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In a numerical low rank decomposition, whether it is non-negative matrix factorization(NMF), or binary matrix factorization(BMF), or non-negative sparse PCA, we have two low-rank matrices to approximate the original matrix by multiplying.

M = U * P

whose dimensionality being:

M: n*m , U: n*k , P: k * m

I'm wondering if there are any elegant ways of visualizing the decomposition result.

Here I have two initiative thoughts:

1) Intuitively, we can draw the three matrices into grided boxes and fill in each cell by it's value. A darker cell means a higher value while a lighter a lower.

2) We can take U and P as two assignment matrix that mapps two dimensions into several latent labels. Thus according to the different labels we can divide the two dimensions into various sets.

Do you have any idea on this? Or have you ever seen any visualization work on this?

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