Hi,
I'm using sklearn.decomposition.NMF to deconvolute a series of Raman
spectra (n_features >> n_samples) into a small number of components and
a mixing matrix. NMF seems to be very well suited for this task, since
it yields positive components that can be physically interpreted as
partial spectra, and a positive mixing matrix. A small sparsity
constraint (typically beta=1e-5) is enforced on components to have
cleaner partial spectra. The typical call looks like this:
>>> nmf = sklearn.decomposition.NMF(n_components=n_components,
init='nndsvda',
sparseness='components', max_iter=1500, beta=1e-5, tol=1e-5)
>>> mix = nmf.fit_transform(spectra)
>>> components = nmf.components_
The number of components is determined using sklearn.decomposition.PCA,
combined with the classic Malinowski indicator function. This gives a
slightly overestimated number of components, which I thought would give
some room for NMF to work properly. Indeed, some of the components are
completely null.
When NMF.n_components is increased manually, the shape of some
components varies, though NMF.reconstruction_err_ does not change much.
Upon serious increase of n_components, some components may even be
"merged". This is a serious problem because it jeopardizes the physical
interpretation of the components as partial spectra.
Should n_components and beta be balanced to avoid this? Or should I
tinker with eta? I get the feeling that sparsity has a different
enforcement depending on the excess number of components allowed, but
I'm not sure how this works.
Thank you,
William Woelffel
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