Initialize nonnegative matrices 𝑊 ( 0 ) and 𝐻 ( 0 )
WhileStopping criteria are not satisfieddo
𝐻 ( 𝐻 ( 𝑊 ( 𝑉 𝑊 𝐻 ) ) ) ( 1 / 2 )
𝑊 𝑊 ( ( 𝑉 𝑊 𝐻 ) 𝐻 )
𝑊 𝑊 d i a g ( 𝑊 1 1 , 𝑊 2 1 , , 𝑊 𝑟 1 ) 1
end while
{ and denotes the Hadamard product and the element-wise division,
respectively, ( ) ( 1 / 2 ) denotes the element-wise square root operation,
d i a g ( 𝑊 1 1 , 𝑊 2 1 , , 𝑊 𝑟 1 ) indicates the 𝑟 × 𝑟 diagonal matrix
whose diagonal elements are the 1-norm of the column basis vectors in
𝑊 }
Algorithm 3: Local nonnegative matrix factorization update rules.