Association Indexes

In T-LAB the association indexes (or similarity coefficients) are used to analyse the co-occurrences of the lexical units (LU) inside the elementary contexts (EC), that is to analyse binary data of the presence/absence type.

For instance, given two LU and ten EC, we can obtain the following example:

The same data can be represented in the following way:

Generalizing and using the letters of the alphabet:

The formulas corresponding to the three association indexes used by T-LAB are the following:

N.B.: In the case of binary data, the cosine is identical to Ochiai's coefficient.

By applying these formulas to our example, we obtain the following coefficients:

Jaccard = 0.333; Dice = 0.600; Cosine = 0.507

If, for example, we have calculated association coefficients of co-occurrence relationships concerning ten LU, we can obtain the following table:

In effect T-LAB produces and analyses analogous tables of N x N dimensions (where N can correspond to hundreds of columns), both using Multidimensional Scaling and Cluster Analysis.