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 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.