Update illustration2d

[jolars]

I added a bit of correlation between the columns in X, which usually helps, and tinkered with the other settings. It's possible to get something that's probably ever more effective, but I think this works as we want it to.

I modified the colors a bit too. I am going to work on coloring the line segments in the hybrid plot now.

[jolars]

I did a little more work on this and now have:

I think this is more or less what we want, since it shows the following:

• The hybrid method can both move clusters in unison (merge) and split
• Our method seems to converge faster
• Our pure CD method cannot split clusters and eventually gets stuck

[Klopfe]

I did a little more work on this and now have:

I think this is more or less what we want, since it shows the following:

• The hybrid method can both move clusters in unison (merge) and split
• Our method seems to converge faster
• Our pure CD method cannot split clusters and eventually gets stuck

Very nice work! Do we wanna let the PGD go all the way to convergence or leave it as it is?

[jolars]

Very nice work! Do we wanna let the PGD go all the way to convergence or leave it as it is?

I'm not sure, what do you think? This way it's quite clear that PGD converges slower, but we could also just let PGD reach convergence and then mention how many steps it takes in the caption. Maybe that's better?

[jolars]

One thing I considered too was whether it would be nicer to have CD and Hybrid start with cd steps, i.e. follow exactly the same path until CD gets stuck, but that wouldn't match what we're doing exactly.

[Klopfe]

Very nice work! Do we wanna let the PGD go all the way to convergence or leave it as it is?

I'm not sure, what do you think? This way it's quite clear that PGD converges slower, but we could also just let PGD reach convergence and then mention how many steps it takes in the caption. Maybe that's better?

I'd prefer the second option but it's not so important.

[Klopfe]

One thing I considered too was whether it would be nicer to have CD and Hybrid start with cd steps, i.e. follow exactly the same path until CD gets stuck, but that wouldn't match what we're doing exactly.

Yes, I would rather keep it the way it is now. I think we clearly see the CD updates in only one direction and see that the first step is a PGD step. It shows what we do really well I think.

[mathurinm]

Very nice work! Do we wanna let the PGD go all the way to convergence or leave it as it is?

I'm not sure, what do you think? This way it's quite clear that PGD converges slower, but we could also just let PGD reach convergence and then mention how many steps it takes in the caption. Maybe that's better?

I think we need to let it go to convergence, since this will highlight that CD does not converge. Otherwise it may look like CD was not given enough iterations too

Maybe also puting all PGD updates in dashed (rightmost panel) would make it clearer why hybrid is "hybrid"?

And the figure is super neat, nice work!

[jolars]

Thanks for the input! Here's the "final" figure. Feel free to make edits if you feel like it.

[mathurinm]

It looks perfect! Thanks a lot. We see the huge steps, and the benefits of correction with PGD