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Results tagged with svd
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user 13669
Singular value decomposition (SVD) of a matrix $\mathbf{A}$ is given by $\mathbf{A} = \mathbf{USV}^\top$ where $\mathbf{U}$ and $\mathbf{V}$ are orthogonal matrices and $\mathbf{S}$ is a diagonal matrix.
27
votes
How do I use the SVD in collaborative filtering?
When you take the SVD of the social graph (e.g., plug it through svd()), you are basically imputing zeros in all those missing spots. … If I don't have a way to do that, then I shouldn't fill them before I do the SVD.*
SVD with Missing Values
Of course, the svd() function doesn't know how to cope with missing values. …
- 2,031
27
votes
Accepted
What happens when you apply SVD to a collaborative filtering problem? What is the difference...
$\DeclareMathOperator*{\argmin}{arg\,min}$
Ok, when you say SVD, presumably you're talking about truncated SVD (where you only keep the $k$ biggest singular values). … There are two different ways to look at the truncated SVD of a matrix. …
- 2,031
3
votes
What fast algorithms exist for computing truncated SVD?
Here's a technique I have used successfully in the past for computing a truncated SVD (on the Netflix dataset). It is taken from this paper. … In a collaborative filtering setting, I should note that most of the values are missing and the point is to predict them, so to use truncated SVD to solve such a problem, you have to use a technique that …
- 2,031
7
votes
PCA when the dimensionality is greater than the number of samples
Coming at this from a different angle:
In PCA, you're approximating the covariance matrix by a $k$-rank approximation (that is, you only keep the top $k$ principal components). If you want to picture …
- 2,031
11
votes
Accepted
SVD of a data matrix (PCA) after smoothing
Why your first thoughts led you astray:
When you take the SVD of a matrix, $U$ and $V$ are unitary (orthogonal). … Then just zero-pad the middle matrix, and you've got the full SVD.
Intermediate smoothing
Presumably you're not going to do such extreme smoothing. So, what does this mean for you? …
- 2,031