个索引，然后在nLabels中获取其对应类别
        voteLabel = nLabels[int(sortedDistanceIdx[i])]
        classCount[voteLabel] = classCount.get(voteLabel, 0) + 1
    #classCount字典中存放了统计的label和对应的出现次数
    sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True) #倒序
    return sortedClassCount[0][0]  #出现次数最大的label

10折交叉验证

一次验证

#返回在该验证集上的错误率
def train(trainingSet, validationSet, kn):
    errorCount = 0
    vIdxs = validationSet.index
    #遍历验证集，对每个样本使用KNN
    for i in range(0, len(validationSet)):
        pred = classifyKNN(validationSet.loc[vIdxs[i], [‘opAge‘, ‘opYear‘, ‘cellNum‘]], trainingSet[[‘opAge‘, ‘opYear‘, ‘cellNum‘]], trainingSet[‘status‘], kn)
        if (pred != validationSet.at[vIdxs[i], ‘status‘]):
            errorCount += 1
    return errorCount / float(len(validationSet))

10次验证

使用10次验证的平均错误率来评价KNN分类器的性能

# dataSet：用来交叉验证的数据集，idxs是对应的索引序列
# k: k折交叉验证
# kn: kn近邻
def crossValidation(dataSet, idxs, k, kn):
    step = len(idxs) / k
    errorRate = 0
    for i in range(k):
        validationIdx = []
        for i in range(i * step, (i + 1) * step):
            validationIdx.append(idxs[i])
        validationSet = dataSet.ix[validationIdx]  # 获得验证集数据
        temp = idxs[:]
        for i in validationIdx:  # 把验证集的索引去除
            temp.remove(i)
        trainingSet = dataSet.ix[temp]  # 获取训练集数据
        errorRate += train(trainingSet, validationSet, kn)
    aveErrorRate = errorRate / float(k)
    return aveErrorRate

测试算法

交叉验证完毕之后，使用全部的trainData，对testingData进行预测

def predict(trainingSet, testingSet, kn):
    errorCount = 0
    for i in range(0, len(testingSet)):
        vIdxs = testingSet.index
        pred = classifyKNN(testingSet.loc[vIdxs[i], [‘opAge‘, ‘opYear‘, ‘cellNum‘]], trainingSet[[‘opAge‘, ‘opYear‘, ‘cellNum‘]], trainingSet[‘status‘], kn)
        print "The prediction label is %s"%(pred)
        print "The real label is %s"%(testingSet.at[vIdxs[i], ‘status‘])
        if (pred != testingSet.at[vIdxs[i], ‘status‘]):
            errorCount += 1
    return errorCount / float(len(testingSet))

print "The cross validation error ratio is %d" %crossValidation(trainData, idxs, 10, 3)
print "The testing data error ratio is %d"%predict(samples,testingSet,3)

运行结果为：

The cross validation error ratio is 0.28
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 2
The real result is 2
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 2
The prediction result is 1
The real result is 1
The prediction result is 2
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 2
The real result is 2
The prediction result is 1
The real result is 2
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 2
The real result is 2
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 2
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 1
The prediction result is 1
The real result is 2
The testing data error ratio is 0.17