在做很多研究问题时常常需要估算不同样本之间的相似性度量(Similarity Measurement)，这时通常采用的方法就是计算样本间的“距离”(Distance)。采用什么样的方法计算距离是很讲究，甚至关系到分类的正确与否。

1、欧式距离

#1) given two data points, calculate the euclidean distance between them

defget_distance(data1, data2):

points=zip(data1, data2)

diffs_squared_distance= [pow(a - b, 2) for (a, b) inpoints]return math.sqrt(sum(diffs_squared_distance))

2、余弦相似度

defcosin_distance(vector1, vector2):

dot_product= 0.0normA= 0.0normB= 0.0

for a, b inzip(vector1, vector2):

dot_product+= a *b

normA+= a ** 2normB+= b ** 2

if normA == 0.0 or normB == 0.0:returnNoneelse:return dot_product / ((normA * normB) ** 0.5)

3、用Numpy进行余弦相似度计算

sim =user_item_matric.dot(user_item_matric.T)

norms=np.array([np.sqrt(np.diagonal(sim))])

user_similarity=(sim / norms / norms.T)

4、用scikit cosine_similarity计算相似度

from sklearn.metrics.pairwise importcosine_similarity

user_similarity=cosine_similarity(user_tag_matric)

5、用scikit pairwise_distances计算相似度

from sklearn.metrics.pairwise importpairwise_distances

user_similarity= pairwise_distances(user_tag_matric, metric='cosine')

需要注意的一点是，用pairwise_distances计算的Cosine distance是1-（cosine similarity）结果

6. 曼哈顿距离

defManhattan(vec1, vec2):

npvec1, npvec2=np.array(vec1), np.array(vec2)return np.abs(npvec1-npvec2).sum()#Manhattan_Distance,

7. 切比雪夫距离

defChebyshev(vec1, vec2):

npvec1, npvec2=np.array(vec1), np.array(vec2)return max(np.abs(npvec1-npvec2))#Chebyshev_Distance

8. 闵可夫斯基距离

#!/usr/bin/env python

from math import*

from decimal importDecimaldefnth_root(value,n_root):

root_value=1/float(n_root)return round(Decimal(value)**Decimal(root_value),3)defminkowski_distance(x,y,p_value):return nth_root(sum(pow(abs(a-b),p_value) for a,b inzip(x,y)),p_value)print(minkowski_distance([0,3,4,5],[7,6,3,-1],3))

9. 标准化欧氏距离

defStandardized_Euclidean(vec1,vec2,v):from scipy importspatial

npvec=np.array([np.array(vec1), np.array(vec2)])return spatial.distance.pdist(npvec, 'seuclidean', V=None)#Standardized Euclidean distance#http://blog.csdn.net/jinzhichaoshuiping/article/details/51019473

10. 马氏距离

defMahalanobis(vec1, vec2):

npvec1, npvec2=np.array(vec1), np.array(vec2)

npvec=np.array([npvec1, npvec2])

sub= npvec.T[0]-npvec.T[1]

inv_sub=np.linalg.inv(np.cov(npvec1, npvec2))returnmath.sqrt(np.dot(inv_sub, sub).dot(sub.T))#MahalanobisDistance

11. 编辑距离

defEdit_distance_str(str1, str2):importLevenshtein

edit_distance_distance=Levenshtein.distance(str1, str2)

similarity= 1-(edit_distance_distance/max(len(str1), len(str2)))return {'Distance': edit_distance_distance, 'Similarity': similarity}#Levenshtein distance