机器学习-kNN-寻找最好的超参数

一 、超参数和模型参数

• 超参数：在算法运行前需要决定的参数
• 模型参数：算法运行过程中学习的参数

- kNN算法没有模型参数
- kNN算法中的k是典型的超参数

　　寻找好的超参数

• 领域知识
• 经验数值
• 实验搜索

二、通过sklearn中的数据集进行测试

　　　　

import numpy as np
from sklearn import datasets
# 装载sklearn中的手写数字数据集
digits = datasets.load_digits()
x = digits.data
y = digits.target
from sklearn.model_selection import train_test_split
from sklearn.neighbors import KNeighborsClassifier
# 将数据分成训练数据集合测试数据集，
# 测试数据集占全部数据的20%，
# 设置随机种子为666
x_train,x_test,y_train,y_test = train_test_split(x,y,test_size=0.2,random_state = 666)
# 设置k为3
knn_clf = KNeighborsClassifier(n_neighbors=3)
# 训练数据模型
knn_clf.fit(x_train,y_train)
# 通过测试数据计算预测结果准确率，并打印出来
print(knn_clf.score(x_test,y_test))

输出结果：0.9888888888888889

三、考虑距离?不考虑距离？

kNN存在一种平票的情况，就是距离最近的k个点中相应类的数量相等，这是需要考虑距离了。

或者可以使用加权距离来计算

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
from sklearn.neighbors import KNeighborsClassifier
x_train,x_test,y_train,y_test = train_test_split(x,y,test_size=0.2,random_state = 666)
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_score = score
            best_k = k
print('best_method = %s'%best_method)
print('best_k = %d'%best_k)
print('best_score = %f'%best_score)

运行结果：

best_method = uniform

best_k = 4

best_score = 0.991667

四、搜索 明可夫斯基距离 相应的p

欧拉距离，曼哈顿距离，明可夫斯基距离

几种距离的定义

由上可以获取一个超参数p。

%%time
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
from sklearn.neighbors import KNeighborsClassifier
x_train,x_test,y_train,y_test = train_test_split(x,y,test_size=0.2,random_state = 666)
best_p = ''
best_score = 0.0
best_k = -1
# for method in ['uniform','distance']:
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_score = score
            best_k = k
print('best_p = %s'%best_p)
print('best_k = %d'%best_k)
print('best_score = %f'%best_score)

运行结果：

best_p = 2

best_k = 3

best_score = 0.988889

Wall time: 47.5 s

四、网格搜索kNN最好的参数 

sklearn中通过网格搜索可以更快更全面的搜索更好的参数。

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
from sklearn.neighbors import KNeighborsClassifier
x_train,x_test,y_train,y_test = train_test_split(x,y,test_size=0.2,random_state = 666)
knn_clf = KNeighborsClassifier(n_neighbors=4,weights='uniform')
knn_clf.fit(x_train,y_train)
knn_clf.score(x_test,y_test)
param_grid = [
    {
        'weights':['uniform'],
        'n_neighbors':[i for i in range(1,11)]
    },
    {
        'weights':['distance'],
        'n_neighbors':[i for i in range(1,11)],
        'p':[i for i in range(1,6)]
    }
]
knn_clf = KNeighborsClassifier()
from sklearn.model_selection import GridSearchCV
grid_search = GridSearchCV(knn_clf,param_grid)
# 需要运行2-5分钟，保持耐心
grid_search.fit(x_train,y_train)

grid_search.best_estimator_ # 最佳的参数对象
grid_search.best_score_   # 准确率
grid_search.best_params_  # 最佳的参数
#为计算机分配资源,输出搜索信息，n_jobs：分配计算机核数，-1位有多少用多少，verbose：为打印信息的等级，值越大，信息越多
grid_search = GridSearchCV(knn_clf,param_grid,n_jobs=-1,verbose=10) 
grid_search.fit(x_train,y_train)

五、更多的距离定义

• 向量空间余弦相似度 Cosine Similarity
• 调整余弦相似度 Adjusted Cosine Similarity
• 皮尔森相关系数 Pearson Correlation Coefficient
• Jaccard相似系数 Jaccard Coefficient