How to Normalize similarity measures from Wordnet

Question

I am trying to calculate semantic similarity between two words. I am using Wordnet-based similarity measures i.e Resnik measure(RES), Lin measure(LIN), Jiang and Conrath measure(JNC) and Banerjee and Pederson measure(BNP). To do that, I am using nltk and Wordnet 3.0. Next, I want to combine the similarity values obtained from different measure. To do that i need to normalize the similarity values as some measure give values between 0 and 1, while others give values greater than 1. So, my question is how do I normalize the similarity values obtained from different measures. Extra detail on what I am actually trying to do: I have a set of words. I calculate pairwise similarity between the words. and remove the words that are not strongly correlated with other words in the set.

Accepted Answer

How to normalize a single measure

Let's consider a single arbitrary similarity measure `M` and take an arbitrary word `w`.

Define `m = M(w,w)`. Then m takes maximum possible value of `M`.

Let's define `MN` as a normalized measure `M`.

For any two words `w, u` you can compute `MN(w, u) = M(w, u) / m`.

It's easy to see that if `M` takes non-negative values, then `MN` takes values in `[0, 1]`.

How to normalize a measure combined from many measures

In order to compute your own defined measure `F` combined of k different measures `m_1, m_2, ..., m_k` first normalize independently each `m_i` using above method and then define:

```
alpha_1, alpha_2, ..., alpha_k
```

such that `alpha_i` denotes the weight of i-th measure.

All alphas must sum up to 1, i.e:

```
alpha_1 + alpha_2 + ... + alpha_k = 1
```

Then to compute your own measure for `w, u` you 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 that `F` takes values in [0,1]

How to Normalize similarity measures from Wordnet

Solution

Problem