In non-negative matrix factorization (NMF), the problem is to minimize $A - WH$. Dimensions are $A$ (m x n), $W$ (m, k) and $H$ (k, n). The matrix $H$ reveals soft clustering assignments of $n$ items over $k$ clusters, and is called clustering indicator matrix. Values in $H$ are constrained to have nonnegative numbers.
I am wondering how to properly interpret this $H$ matrix. There doesn't seem to be constraint (other than nonnegativity constraint) on the range of values that entries in $H$ can take. I'd like to perhaps have a row-wise sum of 1 for all rows in $H$. So, for a given row (cluster), I could perhaps interpret values probabilitisticallly. Would it be correct to simply divide each row's elements by row-sum? I am worried that it's not correct interpretation but I am not able to figure out why.