Hyphenation in compounds with abbreviation remarks

So far I understood, that hyphenation should aid readability.

Examples [1, 2]:

North America-based company

A Gaussian mixture model-based approach

We propose spherical Gaussian-based approximations to calculate this analytically.

Although, this never aligned with my understanding of parsing trees, I would still like to apply this rule.

How does it extend to abbreviation remarks?

Gaussian mixture model (GMM)-based approach

Non-negative matrix factorization (NMF)-inspired method

My own understanding of how to parse the words is as follows, which does not seem to be reflected in how hyphens are used:

{
  {
    {

      Gaussian {
        mixture model
      }
    } (GMM)
  }-based
} approach

Answer

Hyphens are used to compose constituents, either words or phrases, to make words. Consequently, to know whether a hyphen is appropriate, you have to know the categories of constituents, not just what the constituents are. Below, I've tried to amend your diagram for "Gaussian mixture model (GMM)-based approach" by adding category (parts of speech) information. NP means noun phrase, N is noun (a word), A is adjective or other noun-modifier (a word), Participle (a word).

{NP
  {A
    {NP
      A Gaussian {N
        N mixture N model
      }
    } (GMM)
  }-Participle based
} N approach  

There are two types of word compounds in the example. A compound adjective (a word) is made by combining a NP (a phrase) and a Participle (a word), and a compound N (a word) is made by combining two Ns (words). For the latter type of compound, a hyphen is often optional.

I'm not sure I see a problem with the hyphenation. I'm worried, though, about the structure of "Gaussian mixture model", which must be a phrase, not a single word, because "Gaussian" is an adjective, and noun-noun compounds can't contain adjectives. But "Gaussian mixture" should be a constituent, because of the interpretation: mixture of Gaussian distributions.