摘要：本文使用K近鄰模型進行回歸，分類；

00 構造數據

# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
from sklearn import neighbors
x=np.pi*2*np.random.rand(100)
y=np.sin(x)
y[::5]+=(np.random.rand(20)-0.5)*2
dex1=np.random.choice(100,75,replace=False)
dex2=[]
for i in range(100):
    if i not in dex1:
        dex2.append(i)
train_x=x[dex1].reshape(-1,1)
train_y=y[dex1].reshape(-1,1)
test_x=x[dex2].reshape(-1,1)
test_y=y[dex2].reshape(-1,1)

01 KNN回歸

regre=neighbors.KNeighborsRegressor()
regre.fit(train_x,train_y)
regre.score(test_x,test_y)
Out[112]: 0.9719249717643359

regre.kneighbors(test_x,n_neighbors=5,return_distance=True)

研究參數weights，n_neighbors，p對模型預測性能的影響：

fig=plt.figure()
weights=['uniform','distance']
ks=np.linspace(1,len(train_y),50,dtype='int')
for weight in weights:
    scor=[]
    for k in ks:
        regre=neighbors.KNeighborsRegressor(weights=weight,n_neighbors=k)
        regre.fit(train_x,train_y)
        scor.append(regre.score(test_x,test_y))
    plt.plot(ks,scor,label=weight)
    plt.legend()

fig=plt.figure()
ps=[1,2,10]
ks=np.linspace(1,len(train_y),50,dtype='int')
for p in ps:
    scor=[]
    for k in ks:
        regre=neighbors.KNeighborsRegressor(p=p,n_neighbors=k)
        regre.fit(train_x,train_y)
        scor.append(regre.score(test_x,test_y))
    plt.plot(ks,scor,label='p='+str(p))
    plt.legend(loc='best')

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02 獲取sklearn中數據

import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets,neighbors
digits=datasets.load_digits()
dex1=np.random.choice(1797,1500,replace=False)
dex2=[]
for i in range(1797):
    if i not in dex1:
        dex2.append(i)
train_x=digits.data[dex1]
train_y=digits.target[dex1]
test_x=digits.data[dex2]
test_y=digits.target[dex2]

03 KNN分類

classi=neighbors.KNeighborsClassifier()
classi.fit(train_x,train_y)
classi.score(test_x,test_y)
Out[120]: 0.9966329966329966

研究參數weights，n_neighbors，p對模型預測性能的影響：

fig=plt.figure()
weights=['uniform','distance']
ks=np.linspace(1,len(train_y),100,dtype='int')
for weight in weights:
    scor=[]
    for k in ks:
        classi=neighbors.KNeighborsClassifier(weights=weight,n_neighbors=k)
        classi.fit(train_x,train_y)
        scor.append(classi.score(test_x,test_y))
    plt.plot(ks,scor,label=weight)
    plt.legend(loc='best')

fig=plt.figure()
ps=[1,2,10]
ks=np.linspace(1,len(train_y),100,dtype='int')
for p in ps:
    scor=[]
    for k in ks:
        classi=neighbors.KNeighborsClassifier(p=p,n_neighbors=k)
        classi.fit(train_x,train_y)
        scor.append(classi.score(test_x,test_y))
    plt.plot(ks,scor,label='p='+str(p))
    plt.legend(loc='best')

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04 總結

01 K近鄰模型的重要參數，K值，距離，計權，即上文涉及的；

02 K近鄰模型既可以用于分類（多數表決），也可以用于回歸（均值）；

03 K近鄰模型是典型的 lazy-learning；