consider making regularized LSE the default

[bdpedigo]

seen many examples where it works way better

[nicaurvi]

Could you share those examples? I've not compared the two very much in my work but if you have illustrative examples to compare when one is more beneficial than the other I'd be happy to throw it into a tutorial.

[bdpedigo]

have discussed some examples where regularized LSE worked better (at least for me) with @daxpryce and @Nyecarr - I feel like regularized is what I'd recommend anyone using.

Also, form='I-DAD' is the Laplacian where you want the bottom d eigenvectors/singular vectors, not the top - therefore I think it's actually fairly useless to have as an option with the current LSE. I am fine leaving it in to_laplacian but otherwise I think is unnecessary.

I propose removing the form argument from LaplacianSpectralEmbed, since we don't need 'I - DAD', and 'DAD' is just a special case of 'R-DAD' when the regularizer = 0. The default regularizer for LSE would be the average degree, as it is now.

Does anyone object to this proposal @daxpryce @Nyecarr @asaadeldin11 @j1c @loftusa ?

[daxpryce]

what would the proposed default of regularizer be then? 0, or None?

[bdpedigo]

None (means regularizer is set to the mean degree)

[daxpryce]

so it would be a legit R-DAD by default, and you could fully emulate DAD by setting it to 0. sounds reasonable here!

[daxpryce]

@Nyecarr we should do this sooner rather than later and also make sure it works through Omni so @JonathanLarson can stop monkeypatching it in

[loftusa]

i'm down on this

[bdpedigo]

@daxpryce @Nyecarr just wondering if there is anyone on your side working on this at the moment?

[daxpryce]

we are not!

edit: not for any other reason other than we have other things we're working on, not because it's a bad idea. just to clarify :D