If x1,x2∈Rn, then:

闵可夫斯基距离 Minkowski Distance

欧氏距离 Enclidean Distance

L2 norm

标准化欧式距离/加权欧式距离 Weighted Euclidean Distance

where Sk is the standard deviation.

from numpy import *vectormat=mat([[1,2,3],[4,5,6]])v12=vectormat[0]-vectormat[1]varmat=std(vectormat.T, axis=0)normmat=(vectormat-mean(vectormat))/varmat.Tnormv12=normmat[0]-normmat[1]print(sqrt(normv12*normv12.T))

曼哈顿距离 Manhattan Distance

L1 norm

切比雪夫距离 Chebyshev Distance

L∞ norm

from numpy import *vector1=mat([1,2,3])vector2=mat([4,5,7])print(abs(vector1-vector2).max())

夹角余弦 Cosine

汉明距离 Hamming Distance

In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other. (referred from Wikipedia)

from numpy import *matV=mat([[1,1,0,1,0,1,0,0,1],[0,1,1,0,0,0,1,1,1]])smstr=nonzero(matV [0]-matV[1])print(shape(smstr[0])[0])

杰卡德相似系数 Jaccard Similarity Coefficient

Given two sets, A and B, the Jaccard similarity coefficient is defined as

杰卡德距离 Jaccard Distance

from numpy import *import scipy.spatial.distance as distmatV=mat([[1,1,0,1,0,1,0,0,1],[0,1,1,0,0,0,1,1,1]])print(dist.pdist(matV,'jaccard'))

马氏距离 Mahalanobis Distance

Given m sample vectors X1,…,Xm whose mean value is μ and covariance matrix is S, then the Mahalanobis distance of sample vector X and μ is defined as

that of sample vector Xi and Xj is