Supervised Dimensionality Reduction for Text Data in scikit-learn
Try ISOMAP. There's a super simple built-in function for it in scikits.learn. Even if it doesn't have some of the preservation properties you're looking for, it's worth a try.
I'm trying to use scikit-learn to do some machine learning on natural language data. I've got my corpus transformed into bag-of-words vectors (which take the form of a sparse CSR matrix) and I'm wondering if there's a supervised dimensionality reduction algorithm in sklearn capable of taking high-dimensional, supervised data and projecting it into a lower dimensional space which preserves the variance between these classes. 
The high-level problem description is that I have a collection of documents, each of which can have multiple labels on it, and I want to predict which of those labels will get slapped on a new document based on the content of the document.
At it's core, this is a supervised, multi-label, multi-class problem using a sparse representation of BoW vectors. Is there a dimensionality reduction technique in sklearn that can handle that sort of data? Are there other sorts of techniques people have used in working with supervised, BoW data in scikit-learn?
Thanks!