How surprising a recommendation is, in bits

Accuracy metrics reward recommending what everyone already likes, so a system optimised for them converges on the head of the catalogue. Novelty is the counterweight: self-information, large exactly when few users have seen the item. In bits, so an item half the users know scores 1.

Usage

Novlt(item, popularity)

Arguments

item

Zero-based item indices.

popularity

Interaction counts or probabilities per item.

Value

List with estimate, nov, p, n_items.

Details

Formula: nov(i) = -log2 P(i).

References

Vargas, S. & Castells, P. (2011). RecSys 2011, 109-116.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Novlt(V, V)
#> $estimate
#> [1] NA
#> 
#> $nov
#> [1] 4.169925 3.584963 3.169925 2.847997 2.584963 2.362570 2.169925       NA
#> 
#> $p
#> [1] 0.02777778 0.05555556 0.08333333 0.11111111 0.13888889 0.16666667 0.19444444
#> [8] 0.22222222
#> 
#> $n_items
#> [1] 8
#> 
#> $method
#> [1] "Novelty, self-information in bits"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"