comparing results of PCA and NNMF - what percentage of the original data's variance is retained?

Hello,

I have a big data matrix (100000*200) on which I performed PCA. Luckily PCA works great and only 4 variables recover ~95% of the variance. The way I got this is that I used the command:

cumsum(latent)./sum(latent)

as the example shows on matlab's PCA website (<http://www.mathworks.co.uk/help/stats/princomp.html)>. However for various reasons I want to do non-negative matrix factorisation on the same data matrix. My question is that how can I make an apples-to-apples comparison between the results of PCA and NNMF? That is how can I calculate the percentage of the original data's variance retained after NNMF?

Shall I just add up the variances of the variables and compare it to the same quantity of the original data? If I do that will that give me the same result as the command above in the case of PCA?

best regards, b

Answer 1

[Aditya]

Hi Blaise,

To compare the results of Principal Component Analysis (PCA) and Non-negative Matrix Factorization (NNMF) in terms of variance explained or retained, you'll need to consider the fundamental differences between these two techniques. PCA is a linear decomposition method that focuses on maximizing variance, while NNMF is a non-linear technique that decomposes a matrix into non-negative factors, which may not directly align with variance maximization.

Refer to the following documentation:

PCA : https://www.mathworks.com/help/stats/pca.html

NNMF : https://www.mathworks.com/help/stats/nnmf.html