ProjectionVisualizer: unifying functionality of PCA and Manifold

[bbengfort]

One of the basic high-dimensional visualization techniques that Yellowbrick makes use of is to decompose or project a high dimensional space into 2 or 3 dimensions to display the data as a scatter plot. Projections of this kind reduce the amount of space between points (decreasing sparsity) but can still give us some intuition of structures in the higher dimensionality. Currently, we have three primary decomposition methods that use this technique:

• Manifold: wraps a non-linear transformer from sklearn.manifold to produce embeddings
• PCA: uses linear principal component analysis to decompose to lower dimensionality
• Text: TSNE and UMAP visualizers do the same as Manifold but with text-specific helpers

These visualizers have a lot of shared functionality that can be combined to streamline these kinds of visualizations and make it easier to extend them (e.g. to add ICA, Fast PCA, etc. to the PCA decompositions, or to extend the text visualizers to use the manifold visualizations).

I propose we create a ProjectionVisualizer base class or mixin that knows how to:

• Wrap a transformer to project X into X' of shape (n_instances, 2) or (n_instances, 3)
• Create a scatter plot for 2D or 3D plots (implemented in PCA)
• Identify the type of the target and add colors (implemented in Manifold)
• Subselect the features to use in X for the projection

This shared functionality could then be easily used by PCA, Manifold, etc.

The following notes about the class hierarchy:

• The MultiFeatureVisualizer produces a self.features_ attribute on fit() which is useful in PCA for biplots and to understand the original feature set.
• The DataVisualizer produces self.classes_ from y and is supposed to "provide helper functionality related to target identification" but does not currently implement this yet (it is implemented on Manifold)
• yellowbrick.contrib.ScatterVisualizer might be valuable to be moved to yellowbrick.draw.scatter and use as a mixin to handle part of these cases; though I don't necessarily want to confuse things too much.
• The JointPlot visualizer would also benefit from the target color handling things from above.

This implies that the ProjectionVisualizer is a DataVisualizer and that the DataVisualizer needs to be updated to handle the target identification stuff that is in Manifold. It also implies that JointPlot should be a DataVisualizer as well.

More investigation on this topic is necessary, but I wanted to propose this solution to allow for further discussion by @DistrictDataLabs/team-oz-maintainers and @naresh-bachwani who is working on PCA this summer.

[naresh-bachwani]

Thanks, @bbengfort for summarizing this. This makes things simplified for me.

[bbengfort]

This might also be useful for #889

[rebeccabilbro]

Just a note that this issue would have the potential to close (or at least address portions of) a lot of existing issues:

• Improvements to the Manifold Visualizer #437
• Add legend option to PCA visualizer  #458
• Enhance PCA Decomposition #476
• PCA projections on biplot are not clear for datasets with large number of features #795

[bbengfort]

This was finished #930 and #937