Nonnegative Matrix Factorizations Performing Object Detection and Localization

Algorithm 1

The Lee and Seung multiplicative update rules (NMF).

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

While  Stopping criteria are not satisfied do

 𝑊←𝑊⊙(𝑉𝐻^⊤)⊘(𝑊𝐻𝐻^⊤)

 𝐻←𝐻⊙(𝑊^⊤𝑉)⊘(𝑊^⊤𝑊𝐻)

end while

{⊙ and ⊘ denotes the Hadamard product, that is the element-wise matrix

multiplication and the element-wise division, respectively}