机器学习---常见的距离公式（欧氏距离、曼哈顿距离、标准化欧式距离、余弦距离、杰卡德距离、马氏距离、切比雪夫距离、闵可夫斯基距离、K-L散度）

 from scipy.spatial import distance

    
 a = (1, 2, 3)
    
 b = (4, 5, 6)
    
  
    
 print(distance.euclidean(a, b))
    
    
    
    

 import numpy as np

    
 from scipy.spatial import distance
    
  
    
 A = np.array([7,8,9])
    
 B = np.array([4,5,6])
    
  
    
 # 方式一：直接构造公式计算
    
 dist1 = np.sum(np.abs(A-B))
    
  
    
 # 方式二：内置线性代数函数计算
    
 dist2 = np.linalg.norm(A-B,ord=1)  #ord为范数类型，取值1（一范数）,2（二范数）,np.inf（无穷范数），默认2。
    
  
    
 # 方式三：scipy库计算
    
 dist3 = distance.cityblock(A,B)
    
    
    
    

 from scipy.spatial.distance import pdist

    
 dist2 = pdist(Vec,’seuclidean’)
    
    
    
    

 import numpy as np

    
 from scipy.spatial import distance
    
  
    
 A = np.array([7,8,9])
    
 B = np.array([4,5,6])
    
  
    
 # 方式一：直接构造公式计算
    
 dist1 = np.sum(A*B)/(np.sqrt(np.sum(A**2))*np.sqrt(np.sum(B**2)))
    
  
    
 # 方式二：scipy库计算
    
 dist2 = 1-distance.cosine(A,B)
    
    
    
    

 import numpy as np

    
 from scipy.spatial import distance
    
  
    
 A = np.array([1,2,3])
    
 B = np.array([4,5,6])
    
  
    
 # scipy库计算
    
 dist1 = distance.hamming(A,B)
    
    
    
    

 # 方案一

    
 # 根据公式求解
    
 up = np.double(np.bitwise_and((vec1!=vec2),np.bitwise_or(vec1!=0,vec2!=0)).sum())
    
 down = np.double(np.bitwise_or(vec1!=0,vec2!=0).sum())
    
 dist1=(up/down)
    
 print("杰卡德距离测试结果是:"+str(dist1))
    
 # 方案二
    
 # 根据scipy库求解
    
 from scipy.spatial.distance import pdist
    
 Vec = np.vstack([vec1,vec2])
    
 dist2 = pdist(Vec,'jaccard')
    
 print("杰卡德距离测试结果是:"+str(dist2))
    
    
    
    

 import numpy as np

    
 from scipy.spatial.distance import pdist
    
 a=np.random.random(10)
    
 b=np.random.random(10)
    
 #马氏距离要求样本数要大于维数，否则无法求协方差矩阵
    
 X=np.vstack([a,b])
    
 XT=X.T  #此处进行转置，表示10个样本，每个样本2维
    
  
    
 pdist(XT,'mahalanobis')
    
    
    
    

 # 根据scipy库求解

    
 from scipy.spatial.distance import pdist
    
 Vec = np.vstack([vec1,vec2])
    
 dist2 = pdist(Vec,'chebyshev')
    
 print('切比雪夫距离测试结果是：' + str(dist2))
    
    
    
    

 # 根据scipy库求解

    
 from scipy.spatial.distance import pdist
    
 Vec = np.vstack([vec1,vec2])
    
 dist2 = pdist(Vec,'cityblock',p=1)
    
 print('当P=1时就是曼哈顿距离，测试结果是：' + str(dist2))
    
  
    
 # 根据公式求解，p=1
    
 from numpy import *
    
 dist3 = sum(abs(vec1-vec2))# abs()绝对值
    
 print('当p=1时就是曼哈顿距离，测试结果是：' + str(dist3))
    
    
    
    

 # 利用scipy API进行计算

    
  
    
 KL = scipy.stats.entropy(x, y)
    
 print(KL)
    
  
    
 # 用公式编程就用px和py
    
  
    
 KL = 0.0
    
 for i in range(10):
    
     KL += px[i] * np.log(px[i] / py[i])
    
 print(KL)