Fix Laplacian calculation in spectral partitioning #2568
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Also partially answers #379, though we may want additional testing beyond what is provided here. |
In the previous implementation of spectral partitioning, the eigenvalue computation was actually performed on the original adjacency matrix, not the graph Laplacian thereof. This change provides a utility for computing the graph Laplacian, which is then fed into the new implementation of the Lanczos solver. An additional test is provided to ensure that the end-to-end spectral partitioning quality is as expected.
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| const_cast<index_type_t*>(A.row_offsets_), | ||
| const_cast<index_type_t*>(A.col_indices_), |
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Must we do this instead of removing const-reference from the function signature?
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That is a very good question, and I don't immediately remember why I did it this way. Let me try to figure that out and either fix it or add an explanatory comment.
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Realized that I lifted this from the same logic here. Looks like there were some const-correctness issues in the PR that introduced the new solver. I'll see if I can fix them now.
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We are performing similar casts throughout the codebase around csr_matrix objects. To fix it here and elsewhere, we'll need quite a few changes to csr_matrix to support a const version of the view method. How would we feel about doing that in a follow-up, since it will be a fairly large change in its own right?
| namespace spectral { | ||
| namespace matrix { | ||
| namespace sparse { | ||
| namespace linalg { |
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Sorry, I just realized this was detail code. Can we please pull this into the detail/ directory and expose a wrapper function around it? That's how we hide the impl details (since this is header only) to make it blatantly clear to users where the public APIs are (it's been more challenging to do this than it should be for header-only).
These changes enable the use of the new Lanczos solver for spectral partitioning. This solver gives the correct eigenvalues in some cases where the old solver did not, but a previous attempt to introduce this led to a downstream breakage because the Laplacian was not being calculated correctly in the spectral partitioning logic.
In this PR, we introduce a new
compute_graph_laplacianfunction to correctly generate a new CSR matrix representing the graph Laplacian of the input CSR-formatted adjacency matrix. This resolves #2419. This function is used in the spectral partition function to obtain the correct partitioning using the new Lanczos solver. This eliminates all internal uses ofcomputeSmallestEigenvectors, the old Lanczos implementation, which should allow it to be removed after a deprecation cycle for downstream consumers. This will in turn allow us to resolve #313.Note that the originally-reported breakage from the previous attempt to switch to the new Lanczos solver was used to create the test confirming correct functionality of the current PR.
This PR is marked as a bugfix because it unblocks usage of the corrected Lanczos implementation. It is based on and requires PR #2541, and it will be marked as draft until that PR is merged.