Questions tagged [svd]

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.

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prove for Eckart-young in Frobenius norm

On page 74, linear algebra and learning from data. P74 the prove for Eckart-young in the frobenius norm. I couldnot understand why G = 0 in the proof, anybody can help me? Thank you!
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Suppose I work with vectors from a high dimensional space with $100<N<1000$, e.g. word-embeddings. Say I have, already selected $R$ vectors, with $R\simeq10$, which form a matrix $M \in \mathbb{... 0answers 15 views Applying SVD on dataset with 4 columns I have a dataset with following format and 200000 rows: X Y Z A 5608 142 740 1 4533 142 741 2 5620 143 740 0 4732 142 744 1 5500 143 742 1 5514 142 741 2 I am ... 0answers 24 views Can I use the matrix$U$instead of the matrix$V\$ in Principal Component Analysis?

I'm taking Andrew NG's Machine Learning Course and got to the part of Principal Component Analysis. Andrew's implementation of PCA aroused 2 questions for me. 1. Let's say that we have the data ...
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SVD -> PCA -> t-SNE; Does it make sense?

I have a data set of size (4600, 10000). I did L2 normalization at first, then I did the following two steps to visualize it in a lower dimension: ...
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Is each row of latent factors obtained from matrix decomposition (SVD) dependent on the other rows of the higher dimensional matrix?

I implemented a recommendation system using user-user interaction data, learning missing ratings through alternating least squares and matrix factorization, which as I understand it, adjusts and ...
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Why is there a reconstruction loss in PCA with orthonormal eigenvectors?

I've already read How to reverse PCA and reconstruct original variables from several principal components? and I understand conceptually and visually why there has to be a reconstruction loss. ...
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How to make a scree plot out of SVD data to validate PCA

After doing a singular value decomposition (SVD) of a data set, I'm left with three matrices: 1. An orthogonal Left Singular Vector (U) 2. diagonal matrix with elements in descending order (S) 3. ...