手写kNN算法的实现-用余弦相似度来度量距离

设a为预测点，b为其中一个样本点，在向量空间里，它们的形成的夹角为θ，那么θ越小（cosθ的值越接近1），就说明a点越接近b点。所以我们可以通过考察余弦相似度来预测a点的类型。

from collections import Counter
import numpy as np

class MyKnn:
    def __init__(self,neighbors):
        self.k = neighbors
    
    def fit(self,X,Y):
        self.X = np.array(X)
        self.Y = np.array(Y)
        if self.X.ndim != 2 or self.Y.ndim != 1:
            raise Exception("dimensions are wrong!")
        
        if self.X.shape[0] != self.Y.shape[0]:
            raise Exception("input labels are not correct!")
    
    def predict(self,X_pre):
        
        pre = np.array(X_pre)
        if self.X.ndim != pre.ndim:
            raise Exception("input dimensions are wrong!")
        rs = []
        for p in pre:
            temp = []
            for a in self.X:
                cos = (p @ a)/np.linalg.norm(p)/np.linalg.norm(a)
                temp.append(cos)
            temp = np.array(temp)
            indices = np.argsort(temp)[:-self.k-1:-1]
            ss = np.take(self.Y,indices)
            found = Counter(ss).most_common(1)[0][0]
            print(found)
            rs.append(found)
        return np.array(rs)
        

测试：

# 用鸢尾花数据集来验证我们上面写的算法
from sklearn.datasets import load_iris
# 使用train_test_split对数据集进行拆分，一部分用于训练，一部分用于测试验证
from sklearn.model_selection import train_test_split
# 1.生成一个kNN模型
myknn = MyKnn(5)
# 2.准备数据集：特征集X_train和标签集y_train
X_train,y_train = load_iris(return_X_y=True)
# 留出30%的数据集用于验证测试
X_train,X_test,y_train,y_test = train_test_split(X_train,y_train,test_size=0.3)
# 3.训练模型
myknn.fit(X_train,y_train)
# 4.预测，acc就是预测结果
acc = myknn.predict(X_test)
# 计算准确率
(acc == y_test).mean()

其实如果余弦相似度来进行分类，那么根据文章最开头讲到的，其实取余弦值最大的点作为预测类型也可以：

import numpy as np

class MyClassicfication:
    
    def fit(self,X,Y):
        self.X = np.array(X)
        self.Y = np.array(Y)
        if self.X.ndim != 2 or self.Y.ndim != 1:
            raise Exception("dimensions are wrong!")
        
        if self.X.shape[0] != self.Y.shape[0]:
            raise Exception("input labels are not correct!")
    
    def predict(self,X_pre):
        
        pre = np.array(X_pre)
        if self.X.ndim != pre.ndim:
            raise Exception("input dimensions are wrong!")
        rs = []
        for p in pre:
            temp = []
            for a in self.X:
                cos = (p @ a)/np.linalg.norm(p)/np.linalg.norm(a)
                temp.append(cos)
            temp = np.array(temp)
            index = np.argsort(temp)[-1]
            found = np.take(self.Y,index)
            rs.append(found)
        return np.array(rs)
        

测试：

# 用鸢尾花数据集来验证我们上面写的算法
from sklearn.datasets import load_iris
# 使用train_test_split对数据集进行拆分，一部分用于训练，一部分用于测试验证
from sklearn.model_selection import train_test_split
# 1.生成一个kNN模型
myCla = MyClassicfication
# 2.准备数据集：特征集X_train和标签集y_train
X_train,y_train = load_iris(return_X_y=True)
# 留出30%的数据集用于验证测试
X_train,X_test,y_train,y_test = train_test_split(X_train,y_train,test_size=0.3)
# 3.训练模型
myCla.fit(X_train,y_train)
# 4.预测，acc就是预测结果
acc = myCla.predict(X_test)
# 计算准确率
(acc == y_test).mean()

经测试，上面两种方式的准确率是差不多的。