The Tversky contrast model similarity is a similarity function defined as
where
is the set of positions
is the set of positions
is the set of positions
is a monotonic increasing function (usually a weighted sum).
, and are positive reals numbers (used as weights).
Depending of values of , and this function could not be simmetric.
Examples[]
For , and , and the cardinality of sets, .
For , and , and the cardinality of sets, we have a simmetric function: .
For , and , and the cardinality of sets, we have an asimmetric function: , but .
Normalization[]
A possible way of nomalization is the ratio model similarity defined as
Examples[]
For , and , and the cardinality of sets, .
Variations[]
When instead of a similarity function we get a distance function.
Applications[]
This function is used to compare entities represented as vectors of boolean features. In contrast with Hamming similarity for vectors, only present features are taken into acount. The weights , and serves to ponderate de importance of common features of and , features exlusives of and features exlusives of respectively, providing a wide range of similarity functions.