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Embeddings & Similarity Search • Dimensionality Reduction (PCA, UMAP)Hard⏱️ ~3 min

Advanced Patterns: PCA with Quantization and Refresh Strategies

PCA + QUANTIZATION PIPELINE
A common production pattern combines PCA with product quantization for extreme compression. The pipeline: (1) apply PCA to decorrelate and reduce dimensions, (2) apply scalar or product quantization to the reduced vectors.
Why PCA before quantization? PCA decorrelates dimensions—the principal components are orthogonal. Quantization works better on decorrelated data because each dimension can be quantized independently without losing covariance information. Empirically, PCA + PQ achieves 10-20% better recall than PQ alone at the same code size.
Example: 768-dim to 128-dim PCA (6x reduction), then 32-byte PQ codes (4x additional compression). Total: 24x compression with 90%+ recall maintained.
RANDOM PROJECTION AS ALTERNATIVE
Random projection is simpler than PCA: multiply by a random matrix. The Johnson-Lindenstrauss lemma guarantees that random projection approximately preserves pairwise distances with high probability if the target dimension is O(log N).
Advantages: no training required, no drift (the random matrix never goes stale), trivially parallel. Disadvantages: requires more dimensions than PCA to achieve same quality (typically 2-3x more).
Use random projection when you need simplicity and do not want to manage PCA retraining. Use PCA when you need maximum compression ratio and can afford periodic retraining.
INCREMENTAL PCA
Standard PCA requires all data in memory. For very large datasets or streaming data, use incremental PCA: update the projection as new data arrives without reprocessing historical data.
Incremental PCA processes data in batches, updating covariance estimates and eigenvectors after each batch. Quality is slightly lower than full PCA (5-10% more variance required for same recall) but enables continuous updating.
Use case: indexing new content daily without full retraining. New embeddings are projected using current PCA, and PCA is updated weekly from accumulated new data.
LEARNED DIMENSIONALITY REDUCTION
Instead of unsupervised PCA, train a neural network to reduce dimensions while optimizing task metrics. The network learns which dimensions matter for your specific retrieval or classification task.
Autoencoder approach: encoder reduces dimensions, decoder reconstructs. Train end-to-end on reconstruction loss, or add retrieval loss (triplet loss, contrastive loss) to optimize for similarity preservation.
✅ Best Practice: Start with PCA as baseline. If recall is insufficient, try PCA + PQ. If you need extreme compression, evaluate learned reduction. Complexity should match the problem.

💡 Key Takeaways

✓PCA before quantization decorrelates dimensions, improving PQ recall 10-20%

✓Random projection needs no training and never drifts, but requires 2-3x more dims

✓Incremental PCA enables continuous updates without full retraining

✓Learned reduction (autoencoders) can optimize for task metrics, not just variance

📌 Interview Tips

1Interview Tip: Explain PCA + PQ pipeline—decorrelate first for independent quantization, achieve 90%+ recall at 24x compression.

2Interview Tip: Compare PCA vs random projection—PCA is better quality but requires retraining; random projection is simpler.

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