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

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Blaise 2014-1-17

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https://ww2.mathworks.cn/matlabcentral/answers/112754-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