Sign Inference for Dynamic Signed Networks via Dictionary Learning

Algorithm 1

Adaptive line search scheme for dictionary selection.

(1) Input: 𝜇,𝛼₋₁=0.5, 𝐘₋₁=𝐘₀, 𝐿₋₁=𝐿₀, 𝛾₀≥𝜇,𝜆₀=1

(2) Output: 𝐘_𝑁

(3) for  𝑙=1,2,…,𝑁  do

(4) while true do

(5)  compute 𝛼_𝑘∈(0,1) as the root of 𝐿_𝑙𝛼²_𝑙=1−𝛼_𝑙𝛾_𝑙+𝛼_𝑙𝜇,

   𝛾_𝑙+1=1−𝛼_𝑙𝛾_𝑙+𝛼_𝑙𝜇,  𝛽_𝑙=1−𝛼_𝑙−1𝛾_𝑙𝛾_𝑙+𝐿_𝑙𝛼_𝑙𝛼_𝑙−1;

(6)  compute 𝐒_𝑙=𝐘_𝑙+𝛽_𝑙𝐘_𝑙−𝐘_𝑙−1

(7)  compute 𝐘_𝑙+1=𝐒_𝑙−1/𝐿_𝑙∇𝑞𝐒_𝑙

(8)  if  𝑞𝐘_𝑙+1≤𝑞𝐒_𝑙−1/2𝐿_𝑙∇𝑞𝐒_𝑙²_𝐹  then

(9)   goto Step 14

(10)  else

(11)   𝐿_𝑙=2𝐿_𝑙

(12)  end if

(13)   end while

(14)   set 𝜃=2𝐿_𝑙𝑞𝐒_𝑙−𝑞𝐘_𝑙+1∇𝑞𝐒_𝑙²_𝐹,  𝐿_𝑙+1=ℎ(𝜃)𝐿_𝑙

(15)   set 𝜆_𝑙+1=(1−𝛼_𝑙)𝜆_𝑙

(16) end for