[ENH] Support geographically weighted decomposition (starting with GWPCA)

[aman-coder03]

I have been exploring the existing geographically weighted estimators in gwlearn and was wondering whether it would make sense to extend the framework to unsupervised models, starting with Geographically Weighted PCA (GWPCA).

The idea would be to introduce a small base abstraction (e.g., BaseGWDecomposition) that reuses the current neighborhood and spatial weighting logic, but operates directly on X instead of (X, y). Since sklearn.decomposition.PCA does not support sample_weight, this would likely require computing a weighted covariance matrix (or weighted SVD) for each focal observation.

The goal would be to keep the API consistent with scikit-learn conventions (e.g., components_, explained_variance_) and compatible with libpysal.graph.Graph, similar to the current GW estimators.

If this aligns with the direction of gwlearn, I would be happy to draft an initial implementation for discussion.

Would appreciate your thoughts

[martinfleis]

This is certainly in scope. It is even included in our Google Summer of Code ideas https://github.com/pysal/pysal/wiki/Google-Summer-of-Code-2026#implementation-of-geographically-weighted-matrix-decomposition-algorithms

[aman-coder03]

Can I work on this?

[FirePheonix]

discussion can be certainly done on this.. even I've been working on this, I have a some api code for discussion much related to this..
but, isn't this the delivery of this expected to be during the GSoC contribution period itself? i think it'd be rushing since I've read the code and complexity, thinking of playing long term...

but yes, we should certainly go with what Martin has to say about this:)

[aman-coder03]

My intention here was mainly to start the design discussion and understand how the maintainers would prefer this to be structured within the existing framework.
Happy to collaborate and explore this properly rather than rush it

[martinfleis]

I honestly haven't given it that much thought as I anticipated that some solutions will be suggested by the GSoC student (if we get one). In principle I'd like this to follow Harris et al 2011, while sticking to the API model we have now. So essentially scikit-learn with some additions related to geography. Built again on top of Graph for flexibility of neighborhood definition. Whether we'll be able to use PCA implementation from sklearn like we do with predictive models, that is something I did not spent a minute on. Though it is secondary.

[aman-coder03]

Based on Harris et al 2011 my understanding is that GWPCA would involve computing a spatially weighted covariance matrix for each focal observation and then performing a local eigen decomposition to obtain location-specific components and explained variance.
i would aim to structure it similarly to the current GW estimators reusing the Graph-based neighborhood logic and exposing results with sklearn-style attributes, just adapted to be location-specific.
since sklearn’s PCA doesn’t support sample_weight, a custom weighted covariance + eigen/SVD step might be the cleanest approach. if that sounds reasonable, I can draft a small API sketch for discussion before moving toward implementation.

[AshishRaj97]

I have also been going through Harris et al 2011 to better understand the expectations for GWPCA.
From my understanding the main idea is to compute a spatially weighted covariance matrix at each focal location and then performing a local eigen decomposition to obtain location-specific loadings and explained variance.

since we are estimating a local covariance matrix at every location, if the bandwidth is relatively small compared to the no. of features we could get into rank deficiency or unstable components. In the current GW estimators we have already used min-proportion for local degeneracy, i am thinking whether something similar would make sense here.

i was also thinking about interpretability becuase eigenvectors are sign arbitrary, we might see sudden sign flips between nearby locations even if the underlying structure is similar. it may be worth discussing about alingment strategy should be considered or whether it is better left to users.

From design perspective, building this on top of Graph keeping the api conssitent with sklearn estimators seems like the right direction.

[martinfleis]

This is a reference implementation https://github.com/cran/GWmodel/blob/master/R/gwpca.r In case of doubt, consult that.

[aman-coder03]

Thanks @martinfleis i have started reviewing the GWmodel implementation to understand the exact workflow
i will translate that logic into a gwlearn-style design using Graph for neighborhoods and draft a small API sketch aligned with the current estimators.
will follow up shortly with something concrete for discussion(maybe API sketch)

[martinfleis]

I don't have much capacity to engage with that right now, so it might wait for a response for a bit.