A Wordnet from the Ground Up

4.5. Hybrid Combinations 151We introduce the following notation:• x is a lemma, representing one or more LUs, to be added to the wordnet, y, y ′are lemmas from the wordnet, S, S ′ – wordnet synsets;• hypo(S, n), hyper(S, n) are sets of hyponym or hypernym synsets, respectively,of the synset S up to n levels;• dist h (S, S ′ ) is the number of hypernymy or hyponymy links (depending on thedirection) between S and S ′ ;• r is the context radius – it defines the size of the context influencing the calculationof the lemma-to-synset fit (the value was set experimentally to 2);• hMSR (set experimentally to 0.4) is the threshold defining highly reliable MSRvalues – it corresponds to the observed high and reliable values of MSR;• minMSR (set to 0.1) is the MSR value below which associations seem to bebased on weak, accidental clues;• maxSens (set to 5) is the maximal number of presented activation areas (possibleattachment areas) – the number of correct proposals is mostly low, so wewanted to keep the number of attachment areas small in order not to clutter thescreen.Phase I. Lemma-to-synset calculation1. votes(x, S) = ∑ y∈Sfit(x, y)2. fit(x, S) =δ (h=1)(votes(x, S) + ∑ votes(x, S ′ ))S ′ ∈hypo(S,r)∪hyper(S,r)2 ∗ dist(S, S ′ )where δ : N × N → {0, 1}, such that δ(n, s) = 1if and only if (n ≥ 1.5 ∗ h and s ≤ 2) or (n ≥ 2 ∗ h and s > 2)( ∑3. fit(x, S) = δ (h=hMSR) y∈Sscore(x, y) +∑S ′ ∈hypo(S,r)∪hyper(S,r)Phase II. Identify lemma senses: areas and centres∑ y ∈ S ′ score(x, y))2 ∗ dist(S, S ′ )1. synAtt(x) = {S : S = {S : fit(x, S) ∨ weak fit(x, S)}, and S is aconnected hypernymy graph}2. maxScore(x, S) = score (x, max S∈S score(x, S))