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The largest part of the network consists of one large connected component of 3.4 million users, the rest are components of size smaller than 1000 users.
Learning setup: The dictionary learning setup is the same as in the experiments for 30 and 50% corruption levels in Section 5.2.1, where for ITKrMM, we consider low-rank components of size L=1 and L=3, abbreviated as ITKrMM1 and ITKrMM3 respectively.
There are also 19 smaller connected components of size ranging from 2 to 15.
First,∼10% of components of size 2 break up into singletons in this range.
(I eliminate isolated reactions, that is, components of size one from this graph).
Proteins that were members of connected components of size greater than one, were classified as "with paralogs", or "singletons" otherwise.
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More importantly, attempting to extract PDSs from this results in one super component of size 350, and 3 components of sizes 4, 4 and 6.
Reiterate the process until a component of size (ge c/alpha ) is generated or, otherwise, a profile consisting of isolated strong components smaller than (c/alpha ) is generated.
Our first observation is that the dictionaries learned by KSVD and ITKrM on clean data with S=5 and after removing a low-rank component of size L=3 or L=7 perform best, indicating the importance of removing the low-rank component to get a well-conditioned dictionary.
Algorithmic setup: Via ITKrMM, we first learn the low-rank component of size L=1,3,7, and a dictionary of size K=2d−L, resulting in a system with redundancy 2. We set the sparsity level in the dictionary learning to S=8−L for L=1,3 corresponding to an overall sparsity L+S=8 and to S=5 for L=7, corresponding to an overall sparsity L+S=12.
For the large connected component of size 3429, we ran a graph-clustering method called spectral clustering [ 44] to further divide it into eight smaller subnetworks.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com