Computing dissimilarity/distance/diversity/similarity of molecules

[FanwangM]

An essential component of our package is to have a submodule to compute the dissimilarity/distance/diversity/similarity where normally we assume diversity = 1 - similarity.

A good summary of this is Table 2 in Drug Dev. Res.,72(1):74 - 84, 2011. Given a fact that this is a public repo, I am not going to share the screenshot here.

The Tanimoto coefficient is a classic and gold stand similarity metric for molecular fingerprints and we should support it. But it was found that it favors small molecules when used in molecule subset selection and a modification was proposed. My guess is that we should make this the default for molecular fingerprint inputs.

I will keep adding new things. Any idea will be appreciated.
@PaulWAyers @JuansaCollins @RichRick1 @Khaleeh @alnaba1

[PaulWAyers]

A good review is below. Interesting that the guy who wrote it is now the head of research at Pfizer(!)
9783527613083.ch12.pdf

[FanwangM]

Some implementations of similarity measurements, https://e3fp.readthedocs.io/en/latest/api/e3fp.fingerprint.metrics.html

[PaulWAyers]

Some hints on how to do this can be gleaned from e3fp.
https://github.com/keiserlab/e3fp/blob/b556110243fb535243cdea8d10875f9e4046bbfa/e3fp/fingerprint/metrics/__init__.py
https://github.com/keiserlab/e3fp/blob/b556110243fb535243cdea8d10875f9e4046bbfa/e3fp/fingerprint/metrics/array_metrics.py

[PaulWAyers]

This is also useful for selecting samples. Key ideas (From #2 ) are

• determinantal point processes
• KDtrees to make minimax methods faster.

[PaulWAyers]

• Similarity and scaled similarity (S(i,j)/SQRT(S(i,i)S(j,j))
• 5 different methods for computing dissimilarity

One of these five (or not?) should be S(i,i) + S(j,j)- 2S(i,j) where S(i,j) is the similarity. This is the distance via a covariance matrix and is important in Gaussian processes.

One can also consider S(i,j)/SQRT(S(i,i)S(j,j)) and compute the distance-squared from that. That's a correlation matrix/distance.

[PaulWAyers]

Different methods for converting similarities to dissimilarities (and vice versa in some cases)
https://rdrr.io/cran/smacof/man/sim2diss.html

[PaulWAyers]

Keepers from this issue:

1. Interconversion between similarities and dissimlarities
2. kdtree (for long term)

[FanwangM]

Given the topics have been split into smaller chunks, I will close it for now.