Geometric Aspects of Semantic IndexingDr. Heinrich Hartmann (Oxford)

WeST Koblenz, 31.08.2012

Outline

1. Latent Semantic Analysis

2. Geometry of SVD

3. Common Ground

Part 1Latent Semantic Analysis

Problem. Given a set of documents(D1,...,DN)

which documents have a similar topic?

Answer. Latent Semantic Analysis (Deerwester, et. al. 1990)

Latent Semantic Analysis - 2

Latent Semantic Analysis - 3

Latent Semantic Analysis - 4

Latent Semantic Analysis - 5

Part 2Geometry of SVD

Study geometry of the associated map!

Part 3Common Ground

Common GroundThe extremal vector

Which meaning has the extremal vector?

Inside the term-space.

Common GroundExample 1

Common GroundExample 2

Common GroundExample 3

Common GroundConclusion

The extremal vector represents the Dominant Topic.

Thank You