[Dimensionality reduction] Add supervised dimensionality reduction task

[michalk8]

Describe the problem concisely. Include references to papers where the task is attempted. This issue introduces the subtask of supervised dimensionality reduction - some dimensionality reduction methods can improve the result by including auxiliary information, such as class labels (cell types, etc.).

Propose datasets Include links to at least one publicly available dataset that could be used. All the datasets in label projection task can be used as a starting point.

Propose methods Include links to codebases of at least two methods that perform the task. Supervised UMAP/LDA from umap-learn and scikit-learn.

Propose metrics Describe at least one metric by which to measure success on the task. It must be able to be applied to the proposed datasets. Silhoutte score or scores mentioned from https://genomebiology.biomedcentral.com/articles/10.1186/s13059-020-02128-7

[LuckyMD]

This is a great idea! I wasn't actually aware of supervised dim red tasks... it sounds like a very specialized use case... but interesting nonetheless. Would this task involve dim red to 2 dimensions (visualization) or to more (summarization)? Whichever you choose, i would borrow some metrics from that task to have some consistency. For metrics to evaluate e.g., clustering in this space, you could also borrow some from #241. This might have some overlap with the multi-modal manifold mapping task proposed in #281 as well.

[github-actions[bot]]

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