Randomized Constrained Matrix Decompositions
summary
Argues that embedding sparse PCA into variable projection and then applying a randomized range finder with power iterations and blocked QR yields a scalable solver that trades a bit of accuracy for huge speed and memory gains. Implements elastic-net and L0 penalties with proximal/coordinate updates, uses sketches (uniform, Gaussian, count sketch) and reports count sketch beating deterministic on a toy, handles a 36 GB dataset (700k spatial points × 37 years) on a laptop, lowers peak memory from ~6 GB to <4 GB and converges in ~100–150 iterations.
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chapters (7)
- 0:00Introduction to sparse PCA
- 2:40Formulating the problem
- 6:18Variable projection method
- 8:46Randomized PCA techniques
- 13:47Scaling with blocked schemes
- 17:13Climate data applications
- 21:03Q&A and discussion
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