This capstone note closes Topic 7 and Stage 3 by showing the SVD-truncation machinery — the Eckart-Young theorem, the full eigenportfolio derivation — is not finance-specific at all. Applied to a pixel-intensity matrix, it is image compression; applied to a term-document matrix, it is latent semantic analysis, a foundational technique in information retrieval and an ancestor of modern text embeddings. Seeing the identical mathematics in two genuinely different domains is the clearest possible demonstration that the SVD's optimality (Theorem 1 of the Eckart-Young note) is a structural fact about matrices, not a coincidence of financial data.
Learning objectives. By the end of this note you should be able to:
- describe image compression as a direct Eckart-Young application;
- describe latent semantic analysis as PCA applied to a term-document matrix;
- compute a compression ratio from a chosen rank ;
- explain what "latent" concepts mean in the LSA context, using the eigenportfolio analogy.
In this lesson
- Image compression
- Latent semantic analysis
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