Singular Value Decomposition (SVD) Tutorial
Singular Value Decomposition (SVD) Tutorial - Extending the SVD with More Factors PDF Print E-mail
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Singular Value Decomposition (SVD) Tutorial
How does SVD work?
Extending the SVD with More Factors
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The Full SVD Factorization

The full SVD for this example matrix (9 holes by 3 players) has 3 sets of factors. In general, a m x n matrix where m >= n can have at most n factors, so our 9 x 3 matrix cannot have more than 3 sets of factors. Here is the full SVD factorization (to two decimal places).


Phil Tiger Vijay
4 4 5
4 5 5
3 3 2
4 5 4
4 4 4
3 5 4
4 4 3
2 4 4
5 5 5
=

HoleDifficulty 1-3
4.34 -0.18 -0.90
4.69 -0.38 -0.15
2.66 0.80 0.40
4.36 0.15 0.47
4.00 0.35 -0.29
4.05 -0.67 0.68
3.66 0.89 0.33
3.39 -1.29 0.14
5.00 0.44 -0.36
*

PlayerAbility 1-3
Phil Tiger Vijay
0.91 1.07 1.00
0.82 -0.20 -0.53
-0.21 0.76 -0.62

By SVD convention, the HoleDifficulty and PlayerAbility vectors should all have length 1, so the conventional SVD factorization is:


Phil Tiger Vijay
4 4 5
4 5 5
3 3 2
4 5 4
4 4 4
3 5 4
4 4 3
2 4 4
5 5 5
=

HoleDifficulty 1-3
0.35 0.09 -0.64
0.38 0.19 -0.10
0.22 -0.40 0.28
0.36 -0.08 0.33
0.33 -0.18 -0.20
0.33 0.33 0.48
0.30 -0.44 0.23
0.28 0.64 0.10
0.41 -0.22 -0.25
*

ScaleFactor 1-3
21.07 0 0
0 2.01 0
0 0 1.42
*

PlayerAbility 1-3
Phil Tiger Vijay
0.53 0.62 0.58
-0.82 0.20 0.53
-0.21 0.76 -0.62

Latent Semantic Analysis Tutorial

We hope that you have some idea of what SVD is and how it can be used. Next we'll cover how SVD is used in our Latent Semantic Analysis Tutorial. Although the domain is different, the concepts are the same. We are trying to predict patterns of how words occur in documents instead of trying to predict patterns of how players score on golf holes.


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