Diversity Gini Index

Summary

Measures Recommendations' diversity. The index is 0 when all items are chosen equally often, and 1 when a single item is always chosen.

Description

The diversity ($G$) of the recommendations according to Gini Index. The index is 0 when all items are chosen equally often, and 1 when a single item is always chosen (see book). Generally, the Gini Index mathematical expression is defined as:

$G=\frac{1}{n-1}\sum_{j=1}^{n}(2j-n-1)p(i_j)$, where $i_1,\ldots,i_n$ is the list of items ordered according to increasing $p(i)$ and each item $i$ accounts for a proportion $p(i)$ of user recommendations. In RS Metrics the computation is determined by the following formula: $Diversity=\frac{1}{n-1}\sum_{j=1}^{n}(2j-n-1)\left(\frac{count(j)}{recommendations}\right)$

Output

Type	Float
Min	0
Max	1

info

The index is 0 when all items are chosen equally often, and 1 when a single item is always chosen.

Prerequisites:

• recommendations without anonymous users
• all available services

Process Flow:

• Clean up

Recommendations clean up; entries removal where users or services are not found in "users" or "services" files accordingly

• Services Impact

Calculation of the impact of the services, by counting how many times each service i was suggested to all possible users: count(j)

• Sort Services Impact from low to high

Sort the number of how many times each service (i.e. i) was suggested from the lower to the higher value, in order to apply the respective weight (j). The computation includes services with 0 recommendation occurrence

• Recommended Probability of the Services

For each service calculate its recommended probability by dividing the number of service's occurrence found in the recommendations to the total number of recommendations

• Service-based product computation

Calculation of the product of the recommended probability from previous step and services' respective index j, for each service individually

• Gini Index computation

Computation of the overall value by summing all values from previous step