Dimensionality reduction techniques like PCA (Principal Component Analysis) can reduce storage needs for indexing by compressing high-dimensional data into fewer dimensions. When applied before building an index (e.g., for search or retrieval systems), PCA transforms the original features into a smaller set of orthogonal components that capture the most variance in the data. For example, a dataset with 1,000 features per item could be reduced to 50 principal components, cutting storage requirements by 95%. This compression simplifies the index structure (e.g., smaller vectors in a FAISS or Annoy index) and reduces memory/disk usage. It also speeds up similarity searches, as lower-dimensional distance calculations are computationally cheaper. For instance, in image retrieval, PCA might compress raw pixel or deep learning embeddings into a compact representation without discarding critical patterns.
However, this approach has trade-offs. First, PCA assumes linear relationships in the data and may fail to capture non-linear patterns. For example, in datasets with complex manifolds (e.g., word embeddings or graph data), PCA might discard subtle but meaningful variations. Second, reducing dimensions inherently loses some information, which can degrade retrieval accuracy. A nearest-neighbor search in the compressed space might miss relevant items that were distinguishable in the original high-dimensional space. Third, applying PCA adds preprocessing overhead. Computing principal components requires O(n³) time for covariance matrix decomposition, which becomes impractical for extremely large datasets. Additionally, the model must be periodically retrained if the data distribution changes over time, complicating maintenance.
Finally, there are domain-specific risks. For instance, in applications like fraud detection or genomics, discarding "less important" features via PCA could inadvertently remove critical signals. Similarly, indexing compressed representations may reduce interpretability, making it harder to debug why certain results are returned. Developers must balance storage gains against these trade-offs. Testing retrieval performance (e.g., recall@k) with and without PCA on a validation set is essential. Alternatives like autoencoders or t-SNE might better preserve non-linear relationships but often introduce higher computational costs or scalability limitations.