Divergence-from-Randomness Models

Synonyms

Deviation from randomness

Definition

Divergence-from-randomness (DFR) information retrieval models are term-document matching functions that are obtained by the product of two divergence functions. An example of DFR function is that related to Jensen’s information of two probability distributions [9, pp. 26–28]:

$$ \sum_i{I}_1\left({\hat{p}}_i^{+}||{\hat{p}}_i\right).{I}_2\left({\hat{p}}_i^{+}||{\hat{p}}_i\right) $$

where ${I}_1\left({\hat{p}}_i^{+}||{\hat{p}}_i\right)={\hat{p}}_i^{+}-{\hat{p}}_i=\varDelta {\hat{p}}_i\ \mathrm{and}\\ {I}_2\left({\hat{p}}_i^{+}||{\hat{p}}_i\right)={ \log}_2\frac{{\hat{p}}_i+\varDelta {\hat{p}}_i}{{\hat{p}}_i}$.

The DFR generalizes the Jensen’s information as follows:

$$ \sum_i{I}_1\left({\hat{p}}_i^{+}||{\hat{p}}_i\right).{I}_2\left({\hat{p}}_i^{+}||{p}_i\right) $$

where

• p is a prior probability density function of terms (or documents) in the collection.

• $\hat{p}$ is the frequency of the term in a document (or in a subset of documents).