PCA (Principal Component Analysis) can significantly reduce the memory footprint of vector embeddings. Using MSMarco with MiniLM (384 dimensions) as an example, the post walks through how covariance matrices and eigendecomposition identify redundant dimensions, then shows how to project embeddings into a lower-dimensional space using NumPy. Experimental results show that reducing from 384 to 200 dimensions retains ~88.5% of eigenvalue variance and achieves 0.879 recall vs. brute-force ground truth. The tradeoff depends on the embedding model's efficiency and the corpus distribution — models that already spread information evenly across dimensions compress poorly with PCA.
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