Concept - Truncated SVD
Definition
Dimensionality reduction by zeroing out all but the largest singular values in (“abandon unimportant topics”, s.185, s.187). Documents become ; new documents are mapped with (s.188-189, s.192). must be less than the original matrix rank (s.189).
Why (s.186)
Singular values tell the importance of each dimension. Setting the less important to zero keeps important information, drops details. Details may be noise (reduced LSI is less noisy) or make similar things dissimilar (reduced LSI represents similarity better).
Example (s.187-188)
Keep 2.162501 and 1.594382 (topic1, topic2). New feature space has 2 dimensions; cosine(doc4, doc5) = 0.75020516 versus ~0 in the full space. New doc (0,0,1,1,1) -> (-0.867549, 0.195819) (s.189).
Related
Concept - Singular Value Decomposition (SVD) | Concept - Latent Semantic Analysis (LSA) | Concept - Cosine Similarity | Concept - Feature Selection