add multibatchPCA approach?

• [ X] New analysis tool: A simple analysis tool you have been using and are missing in sc.tools?

It may be useful to adopt a PCA option similar to multiBatchPCA in the R batchelor package.
This is a useful approach where there are imbalances in batch size and PCA is conducted across a merged experiment.
It is pretty slow in R.

From their documentation:

"Our approach is to effectively weight the cells in each batch to mimic the situation where all batches
have the same number of cells. This ensures that the low-dimensional space can distinguish subpopulations in smaller batches. Otherwise, batches with a large number of cells would dominate
the PCA, i.e., the definition of the mean vector and covariance matrix. This may reduce resolution
of unique subpopulations in smaller batches that differ in a different dimension to the subspace of
the larger batches."

Start by reviewing the existing sc.tools analysis tools and the R batchelor multiBatchPCA documentation. Define the intended behavior for PCA on merged experiments with imbalanced batch sizes, including how cells are weighted across batches. Done means Scanpy offers a documented PCA option that preserves resolution for subpopulations in smaller batches.