Random-Forest-based Similarity Matrix for clustering: how does it behave? I am in the following context:

Data: static, baseline health data at the patient level, 40 features, sparse (~ 25 binary features with many 0 or many 1 + other categorical features)

Objective : to cluster instances into clinically meaningful sub-population or clinical context, to get a sense of at risk sub-populations (on a Follow-Up outcome)

Considered approach  (see this short blog article (2 minute's read) for its rationale):


Fit a random forest on the Follow-Up outcome, using all features (no denoising or removing correlation)
Use co-occurence in trees leaves to get a similarity matrix of the patients
Turn in into a distance matrix
Cluster patients with this distance matrix


My questions are as follow:


I have only found literature using this methodology for unsupervised clustering (i.e. RF is learned on random target variable) : Shi and Horvath 2016 and Dalleau 2018 (unpublished). Does anyone have insights on those methods in general (other references, personnal experience...)?
Do you know of any article written about the supervised use of RF to create similarity matrices (with or without mention of clustering)?
I recently presented a poster at a conference where we used the same approach you describe for clustering. Generally, I think it's a great approach for clustering, as you can get clusters which have a distance that is relative to an outcome or variable that you are interested in. 

For some insight, I have a few pointers:
1) When getting the co-occurence in trees, depending on how many subjects you have, this can end up being a very sparse matrix. To make the matrix less sparse you can increase the minimum number of samples required in terminal nodes. 
2) After you get the similarity matrix, do a PCA on this, ending with individuals in rows and PCs in columns. Get the distance between individuals in this PCA space, restricting to some top number of components that you find acceptable. I recommend this because the similarity matrices can be huge if you have a lot of cases.