18种和“距离(distance)”、“相似度(similarity)”相关的量的小结

d=∑i=1n(xi−yi)2−−−−−−−−−−√

d=∑i=1n|xi−yi|

d=∑i=1n(xi−yi)p−−−−−−−−−−√p

J(A,B)=|A⋂B||A⋃B|

K=n(A⋂B)n(A)×n(B)−−−−−−−−−−√

r=∑ni=1(Xi−x¯)(yi−y¯)∑ni=1(Xi−x¯)2−−−−−−−−−−−−√∑ni=1(yi−y¯)2−−−−−−−−−−−√

S=x⋅y|x||y|

d=(x⃗−y⃗)TS−1(x⃗−y⃗)−−−−−−−−−−−−−−−−√

D(P||Q)=∑i=1nP(i)logP(i)Q(i)

pmi=logp(x,y)p(x)p(y)=logp(y|x)p(y)

NGD(x,y)=max{logf(x),logf(y)}−logf(x,y)logM−min{logf(x),logf(y)}

⎧⎩⎨⎪⎪⎪⎪⎪⎪max(i,j)min⎧⎩⎨⎪⎪leva,b(i−1,j)+1leva,b(i,j−1)+1leva,b(i−1,j−1)+1(ai≠bj)if min(i,j)=0,otherwise.

⎧⎩⎨⎪⎪⎪⎪013(m|s1|+m|s2|+m−tm)ifm=0otherwise

d=∑i=1n|xi−yi|

H2(P,Q)=12√∫(dPdλ−−−√−dQdλ−−−√)2dλ−−−−−−−−−−−−−−−−−−√

当dP/dλ、dQ/dλ为概率密度函数时，进一步有

H2(P,Q)=1−∫f(x)g(x)−−−−−−−√dx−−−−−−−−−−−−−−−√

d(p⃗,q⃗)=∑i=1n|pi−qi||pi|+|qi|

where

p⃗=(p1,p2,⋯,pn)

q⃗=(q1,q2,⋯,qn)

DChebyshev(p,q)=maxi(|pi−qi|)=limk→∞(∑i=1n|pi−qi|k)1/k