Point-wise Mutual Information

Point-wise Mutual Information

(Yao, et al 2019) reclaimed a clear description of Point-wise Mutual Information as below:

PMI(i,j)=logp(i,j)p(i)p(j)p(i,j)=#(i,j)#Wp(i)=#(i)#W

where #(i) is the number of sliding windows in a corpus hat contain word i

where #(i,j) is the number of sliding windows that contain both word i and j

where #W is the total number of sliding windows in the corpus.

(Levy, et al 2014) simplified PMI formula as below:

PMI(i,j)=log#(i,j)#W#(i)#(j)

Obviously, #W is a constant if we fixed slide window size and corpus, hence we can further simplify the formula as below:

PMI(i,j)=log#(i,j)#(i)#(j)

References

Liang Yao, et al, 2019. Graph Convolutional Networks for Text Classification. AAAI

Omer Levy, et al, 2014. NeuralWord Embedding as Implicit Matrix Factorization. NIPS

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