What are the 3-dimensional subspaces (or quotient spaces) to which the projections are made in the given figures? (Topological Data Analysis)


New member
Jul 9, 2019
I've just started my mathematics thesis on Topological Data Analysis last week and I was given a question to resolve for next week:

"What are the 3-dimensional subspaces to which the projections are made in figure A? Are they really subspaces or are they quotient spaces?"
  • These are the figures which are mentioned:
I am actually not sure how to proceed to resolve this question. I've skimmed over the paper and I didn't spot anything helpful, except for the figure description:

"leads to nine distinct clusters in a two-dimensional state space inferred by generalized regression modelling"

  1. Why do they talk about a two-dimensional state space. The question mentions a three-dimensional space and on the figure we see 3 axes.
  2. Using some method we project an n-dimensional space to a 2 (or 3)-dimensional space. What does he mean by "subspaces/quotient spaces to which the projections are made" How would I check this?
  3. Do I need to find out how the branching analysis or Generalized Regression Modelling works? By G.R.M. do they mean this: Generalized linear model?

I've been told to ask for further clarification on this problem, but my supervisor is currently travelling and hasn't responded to my e-mails yet. So, I'm just hoping that someone might be able to assist before my next meeting. Thanks for any help given. :)