Input:
𝑝
𝑜
𝑠
𝑖
𝑡
𝑖
𝑣
𝑒
𝑐
𝑜
𝑛
𝑠
𝑡
𝑎
𝑛
𝑡
𝑠
∶
𝜇
𝑊
>
0
,
𝜇
𝐻
>
0
𝐶
ℎ
𝑜
𝑜
𝑠
𝑒
𝑎
𝑛
𝑎
𝑝
𝑝
𝑟
𝑜
𝑝
𝑟
𝑖
𝑎
𝑡
𝑒
𝑃
𝑟
𝑜
𝑗
𝑒
𝑐
𝑡
𝑖
𝑜
𝑛
(
⋅
)
𝑡
𝑜
𝑒
𝑛
𝑠
𝑢
𝑟
𝑒
the degree of sparseness
Initialize nonnegative matrices
𝑊
(
0
)
𝐻
(
0
)
while
𝑆
𝑡
𝑜
𝑝
𝑝
𝑖
𝑛
𝑔
𝑐
𝑟
𝑖
𝑡
𝑒
𝑟
𝑖
𝑎
𝑎
𝑟
𝑒
𝑛
𝑜
𝑡
𝑠
𝑎
𝑡
𝑖
𝑠
𝑓
𝑖
𝑒
𝑑
do
𝑊
𝑖
𝑗
←
𝑊
𝑖
𝑗
−
𝜇
𝑊
(
(
𝑊
𝐻
𝐻
⊤
)
𝑖
𝑗
−
(
𝑋
𝐻
⊤
)
𝑖
𝑗
)
𝑊
←
𝑃
𝑟
𝑜
𝑗
𝑒
𝑐
𝑡
𝑖
𝑜
𝑛
(
𝑊
)
𝐻
←
𝐻
𝑖
𝑗
−
𝜇
𝐻
(
(
𝑊
⊤
𝑊
𝐻
)
𝑖
𝑗
−
(
𝑊
⊤
𝑋
)
𝑖
𝑗
)
𝐻
←
𝑃
𝑟
𝑜
𝑗
𝑒
𝑐
𝑡
𝑖
𝑜
𝑛
(
𝐻
)
end while
{
𝜇
𝑊
>
0
and
𝜇
𝐻
>
0
are positive constants representing the step size
of the algorithm and
𝑃
𝑟
𝑜
𝑗
𝑒
𝑐
𝑡
𝑖
𝑜
𝑛
(
⋅
)
indicates the appropriate projection
operator}
Algorithm 4:
NMF with space constraints.