Lecture_13_02 - Matrix Decomposition and Latent Semantic...

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Matrix Decomposition and Latent Semantic Indexing (LSI) Introduction to Information Retrieval INF 141/ CS 121 Donald J. Patterson
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Outline Latent Semantic Indexing Introduction Linear Algebra Refresher
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Star Cluster NGC 290 - ESA & NASA Latent Semantic Indexing - Introduction
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Star Cluster NGC 290 - ESA & NASA Latent Semantic Indexing - Introduction A picture of the sky is two dimensional The stars are not in two dimensions When we take a photo of stars we are projecting them into 2-D projecting can be defined mathematically When we see two stars that are close.. They may not be close in space When we see two stars that appear far... They may not be far in 3-D space
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Star Cluster NGC 290 - ESA & NASA Latent Semantic Indexing - Introduction When we see two stars that are close in a photo They really are close for some applications For example pointing a big telescope at them Large shared telescopes order their views according to how “close” they are.
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Overhead projector example Latent Semantic Indexing - Introduction
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Overhead projector example Latent Semantic Indexing - Introduction Depending on where we put the light (and the wall) we can make things in three dimensions appear close or far away in two dimensions. Even though the “real” position of the 3-d objects never moved.
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Mathematically speaking Latent Semantic Indexing - Introduction This is taking a 3-D point and projecting it into 2-D The arrow in this picture acts like the overhead projector ( 10, 10, 10) ( x, y, z) ( 10, 10) ( x, y) 10 10 10 10 10
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Mathematically speaking Latent Semantic Indexing - Introduction We can project from any number of dimensions into any other number of dimensions. Increasing dimensions adds redundant information But sometimes useful Support Vector Machines (kernel methods) do this effectively Latent Semantic Indexing always reduces the number of dimensions
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Mathematically speaking Latent Semantic Indexing - Introduction Latent Semantic Indexing always reduces the number of dimensions ( 10, 10) (x,y) ( 10 ) (x) 10 10 10
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Mathematically speaking Latent Semantic Indexing - Introduction Latent Semantic Indexing can project on an arbitrary axis, not just a principal axis
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Mathematically speaking Latent Semantic Indexing - Introduction
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