Dictionary Learning Based on Nonnegative Matrix Factorization Using Parallel Coordinate Descent

Algorithm 1

PCDDL.

 Require:    Data Matrix 𝐘∈ℝ₊^𝑚×𝑛, initial matrices 𝐖∈ℝ₊^𝑚×𝑟, 𝐇∈ℝ₊^𝑟×𝑛, and 𝜆;

 (1)  while stopping criterion not satisfied do

 (2)  Computing 𝐏=𝐘𝐇^𝑇 and 𝐐=𝐇𝐇^𝑇;

 (3)  for  𝑘=1 to 𝑟  do

 (4)   𝐖_∶𝑘𝐏←max0,^∶𝑘−∑^𝑟_{𝑙=1,𝑙≠𝑘}𝐖_∶𝑙𝐐_𝑙𝑘𝐐_𝑘𝑘

 (5)   Normalizing 𝐖_∶𝑘←𝐖_∶𝑘𝐖_∶𝑘2

 (6)  end for

 (7)  Computing 𝐔=𝐖^𝑇𝐘 and 𝐕=𝐖^𝑇𝐖;

 (8)  for  𝑘=1 to 𝑟  do

 (9)   𝐇_𝑘∶𝐔←max0,^𝑘∶−∑^𝑟_{𝑙=1,𝑙≠𝑘}𝐕_𝑘𝑙𝐇_𝑙∶−𝜆𝐕_𝑘𝑘

 (10)  end for

 (11)  Using the fixed 𝜆 or adaptively tuning 𝜆 according to the change of the sparsity of 𝐇;

 (12)  end while