α-nDCG

Synonyms

Alpha-nDCG

Definition

α-nDCG is a variant of Normalised Discounted Cumulative Gain (nDCG). It is an evaluation measure for diversified search, where it is assumed that a topic q has multiple possible intents {i}, and that intent probabilities Pr(i|q) and per-intent relevance assessments are available. For a given diversified ranked list, let I_i(r) = 1 if the document at rank r is relevant to intent i and let I_i(r) = 0 otherwise; let $C_{i}(r)=\sum _{k=1}^{r}I_{i}(k)$. For a given parameter α (typically set to 0.5), let the novelty-biased gain at r be $\textit {ng}(r)=\sum _{i}I_{i}(r)(1-\alpha )^{C_{i}(r-1)}.$ This reflects the view that (a) the value of a document is basically given by the number of intents it covers; but that (b) for each intent, whenever a relevant document is found, the value of the next relevant document should be discounted (the diminishing return property). α-nDCG at measurement depth (or document cutoff) d is defined as:

$$\displaystyle...