Hi all,

I have two multi-dimensional vectors representing documents $\vec{a}$ and $\vec{b}$.

Considering cases where there is no overlap between $a$ and $b$ ($a \cap b = \emptyset $), traditional vector-distance measures do not work. For this reason I introduce a fuzzy measure between vector terms: $sim(t_{a},t_{b}) \in [0,1]$

This way I can compute the similarity matrix $M_{ab} |\vec{a}| \times |\vec{b}|$ with function $sim$. So I have the following elements:

- vectors $\vec{a},\vec{b}$
- matrices $M_{ab}$ representing the fuzzy similarity between all terms of the vectors

I would like to compute the distance between $a$ and $b$ in relation to $M$. A naive solution could consist of multiplying $a$ for the maximum element in each row of $M$ (columns for $b$)

$ sim(\vec{a},\vec{b}) = weights_a \cdot maxRows( M_{ab} )$

$ sim(\vec{b},\vec{a}) = weights_b \cdot maxColumns( M_{ab} )$

(as described in Corley, Courtney, and Rada Mihalcea. Measuring the semantic similarity of texts (June 30, 2005): 13-18.)

How would you compute the similarity between $a$ and $b$ in this context? Do you think that the Hungarian algorithm might give an alternative way of computing it?

Thanks for any hints!

Mulone