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Results tagged with svd
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user 109500
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.
2
votes
0
answers
335
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Is there a supervised/semi supervised version of pca for dimensionality reduction?
PCA can give me the proper result if "Large variances have important dynamics" holds true for the data. In other words if I want to know along which components the variance of my data is maximized, pc …
- 603
2
votes
0
answers
206
views
Why 1 norm of reconstruction error is not used/minimized for low rank approximation using PCA?
In pca, I see reconstruction error is calculated in terms of either frobenius norm or spectral norm. And I also saw they have a closed bound in terms of singular values.
My question is why 1 norm of r …
- 603
0
votes
0
answers
21
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What is the difference between S (singular values) returned by SVD function and latent retur... [duplicate]
I ask this because from my understanding, they both are same, because they both denote variance along most important dynamics. So their corresponding values should be the same, but as clearly seen in …
- 603
1
vote
1
answer
1k
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What is the fastest way to calculate the leading singular value of a very large matrix (10ml...
I only know of the following power iteration. But it needs to create a huge matrix A'*A when both of rows and columns are pretty large. And A is a dense matrix as well. Is there any alternative to pow …
- 603
2
votes
1
answer
819
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Why spectral norm low-rank approximation error is stronger than frobenius norm?
Suppose a rank $k$ matrix $Z$ with orthonormal columns $z_1,..., z_k$ satisfies
Frobenius Norm Error: $$\|A − ZZ^TA_k\|_F ≤ (1 + \epsilon)\|A − A_k\|_F -- (1)$$
It is said that Frobenius norm error i …
- 603