I've performed single cell analysis in which each gene represents a feature to cluster upon; there are about 20,000 genes expressed across all the cells in the dataset. I use the top 1500 or so variably expressed genes to perform graph-based clustering on. This results in about 60 clusters. My goal is to computationally define the genes that would most optimally recapitulate this clustering at several levels of feature subsampling. i.e: What 80/200/500 genes give the closest clustering when compared to the clustering performed with 1500 genes? Importantly, many of the best genes will be those that are pretty explicitly found in one or two clusters, though many other genes may be critical to defining a 'meta-cluster' that helps define 15 of my 60 clusters -- so the corresponding list of best genes to recapitulate this clustering won't necessarily be those that are the most explicit to a few clusters, but also ones that are explicit to 10-50% of clusters.
I plan to use the Jaccard index as a measure of cluster similarity (quality of the downsampling to recapitulate clustering). Is this a good measure? Or is there something that may work better to represent global clustering similarity? I've also read about using Adjusted Mutual Information to assess this, but honestly don't know why one would be better or worse.
My issue is that there are thousands of genes to choose from, so subsampling genes --> clustering --> computing Jaccard coeff for each set of genes could work in theory, but take forever.
I don't expect anyone to outright answer my question, but hope someone can provide some useful guidance on approaches I should look into and why. Any papers that discuss something similar to this would also be very welcome!