Link Prediction via Convex Nonnegative Matrix Factorization on Multiscale Blocks

Algorithm 1

Algorithm for 𝐾-CNMF.

input: 𝐴^𝑜//observed network

    𝐿, 𝐾//desired rank, scale parameter

output: 𝐴//predicting matrix

𝐴=(0)

for 𝑘 in range of (1,𝐾)

 do 𝐾-means to partition matrix into 𝐵={𝐵₁,…,𝐵_𝑘²}

 for block 𝐵_𝑖∈𝐵

  do CNMF with rank min(𝑐𝑜𝑙(𝐵_𝑖),𝑟𝑜𝑤(𝐵_𝑖),𝐿)

  𝐴=𝐴+𝐵_𝑖𝑊𝐺//sum the corresponding entities

 end for

end for