NPMI

Normalized pointwise mutual information (NPMI) is a measure of association between two discrete events, commonly words, that quantifies how much their joint occurrence deviates from what would be expected if they were independent, after adjusting for their individual frequencies. It is defined as NPMI(w1,w2) = PMI(w1,w2) / -log p(w1,w2), where PMI(w1,w2) = log [ p(w1,w2) / (p(w1) p(w2)) ]. The logarithm is typically natural or base 2, and the normalization yields a range from -1 to 1. A value near 1 indicates a strong positive association, 0 indicates independence, and values near -1 suggest mutual exclusivity.

Estimation is usually performed from a text corpus. p(w) is approximated by the frequency of w divided by the total number of tokens, and p(w1,w2) by the frequency of their co-occurrence (for example within a fixed window or as a bigram) divided by the total number of observed opportunities. Because NPMI involves p(w1,w2) in the denominator of the normalization, it is sensitive to rare events and often requires smoothing or frequency thresholds to avoid unstable scores.

NPMI is used to identify collocations and informative word pairs, and serves as a feature in various natural language processing tasks such as topic modeling and semantic similarity judgments. It is related to PMI but provides a bounded, more comparably scaled measure, aiding cross-dataset comparisons.

Limitations include dependence on corpus size, windowing strategy, and smoothing choices; rare-word bias can persist. Variants and related measures include PMI itself and other normalized co-occurrence metrics.