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hello welcome my name is Ahmet and welcome to another tutorial so what is n MF n MF is non-negative matrix factorization imagine I have a matrix X with the dimension of n by M which is a non-negative matrix by non-negative matrix Iamp;#39;m in it doesnamp;#39;t have any negative entries and we want to factorize this matrix into two non-negative matrices W and H in the way that W is n by K and H is K by M so in order to do it we need to solve a minimization problem we need to minimize the distance between X and W times H with respect to W on H and we have to keep in mind that W an age donamp;#39;t have any negative entries but this problem is an np-hard problem because it is convex in W or H but not in both if you ask why here is the proof consider this color case where m and n equal to 1 then the problem is going to be like this and then if we compute the first and second gradient of it we are going to see that the Hessian or the second gradient is not positive semi-definite
