I would like to better understand the strengths of the Louvain method versus K-means for high-dimensional sparse data (e.g. zero-inflated negative binomial gene expression counts or natural language processing matrices).
A common procedure is to reduce dimensionality with PCA and then cluster on principal component space. In this context, what is the main value of the Louvain method versus K-means?
From How to understand the drawbacks of K-means, aside of the obvious advantage of not relying on the assumption of K number of clusters (albeit, the Louvain method relies on parameters like the number of relevant nearest-neighbors to build a graph), I conclude that the Louvain method, on the contrary, does not assume equal size, density or shape of the clusters.
Is this intuition correct?