python - How to Normalize similarity measures from Wordnet -

i trying calculate semantic similarity between 2 words. using wordnet-based similarity measures i.e resnik measure(res), lin measure(lin), jiang , conrath measure(jnc) , banerjee , pederson measure(bnp).

to that, using nltk , wordnet 3.0. next, want combine similarity values obtained different measure. need normalize similarity values measure give values between 0 , 1, while others give values greater 1.

so, question how normalize similarity values obtained different measures.

extra detail on trying do: have set of words. calculate pairwise similarity between words. , remove words not correlated other words in set.

how normalize single measure

let's consider single arbitrary similarity measure m , take arbitrary word w.

define m = m(w,w). m takes maximum possible value of m.

let's define mn normalized measure m.

for 2 words w, u can compute mn(w, u) = m(w, u) / m.

it's easy see if m takes non-negative values, mn takes values in [0, 1].

how normalize measure combined many measures

in order compute own defined measure f combined of k different measures m_1, m_2, ..., m_k first normalize independently each m_i using above method , define:

alpha_1, alpha_2, ..., alpha_k 

such alpha_i denotes weight of i-th measure.

all alphas must sum 1, i.e:

alpha_1 + alpha_2 + ... + alpha_k = 1 

then compute own measure w, u do:

f(w, u) = alpha_1 * m_1(w, u) + alpha_2 * m_2(w, u) + ... + alpha_k * m_k(w, u) 

it's clear f takes values in [0,1]