导入数字识别的数据集
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from sklearn import datasets
digits=datasets.load_digits()
digits.keys()
dict_keys(['data', 'target', 'target_names', 'images', 'DESCR'])
print(digits.DESCR)
.. _digits_dataset:
Optical recognition of handwritten digits dataset
--------------------------------------------------
**Data Set Characteristics:**
:Number of Instances: 5620
:Number of Attributes: 64
:Attribute Information: 8x8 image of integer pixels in the range 0..16.
:Missing Attribute Values: None
:Creator: E. Alpaydin (alpaydin '@' boun.edu.tr)
:Date: July; 1998
This is a copy of the test set of the UCI ML hand-written digits datasets
https://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits
The data set contains images of hand-written digits: 10 classes where
each class refers to a digit.
Preprocessing programs made available by NIST were used to extract
normalized bitmaps of handwritten digits from a preprinted form. From a
total of 43 people, 30 contributed to the training set and different 13
to the test set. 32x32 bitmaps are divided into nonoverlapping blocks of
4x4 and the number of on pixels are counted in each block. This generates
an input matrix of 8x8 where each element is an integer in the range
0..16. This reduces dimensionality and gives invariance to small
distortions.
For info on NIST preprocessing routines, see M. D. Garris, J. L. Blue, G.
T. Candela, D. L. Dimmick, J. Geist, P. J. Grother, S. A. Janet, and C.
L. Wilson, NIST Form-Based Handprint Recognition System, NISTIR 5469,
1994.
.. topic:: References
- C. Kaynak (1995) Methods of Combining Multiple Classifiers and Their
Applications to Handwritten Digit Recognition, MSc Thesis, Institute of
Graduate Studies in Science and Engineering, Bogazici University.
- E. Alpaydin, C. Kaynak (1998) Cascading Classifiers, Kybernetika.
- Ken Tang and Ponnuthurai N. Suganthan and Xi Yao and A. Kai Qin.
Linear dimensionalityreduction using relevance weighted LDA. School of
Electrical and Electronic Engineering Nanyang Technological University.
2005.
- Claudio Gentile. A New Approximate Maximal Margin Classification
Algorithm. NIPS. 2000.
X=digits.data
X.shape
(1797, 64)
y=digits.target
y.shape
(1797,)
y[:100]
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1,
2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 5, 5, 6, 5, 0, 9, 8, 9, 8, 4, 1, 7,
7, 3, 5, 1, 0, 0, 2, 2, 7, 8, 2, 0, 1, 2, 6, 3, 3, 7, 3, 3, 4, 6,
6, 6, 4, 9, 1, 5, 0, 9, 5, 2, 8, 2, 0, 0, 1, 7, 6, 3, 2, 1, 7, 4,
6, 3, 1, 3, 9, 1, 7, 6, 8, 4, 3, 1])
取前10行元素
X[:10]
array([[ 0., 0., 5., 13., 9., 1., 0., 0., 0., 0., 13., 15., 10.,
15., 5., 0., 0., 3., 15., 2., 0., 11., 8., 0., 0., 4.,
12., 0., 0., 8., 8., 0., 0., 5., 8., 0., 0., 9., 8.,
0., 0., 4., 11., 0., 1., 12., 7., 0., 0., 2., 14., 5.,
10., 12., 0., 0., 0., 0., 6., 13., 10., 0., 0., 0.],
[ 0., 0., 0., 12., 13., 5., 0., 0., 0., 0., 0., 11., 16.,
9., 0., 0., 0., 0., 3., 15., 16., 6., 0., 0., 0., 7.,
15., 16., 16., 2., 0., 0., 0., 0., 1., 16., 16., 3., 0.,
0., 0., 0., 1., 16., 16., 6., 0., 0., 0., 0., 1., 16.,
16., 6., 0., 0., 0., 0., 0., 11., 16., 10., 0., 0.],
[ 0., 0., 0., 4., 15., 12., 0., 0., 0., 0., 3., 16., 15.,
14., 0., 0., 0., 0., 8., 13., 8., 16., 0., 0., 0., 0.,
1., 6., 15., 11., 0., 0., 0., 1., 8., 13., 15., 1., 0.,
0., 0., 9., 16., 16., 5., 0., 0., 0., 0., 3., 13., 16.,
16., 11., 5., 0., 0., 0., 0., 3., 11., 16., 9., 0.],
[ 0., 0., 7., 15., 13., 1., 0., 0., 0., 8., 13., 6., 15.,
4., 0., 0., 0., 2., 1., 13., 13., 0., 0., 0., 0., 0.,
2., 15., 11., 1., 0., 0., 0., 0., 0., 1., 12., 12., 1.,
0., 0., 0., 0., 0., 1., 10., 8., 0., 0., 0., 8., 4.,
5., 14., 9., 0., 0., 0., 7., 13., 13., 9., 0., 0.],
[ 0., 0., 0., 1., 11., 0., 0., 0., 0., 0., 0., 7., 8.,
0., 0., 0., 0., 0., 1., 13., 6., 2., 2., 0., 0., 0.,
7., 15., 0., 9., 8., 0., 0., 5., 16., 10., 0., 16., 6.,
0., 0., 4., 15., 16., 13., 16., 1., 0., 0., 0., 0., 3.,
15., 10., 0., 0., 0., 0., 0., 2., 16., 4., 0., 0.],
[ 0., 0., 12., 10., 0., 0., 0., 0., 0., 0., 14., 16., 16.,
14., 0., 0., 0., 0., 13., 16., 15., 10., 1., 0., 0., 0.,
11., 16., 16., 7., 0., 0., 0., 0., 0., 4., 7., 16., 7.,
0., 0., 0., 0., 0., 4., 16., 9., 0., 0., 0., 5., 4.,
12., 16., 4., 0., 0., 0., 9., 16., 16., 10., 0., 0.],
[ 0., 0., 0., 12., 13., 0., 0., 0., 0., 0., 5., 16., 8.,
0., 0., 0., 0., 0., 13., 16., 3., 0., 0., 0., 0., 0.,
14., 13., 0., 0., 0., 0., 0., 0., 15., 12., 7., 2., 0.,
0., 0., 0., 13., 16., 13., 16., 3., 0., 0., 0., 7., 16.,
11., 15., 8., 0., 0., 0., 1., 9., 15., 11., 3., 0.],
[ 0., 0., 7., 8., 13., 16., 15., 1., 0., 0., 7., 7., 4.,
11., 12., 0., 0., 0., 0., 0., 8., 13., 1., 0., 0., 4.,
8., 8., 15., 15., 6., 0., 0., 2., 11., 15., 15., 4., 0.,
0., 0., 0., 0., 16., 5., 0., 0., 0., 0., 0., 9., 15.,
1., 0., 0., 0., 0., 0., 13., 5., 0., 0., 0., 0.],
[ 0., 0., 9., 14., 8., 1., 0., 0., 0., 0., 12., 14., 14.,
12., 0., 0., 0., 0., 9., 10., 0., 15., 4., 0., 0., 0.,
3., 16., 12., 14., 2., 0., 0., 0., 4., 16., 16., 2., 0.,
0., 0., 3., 16., 8., 10., 13., 2., 0., 0., 1., 15., 1.,
3., 16., 8., 0., 0., 0., 11., 16., 15., 11., 1., 0.],
[ 0., 0., 11., 12., 0., 0., 0., 0., 0., 2., 16., 16., 16.,
13., 0., 0., 0., 3., 16., 12., 10., 14., 0., 0., 0., 1.,
16., 1., 12., 15., 0., 0., 0., 0., 13., 16., 9., 15., 2.,
0., 0., 0., 0., 3., 0., 9., 11., 0., 0., 0., 0., 0.,
9., 15., 4., 0., 0., 0., 9., 12., 13., 3., 0., 0.]])
取其中某一行
some_digit=X[666]
y[666]
0
用图像显示
some_digit_image=some_digit.reshape(8,8)
plt.imshow(some_digit_image,cmap=matplotlib.cm.binary)
plt.show()
from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.2,random_state=666)
from sklearn.neighbors import KNeighborsClassifier
kNNClassifier=KNeighborsClassifier(n_neighbors=3)
kNNClassifier.fit(X_train,y_train)
y_predict=kNNClassifier.predict(X_test)
y_predict
array([8, 1, 3, 4, 4, 0, 7, 0, 8, 0, 4, 6, 1, 1, 2, 0, 1, 6, 7, 3, 3, 6,
3, 2, 3, 4, 0, 2, 0, 3, 0, 8, 7, 2, 3, 5, 1, 3, 1, 5, 8, 6, 2, 6,
3, 1, 3, 0, 0, 4, 9, 9, 2, 8, 7, 0, 5, 4, 0, 9, 5, 5, 5, 7, 4, 2,
8, 8, 7, 1, 4, 3, 0, 2, 7, 2, 1, 2, 4, 0, 9, 0, 6, 6, 2, 0, 0, 5,
4, 4, 3, 1, 3, 8, 6, 4, 4, 7, 5, 6, 8, 4, 8, 4, 6, 9, 7, 7, 0, 8,
8, 3, 9, 7, 1, 8, 4, 2, 7, 0, 0, 4, 9, 6, 7, 3, 4, 6, 4, 8, 4, 7,
2, 6, 9, 5, 8, 7, 2, 5, 5, 9, 7, 9, 3, 1, 9, 4, 4, 1, 5, 1, 6, 4,
4, 8, 1, 6, 2, 5, 2, 1, 4, 4, 3, 9, 4, 0, 6, 0, 8, 3, 8, 7, 3, 0,
3, 0, 5, 9, 2, 7, 1, 8, 1, 4, 3, 3, 7, 8, 2, 7, 2, 2, 8, 0, 5, 7,
6, 7, 3, 4, 7, 1, 7, 0, 9, 2, 8, 9, 3, 8, 9, 1, 1, 1, 9, 8, 8, 0,
3, 7, 3, 3, 4, 8, 2, 1, 8, 6, 0, 1, 7, 7, 5, 8, 3, 8, 7, 6, 8, 4,
2, 6, 2, 3, 7, 4, 9, 3, 5, 0, 6, 3, 8, 3, 3, 1, 4, 5, 3, 2, 5, 6,
9, 6, 9, 5, 5, 3, 6, 5, 9, 3, 7, 7, 0, 2, 4, 9, 9, 9, 2, 5, 6, 1,
9, 6, 9, 7, 7, 4, 5, 0, 0, 5, 3, 8, 4, 4, 3, 2, 5, 3, 2, 2, 3, 0,
9, 8, 2, 1, 4, 0, 6, 2, 8, 0, 6, 4, 9, 9, 8, 3, 9, 8, 6, 3, 2, 7,
9, 4, 2, 7, 5, 1, 1, 6, 1, 0, 4, 9, 2, 9, 0, 3, 3, 0, 7, 4, 8, 5,
9, 5, 9, 5, 0, 7, 9, 8])
y_test
array([8, 1, 3, 4, 4, 0, 7, 0, 8, 0, 4, 6, 1, 1, 2, 0, 1, 6, 7, 3, 3, 6,
3, 2, 3, 4, 0, 2, 0, 3, 0, 8, 7, 2, 3, 5, 1, 3, 1, 5, 8, 6, 2, 6,
3, 1, 3, 0, 0, 4, 9, 9, 2, 8, 7, 0, 5, 4, 0, 9, 5, 5, 8, 3, 4, 2,
8, 8, 7, 1, 4, 3, 0, 2, 7, 2, 1, 2, 4, 0, 9, 0, 6, 6, 2, 0, 0, 5,
4, 4, 9, 1, 3, 8, 6, 4, 4, 7, 5, 6, 8, 4, 8, 4, 6, 9, 7, 7, 0, 8,
8, 3, 9, 7, 1, 8, 4, 2, 7, 0, 0, 4, 9, 6, 7, 3, 4, 6, 4, 8, 4, 7,
2, 6, 9, 5, 8, 7, 2, 5, 5, 9, 7, 9, 3, 1, 9, 4, 4, 1, 5, 1, 6, 4,
4, 8, 1, 6, 2, 5, 2, 1, 4, 4, 3, 9, 4, 0, 6, 0, 8, 3, 8, 7, 3, 0,
3, 0, 5, 9, 2, 7, 1, 8, 1, 4, 3, 3, 7, 8, 2, 7, 2, 2, 8, 0, 5, 7,
6, 7, 3, 4, 7, 1, 7, 0, 9, 2, 8, 9, 3, 8, 9, 1, 1, 1, 9, 8, 8, 0,
3, 7, 3, 3, 4, 8, 2, 1, 8, 6, 0, 1, 7, 7, 5, 8, 3, 8, 7, 6, 8, 4,
2, 6, 2, 3, 7, 4, 9, 3, 5, 0, 6, 3, 8, 3, 3, 1, 4, 5, 3, 2, 5, 6,
9, 6, 9, 5, 5, 3, 6, 5, 9, 3, 7, 7, 0, 2, 4, 9, 9, 9, 2, 5, 6, 1,
9, 6, 9, 7, 7, 4, 5, 0, 0, 5, 3, 8, 4, 4, 3, 2, 5, 3, 2, 2, 3, 0,
9, 8, 2, 1, 4, 0, 6, 2, 8, 0, 6, 4, 9, 9, 8, 3, 9, 8, 6, 3, 2, 7,
9, 4, 2, 7, 5, 1, 1, 6, 1, 0, 4, 5, 2, 9, 0, 3, 3, 0, 7, 4, 8, 5,
9, 5, 9, 5, 0, 7, 9, 8])
计算准确率
sum(y_test==y_predict)/len(y_test)
0.9888888888888889
调用sklearn中的accuracy_score
from sklearn.metrics import accuracy_score
accuracy_score(y_test,y_predict)
0.9888888888888889
不预测y_predict,只关心分类的准确率
kNNClassifier.score(X_test,y_test)
0.9888888888888889
超参数
1.寻找最好的k
import numpy as np
from sklearn import datasets
digits=datasets.load_digits()
X =digits.data
y =digits.target
from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.2,random_state=666)
from sklearn.neighbors import KNeighborsClassifier
knn_clf=KNeighborsClassifier(n_neighbors=3)
knn_clf.fit(X_train,y_train)
knn_clf.score(X_test,y_test)
0.9888888888888889
best_score=0.0
best_k= -1
for k in range(1,11):
knn_clf=KNeighborsClassifier(n_neighbors=k)
knn_clf.fit(X_train,y_train)
score = knn_clf.score(X_test,y_test)
if score > best_score:
best_k = k
best_score = score
print("best_k=",best_k)
print("best_score=",best_score)
best_k= 4
best_score= 0.9916666666666667
考虑距离？不考虑距离？
P也是一个超参数
best_method=""
best_score=0.0
best_k= -1
for method in ["uniform","distance"]:
for k in range(1,11):
knn_clf=KNeighborsClassifier(n_neighbors=k,weights=method)
knn_clf.fit(X_train,y_train)
score = knn_clf.score(X_test,y_test)
if score > best_score:
best_method=method
best_k = k
best_score = score
print("best_method=",best_method)
print("best_k=",best_k)
print("best_score=",best_score)
best_method= uniform
best_k= 4
best_score= 0.9916666666666667
搜索明可夫斯基距离相应的P
%%time
best_p=-1
best_score=0.0
best_k= -1
for k in range(1,11):
for p in range(1,6):
knn_clf=KNeighborsClassifier(n_neighbors=k,weights="distance",p=p)
knn_clf.fit(X_train,y_train)
score = knn_clf.score(X_test,y_test)
if score > best_score:
best_p=p
best_k = k
best_score = score
print("best_p=",best_p)
print("best_k=",best_k)
print("best_score=",best_score)
best_p= 2
best_k= 3
best_score= 0.9888888888888889
Wall time: 37.9 s