kNN-k近邻算法

• 思想季度简单
• 应用数学只是少
• 效果好
• 可以解释机器学习算法使用过程中的很多细节问题
• 更完整的刻画机器学习应用的流程

假如k=3，就是寻找与该样本最近的3个样本来投票，票数多的样本就认为该待测样本与多数多的样本相似

import numpy as np
import matplotlib.pyplot as plt

raw_data_X = [[3.393533211,2.331273381],
             [3.110073483,1.781539368],
             [1.343808831,3.368360954],
             [3.582294042,4.679179110],
             [2.280362439,2.866990263],
             [7.423436942,4.696522875],
             [5.745051997,3.533989803],
             [9.172168622,2.511101045],
             [7.792783481,3.424088941],
             [7.939820817,0.791637231]]
raw_data_y = [0,0,0,0,0,1,1,1,1,1]

X_train = np.array(raw_data_X)
y_train = np.array(raw_data_y)

plt.scatter(X_train[y_train==0,0],X_train[y_train==0,1],color="g")
plt.scatter(X_train[y_train==1,0],X_train[y_train==1,1],color="r")
plt.show()

x = np.array([8.093607318,3.365731514])

plt.scatter(X_train[y_train==0,0],X_train[y_train==0,1],color="g")
plt.scatter(X_train[y_train==1,0],X_train[y_train==1,1],color="r")
plt.scatter(x[0],x[1],color="b")
plt.show()

kNN过程

from math import sqrt
distance = []
for x_train in X_train:
    d = sqrt(np.sum((x_train -x )**2))
    distance.append(d)

distance

[4.812566907609877,
 5.2292709090309994,
 6.749798999160064,
 4.6986266144110695,
 5.83460014556857,
 1.4900114024329525,
 2.354574897431513,
 1.3761132675144652,
 0.3064319992975,
 2.5786840957478887]

# 求所有点与待测点之间的距离
distances = [sqrt(np.sum((x_train - x)**2)) for x_train in X_train]

# 将距离排序并获得相应的索引
np.argsort(distances)

array([8, 7, 5, 6, 9, 3, 0, 1, 4, 2])

nearest = np.argsort(distances)

k = 6

# 取前六个对应的y值
topK_y = [y_train[i] for i in nearest[:k]]

topK_y

[1, 1, 1, 1, 1, 0]

from collections import Counter
Counter(topK_y)

Counter({0: 1, 1: 5})

votes = Counter(topK_y)

predict_y = votes.most_common(1)[0][0]
predict_y

1

使用scikit-learn中的kNN

from sklearn.neighbors import KNeighborsClassifier

kNN_clssifier = KNeighborsClassifier(n_neighbors=6)

kNN_clssifier.fit(X_train,y_train)

KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
           metric_params=None, n_jobs=1, n_neighbors=6, p=2,
           weights='uniform')

kNN_clssifier.predict(x.reshape(1,-1))

array([1])