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Thanks for the PR @yaichm.

Please follow the instructions of the automated comment above to resolve the failing linter continuous integration.

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The benchmark result graphs comparing execution time and reconstruction error with existing solvers will be added in the comment below.

Looking forward to it. Please feel free to ping me once done.

In this Kernel PCA benchmark (focus on the left side of the graph), our custom randomized_value solver shows better scalability compared to standard solvers when the number of components is large.

When increasing the number of samples, our randomized_value solver consistently achieves much lower execution times compared to the full solver. Even with large datasets, randomized_value remains highly efficient and scalable.

In this Isomap benchmark , for a small number of components, both solvers show comparable execution times. However, as the number of components increases ( > 10 ), randomized_value significantly outperforms the full solver, achieving much faster execution for large datasets.

The projections obtained with the auto solver and the randomized solver are visually very similar, confirming that the randomized solver preserves the structure and quality of the embedding. This highlights its reliability alongside its faster execution.

The reconstruction error is very similar between the auto and randomized solvers across different sample sizes. This confirms that the randomized solver preserves the quality of the reconstruction while offering faster execution.

I’ve followed the automated instructions and fixed the linter issues.

The benchmark result graphs have also been added.

@ogrisel , feel free to review whenever you are available.

Thanks to the team for finalizing these results !

So to summarize

• on KernelPCA, we see similar results with method 5.3 (randomized eigenvalues) than with the "trick" of using 4.3 (randomized SVD). This makes me quite confident that the implementation is correct
• on Isomap, where the "trick" could not be used (since matrices are not guaranteed to be PSD),
  • when the number of components is low (2), there is no drawback: the speed is the same than the current method based on arpack, and the result on sample dataset is identical (same visual figure, same reconstruction error)
  • we see clear speed benefits when the number of components is high (right figure of this message, where 50 components are selected). @yaichm It would be interesting to see the reconstruction error corresponding to this situation, to make sure that the speed gain was not obtained at the cost of increasing the reconstruction error

As requested by @smarie, here is the image showing the reconstruction error for 50 components.