K折交叉验证

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#K折交叉验证

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本文详细介绍了K折交叉验证的概念及其在机器学习中的应用。包括K折交叉验证的基础流程、不同交叉验证方法（如KFold、LeaveOneOut、ShuffleSplit等）的特点，并通过实例展示了如何使用Python的sklearn库进行交叉验证。

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K折交叉验证

先导入需要的库及数据集

In [1]: import numpy as np

In [2]: from sklearn.model_selection import train_test_split

In [3]: from sklearn.datasets import load_iris

In [4]: from sklearn import svm

In [5]: iris = load_iris()

In [6]: iris.data.shape, iris.target.shape
Out[6]: ((150, 4), (150,))

1.`train_test_split`

对数据集进行快速打乱（分为训练集和测试集）

这里相当于对数据集进行了shuffle后按照给定的test_size 进行数据集划分。

In [7]: X_train, X_test, y_train, y_test = train_test_split(
   ...:         iris.data, iris.target, test_size=.4, random_state=0)
   #这里是按照6:4对训练集测试集进行划分

In [8]: X_train.shape, y_train.shape
Out[8]: ((90, 4), (90,))

In [9]: X_test.shape, y_test.shape
Out[9]: ((60, 4), (60,))

In [10]: iris.data[:5]
Out[10]: 
array([[ 5.1,  3.5,  1.4,  0.2],
       [ 4.9,  3. ,  1.4,  0.2],
       [ 4.7,  3.2,  1.3,  0.2],
       [ 4.6,  3.1,  1.5,  0.2],
       [ 5. ,  3.6,  1.4,  0.2]])

In [11]: X_train[:5]
Out[11]: 
array([[ 6. ,  3.4,  4.5,  1.6],
       [ 4.8,  3.1,  1.6,  0.2],
       [ 5.8,  2.7,  5.1,  1.9],
       [ 5.6,  2.7,  4.2,  1.3],
       [ 5.6,  2.9,  3.6,  1.3]])

In [12]: clf = svm.SVC(kernel='linear', C=1).fit(X_train, y_train)

In [13]: clf.score(X_test, y_test)
Out[13]: 0.96666666666666667

2.`cross_val_score`

对数据集进行指定次数的交叉验证并为每次验证效果评测

其中，score 默认是以 scoring=’f1_macro’进行评测的，余外针对分类或回归还有：
这里写图片描述
这需要from　sklearn import metrics ,通过在cross_val_score 指定参数来设定评测标准；
当cv 指定为int 类型时，默认使用KFold 或StratifiedKFold 进行数据集打乱，下面会对KFold 和StratifiedKFold 进行介绍。


In [15]: from sklearn.model_selection import cross_val_score

In [16]: clf = svm.SVC(kernel='linear', C=1)

In [17]: scores = cross_val_score(clf, iris.data, iris.target, cv=5)

In [18]: scores
Out[18]: array([ 0.96666667,  1.        ,  0.96666667,  0.96666667,  1.        ])

In [19]: scores.mean()
Out[19]: 0.98000000000000009

除使用默认交叉验证方式外，可以对交叉验证方式进行指定，如验证次数，训练集测试集划分比例等

In [20]: from sklearn.model_selection import ShuffleSplit

In [21]: n_samples = iris.data.shape[0]

In [22]: cv = ShuffleSplit(n_splits=3, test_size=.3, random_state=0)

In [23]: cross_val_score(clf, iris.data, iris.target, cv=cv)
Out[23]: array([ 0.97777778,  0.97777778,  1.        ])

在cross_val_score 中同样可使用pipeline 进行流水线操作

In [24]: from sklearn import preprocessing

In [25]: from sklearn.pipeline import make_pipeline

In [26]: clf = make_pipeline(preprocessing.StandardScaler(), svm.SVC(C=1))

In [27]: cross_val_score(clf, iris.data, iris.target, cv=cv)
Out[27]: array([ 0.97777778,  0.93333333,  0.95555556])

3.`cross_val_predict`

cross_val_predict 与cross_val_score 很相像，不过不同于返回的是评测效果，cross_val_predict 返回的是estimator 的分类结果（或回归值），这个对于后期模型的改善很重要，可以通过该预测输出对比实际目标值，准确定位到预测出错的地方，为我们参数优化及问题排查十分的重要。

In [28]: from sklearn.model_selection import cross_val_predict

In [29]: from sklearn import metrics

In [30]: predicted = cross_val_predict(clf, iris.data, iris.target, cv=10)

In [31]: predicted
Out[31]: 
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])

In [32]: metrics.accuracy_score(iris.target, predicted)
Out[32]: 0.96666666666666667

4.`KFold`

K折交叉验证，这是将数据集分成K份的官方给定方案，所谓K折就是将数据集通过K次分割，使得所有数据既在训练集出现过，又在测试集出现过，当然，每次分割中不会有重叠。相当于无放回抽样。

In [33]: from sklearn.model_selection import KFold

In [34]: X = ['a','b','c','d']

In [35]: kf = KFold(n_splits=2)

In [36]: for train, test in kf.split(X):
    ...:     print train, test
    ...:     print np.array(X)[train], np.array(X)[test]
    ...:     print '\n'
    ...:     
[2 3] [0 1]
['c' 'd'] ['a' 'b']


[0 1] [2 3]
['a' 'b'] ['c' 'd']

如果要想输出迭代次数

from sklearn.model_selection import KFold
kf = KFold(n_splits = 2)
for i ,(train_index,test_index) in kf(X,y):
	X_train, X_test = X[train_index], X[test_index]
	y_train, y_test = y[train_index], y[test_index]

5.`LeaveOneOut`

LeaveOneOut 其实就是KFold 的一个特例，因为使用次数比较多，因此独立的定义出来，完全可以通过KFold 实现。


In [37]: from sklearn.model_selection import LeaveOneOut

In [38]: X = [1,2,3,4]

In [39]: loo = LeaveOneOut()

In [41]: for train, test in loo.split(X):
    ...:     print train, test
    ...:     
[1 2 3] [0]
[0 2 3] [1]
[0 1 3] [2]
[0 1 2] [3]


#使用KFold实现LeaveOneOtut
In [42]: kf = KFold(n_splits=len(X))

In [43]: for train, test in kf.split(X):
    ...:     print train, test
    ...:     
[1 2 3] [0]
[0 2 3] [1]
[0 1 3] [2]
[0 1 2] [3]

6.`LeavePOut`

这个也是KFold 的一个特例，用KFold 实现起来稍麻烦些，跟LeaveOneOut 也很像。


In [44]: from sklearn.model_selection import LeavePOut

In [45]: X = np.ones(4)

In [46]: lpo = LeavePOut(p=2)

In [47]: for train, test in lpo.split(X):
    ...:     print train, test
    ...:     
[2 3] [0 1]
[1 3] [0 2]
[1 2] [0 3]
[0 3] [1 2]
[0 2] [1 3]
[0 1] [2 3]

7.`ShuffleSplit`

ShuffleSplit 咋一看用法跟LeavePOut 很像，其实两者完全不一样，LeavePOut 是使得数据集经过数次分割后，所有的测试集出现的元素的集合即是完整的数据集，即无放回的抽样，而ShuffleSplit 则是有放回的抽样，只能说经过一个足够大的抽样次数后，保证测试集出现了完成的数据集的倍数。注意和 train_test_split() 的区别,ShuffleSplit只是分割数据，返回的是分割后数据的索引。

In [48]: from sklearn.model_selection import ShuffleSplit

In [49]: X = np.arange(5)

In [50]: ss = ShuffleSplit(n_splits=3, test_size=.25, random_state=0)

In [51]: for train_index, test_index in ss.split(X):
    ...:     print train_index, test_index
    ...:     
[1 3 4] [2 0]
[1 4 3] [0 2]
[4 0 2] [1 3]

8.`StratifiedKFold`

利用StratifiedKFold方法分层采样：依照标签的比例来抽取数据，本案例集标签0和1的比例是1：1，因此在抽取数据时也是按照标签比例1：1来提取的

#依照标签的比例来抽取数据，本案例集标签0和1的比例是1：1
#因此在抽取数据时也是按照标签比例1：1来提取的
sfolder = StratifiedKFold(n_splits=4,random_state=0)
# 就是根据y，也就是target类别来进行分的
for train, test in sfolder.split(X,y):
    print('Train: %s | test: %s' % (train, test))
>>>
Train: [1 3 4 5 6 7] | test: [0 2]niuk
Train: [0 2 4 5 6 7] | test: [1 3]
Train: [0 1 2 3 5 7] | test: [4 6]
Train: [0 1 2 3 4 6] | test: [5 7]

9.`GroupKFold`

这个跟StratifiedKFold 比较像，不过测试集是按照一定分组进行打乱的，即先分堆，然后把这些堆打乱，每个堆里的顺序还是固定不变的。

In [57]: from sklearn.model_selection import GroupKFold

In [58]: X = [.1, .2, 2.2, 2.4, 2.3, 4.55, 5.8, 8.8, 9, 10]

In [59]: y = ['a','b','b','b','c','c','c','d','d','d']

In [60]: groups = [1,1,1,2,2,2,3,3,3,3]

In [61]: gkf = GroupKFold(n_splits=3)

In [62]: for train, test in gkf.split(X,y,groups=groups):
    ...:     print train, test
    ...:     
[0 1 2 3 4 5] [6 7 8 9]
[0 1 2 6 7 8 9] [3 4 5]
[3 4 5 6 7 8 9] [0 1 2]

10.`LeaveOneGroupOut（不重要）`

这个是在GroupKFold 上的基础上混乱度又减小了，按照给定的分组方式将测试集分割下来。

In [63]: from sklearn.model_selection import LeaveOneGroupOut

In [64]: X = [1, 5, 10, 50, 60, 70, 80]

In [65]: y = [0, 1, 1, 2, 2, 2, 2]

In [66]: groups = [1, 1, 2, 2, 3, 3, 3]

In [67]: logo = LeaveOneGroupOut()

In [68]: for train, test in logo.split(X, y, groups=groups):
    ...:     print train, test
    ...:     
[2 3 4 5 6] [0 1]
[0 1 4 5 6] [2 3]
[0 1 2 3] [4 5 6]

11.`LeavePGroupsOut（不重要）`

这个没啥可说的，跟上面那个一样，只是一个是单组，一个是多组

from sklearn.model_selection import LeavePGroupsOut

X = np.arange(6)

y = [1, 1, 1, 2, 2, 2]

groups = [1, 1, 2, 2, 3, 3]

lpgo = LeavePGroupsOut(n_groups=2)

for train, test in lpgo.split(X, y, groups=groups):
    print train, test

[4 5] [0 1 2 3]
[2 3] [0 1 4 5]
[0 1] [2 3 4 5]

12.`GroupShuffleSplit（不重要）`

这个是有放回抽样

In [75]: from sklearn.model_selection import GroupShuffleSplit

In [76]: X = [.1, .2, 2.2, 2.4, 2.3, 4.55, 5.8, .001]

In [77]: y = ['a', 'b','b', 'b', 'c','c', 'c', 'a']

In [78]: groups = [1,1,2,2,3,3,4,4]

In [79]: gss = GroupShuffleSplit(n_splits=4, test_size=.5, random_state=0)

In [80]: for train, test in gss.split(X, y, groups=groups):
    ...:     print train, test
    ...:     
[0 1 2 3] [4 5 6 7]
[2 3 6 7] [0 1 4 5]
[2 3 4 5] [0 1 6 7]
[4 5 6 7] [0 1 2 3]

13.`TimeSeriesSplit`

针对时间序列的处理，防止未来数据的使用，分割时是将数据进行从前到后切割（这个说法其实不太恰当，因为切割是延续性的。。）

In [81]: from sklearn.model_selection import TimeSeriesSplit

In [82]: X = np.array([[1,2],[3,4],[1,2],[3,4],[1,2],[3,4]])

In [83]: tscv = TimeSeriesSplit(n_splits=3)

In [84]: for train, test in tscv.split(X):
    ...:     print train, test
    ...:     
[0 1 2] [3]
[0 1 2 3] [4]
[0 1 2 3 4] [5]

14.参数选择

from sklearn.datasets import load_iris
from sklearn import svm
from sklearn.model_selection import train_test_split
from sklearn.model_selection import cross_val_score
from sklearn.neighbors import KNeighborsClassifier
from sklearn.model_selection import StratifiedKFold

kf = StratifiedKFold(n_splits=3)
iris = load_iris()
print(iris.keys())
data = iris.data
# clf = svm.SVC(kernel= 'rbf')
clf = KNeighborsClassifier(n_neighbors=k)
scores = []
for i in range(1,20):
    cv_score = cross_val_score(KNeighborsClassifier(n_neighbors=i), iris.data, iris.target,cv=kf.split(iris.data, iris.target),scoring='accuracy')
    scores.append(np.mean(cv_score))
print(np.argmax(scores))
print(scores)
import matplotlib.pyplot as plt
plt.plot(range(1,20), scores)
plt.xlabel("k")
plt.ylabel("score")
plt.show()