spectral-embedding-scalability-benchmarking

spectral-embedding-scalability-benchmarking

Summary

Benchmark the matrix-free spectral embedding algorithm (tl.spectral) in SnapATAC2 to validate its claimed linear time and space complexity when applied to single-cell datasets of 10 million or more cells. This skill confirms scalability performance through empirical measurement of runtime and peak memory consumption against the theoretical complexity claim.

When to use

Apply this skill when you have a large single-cell count matrix (≥10 million cells) in CSR format and need to verify whether the matrix-free spectral embedding in SnapATAC2 achieves its documented linear scaling behavior on your hardware and dataset characteristics. Use it as a validation step before committing large-scale analyses or as a performance regression test when upgrading SnapATAC2 versions.

When NOT to use

• Input matrix is already embedded or has been pre-reduced to <10 million cells; use this skill only when validating large-scale scalability is the explicit goal.
• You lack memory profiling tools or cannot isolate the spectral embedding step from the surrounding pipeline; meaningful benchmarking requires isolated, repeatable measurement.
• The research question does not concern algorithmic scalability or performance validation; if you only need the embedding result, apply tl.spectral directly without instrumentation.

Inputs

• Single-cell count matrix with ≥10 million cells in CSR (compressed sparse row) format
• SnapATAC2 AnnData object or compatible matrix container

Outputs

• Wall-clock runtime measurements (seconds) as a function of cell count
• Peak memory usage profile (megabytes or gigabytes) throughout spectral decomposition
• Spectral embedding matrix with weighted eigenvectors
• Performance plot comparing observed time/space complexity to linear scaling expectation

How to apply

Load or generate a single-cell count matrix with ≥10 million cells and initialize it in CSR format compatible with SnapATAC2. Execute tl.spectral using the default cosine similarity metric (as of Release 2.3.0) while capturing wall-clock runtime using Python's time module or system profiler (e.g., cProfile). Monitor peak memory usage throughout spectral decomposition using a memory profiler such as memory_profiler or psutil. Document the number of eigenvectors returned and verify they are weighted by eigenvalues (default behavior in Release 2.3.0) to confirm correct output structure. Finally, plot the measured execution time and peak memory against dataset size and compare the observed slopes to the linear complexity claim; deviation from linearity may indicate algorithmic, hardware, or data-specific constraints.