Rosenberg2007

CREATED: 201004101501 LINK: url:/home/melvin/Modules/Literature/Rosenberg2007.pdf

Entropy based measure to evaluate homogenity and completeness

Harmonic mean of homogeneity and completeness score

Homogeneity: all clusters contain only members of a single class, max when there is one cluster per point

Completeness: all members of a class are members of a cluster, max when all points are in the same cluster

h = 1 if H(C,K) = 0

• 1 - H(C|K)/H(C) otherwise

H(C|K) = - sum_k sum_c (a_ck / N) log (a_ck / sum_c a_ck) H(C) = - sum_c (sum_k a_ck)/N log (sum_k a_ck / N)

c = 1 if H(K,C) = 0

• 1 - H(K|C)/H(K) otherwise

v_b = [(1+b) h c] / (bh + c)

• independent of algorithm, size of data, number of classes, number of clusters
• does not require mapping clusters to classes
• evaluates every point, avoid “problem of matching”