Non-Negative Matrix Factorization (NMF) | Multiplicative Update Rules By Lee And Seung

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NMF Algorithm
Non-negative Matrix Factorisation (NMF): Family of linear algebra algorithms for identifying the latent structure in data represented as a non-negative matrix.

Input: matrix X , rank k.
Output: Two k-dimensional factors W and H approximating X

I used Multiplicative Update Method introduced by Lee and Seung in 1999 in order to factorize the input matrix.

#NMF #Python
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@Ahmad Varasteh I think there might be an error @2:19 for the "W" equation on the bottom right: the numerator should be "XH^T" rather than "W^T X"
Your github code has the correct version

seungyunsong
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2:20 I know this learning rates lead to multiplicative update rules and guarantee non-negativity, but would it be possible that the learning rates are too large at some iteration to guarantee the convergence of NMF?

asdfqwer
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Can you please explain what does basis vectors actually represent In NMF

sindhusankarjeeru
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Thanks a lot ; Please do you have an idea ; how to optimize a boolean matrix factorization (Binary matrices)?

khamishoufar
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Very cool video.. Just a doubt on how do we choose K ?

abhishekpatil
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what does "not always positive semi-definite" mean and how it is related to solvability of the equation? Is there a nice video/website that anyone can recommend for it?

yuzdeotuzz
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What is the advantage of non-negative matrix factorization over matrix factorization without the constraint?

ThePritt
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This video was the what I need, subbed! (I'm the 666th sub)

nabereon
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Explaination not useful for a beginner

ShreyasG-dn