I need you help because I don't really understand why we use RunUMAP and RunPCA to identify clusters ? what's the difference between them.
You don't need a UMAP reduction to find the clusters, you need the PCA. PCA results will be used by the FindNeighbors function to construct the nearest neighbour graph, which in turn will be used by FindClusters.
Also, from the Seurat vignette:
"As in PhenoGraph, we first construct a KNN graph based on the euclidean distance in PCA space, and refine the edge weights between any two cells based on the shared overlap in their local neighborhoods (Jaccard similarity). This step is performed using the FindNeighbors() function, and takes as input the previously defined dimensionality of the dataset (first 10 PCs).
To cluster the cells, we next apply modularity optimization techniques such as the Louvain algorithm (default) or SLM [SLM, Blondel et al., Journal of Statistical Mechanics], to iteratively group cells together, with the goal of optimizing the standard modularity function. The FindClusters() function implements this procedure, and contains a resolution parameter that sets the ‘granularity’ of the downstream clustering, with increased values leading to a greater number of clusters"
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