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.
Questions tagged [svd]
406 questions
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Singular value decomposition of a three-dimensional array
The Singular Value Decomposition (SVD) of a matrix is
$$A_{m\times n} = U_{m\times m}\Lambda_{m\times n} V_{n\times n}'$$
where $U$ and $V$ are orthogonal matrices and $\Lambda$ has (i, i) entry $\lambda_i \geq 0$ for $i = 1, 2, \cdots , min(m, n)$…
MYaseen208
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What is a "thin" svd?
I've seen lots of mention of this in the implementation of SVDs in various programming environments. What does it actually mean?
McPeterson
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Are there useful applications of SVD that use only the smallest singular values?
In a number of singular value decomposition (SVD) applications, for example Latent Semantic Indexing, only the biggest singular values are used to make searches and calculate distances.
Are there useful applications that drop the biggest singular…
Sergey
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Sphering data with SVD components of covariance matrix
The Elements of Statistical Learning says on page 113:
Sphere the data with respect to the common covariance estimates $\hat{\Sigma}$:
$X^* \leftarrow D^{-1/2}U^TX$ where $\hat{\Sigma} = UDU^T$. The common covariance estimate of $X^*$ will now…
Alec
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Definition of orthogonal matrix
I am reading the book Elements of Statistical Learning and trying to understand singular value decomposition (SVD). In particular, what is an orthogonal matrix as it relates to SVD?
According to Wikipedia, an orthogonal matrix is a square matrix,…
Iggy25
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SVD of quasi diagonal matrix
I have a problem where I need to compute many times the SVD of a "quasi-diagonal" matrix.
What I call a quasi-diagonal matrix is a diagonal matrix, except its last column. For example, an (m+1)-quasi-diagonal matrix:
\begin{bmatrix}
d_1 & 0 &…
F. Privé
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Has anyone seen Gibbs phenomenon in SVD?
I read the notes on online about Regularized matrix computation. It said
The truncated SVD solution has “ringing,” e.g., Gibbs’s phenomenon in
truncated Fourier series
I haven't seen any work related that has SVD and producing the Gibbs's…
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The bias of users and items in SVD++
I'm reading Yehuda Koren's paper: "Factorization Meets the Neighborhood: a Multifaceted Collaborative Filtering Model" SIGKDD 2008.
I notice that in the traditional neighborhood method, say the baseline one:
$\hat{r_{ui}} = \mu + b_u + b_i $
Here…
ice_lin
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Truncated SVD: how do I go from [Uk, Sk, Vk'] to low-dimension matrix?
I have a large word-frequency matrix (~6m unique words X ~4k documents) and I'm trying to use truncated singular value decomposition (SVD) to project it onto a matrix with fewer dimensions. I know how to get to $[U_{k}, S_{k}, V_{k}']$, but I don't…
Parzival
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Calculate document similarity with SVD for unseen documents?
Is it possible to transform a document into a latent semantic space calculated with SVD without recomputing the SVD, or even doing a rank one update? I don't care about updating the $U$, $\Sigma$, or $V$ matrices, but I am interested in being able…
alltom
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