Nonnegative Matrix Factorizations Performing Object Detection and Localization

Algorithm 2

NMF with orthogonal constraint on 𝑊.

Initialize nonnegative matrices 𝑊⁽⁰⁾ and 𝐻⁽⁰⁾

While Stopping criteria are not satisfied do

 𝐻←𝐻⊙(𝑉𝐻^⊤)⊘(𝑊𝐻𝐻^⊤)

 𝑊←𝑊⊙((𝑉𝐻^⊤)⊘(𝑊𝑊^⊤𝑉𝐻^⊤))^⋅(1/2)

end while

{⊙ and ⊘ denotes the Hadamard product and the element-wise division,

respectively and (⋅)^⋅(1/2) denotes the element-wise square root operation}