# 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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### Optimal truncation in SVD

I am working with SVD on a matrix $$Y_{m,n} = T_{m,m} \Sigma D^T_{n,n}$$ where $T$ and $D$ describe the row and the column entities of Y, respectively. The truncated SVD takes the first $r$ ...
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### PCA: understanding how to use loading vectors of X to recapture the geometry of X

If we suppose that X is an n x d matrix, and then perform PCA to obtain loading vectors ...
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### Does PCA centering guarantee projection optimality onto an affine set subject to dimensionality constraint?

Say I have $m$ points in $R^n$, not necessarily with sum 0, and I want to project them onto an affine set $S$ with $\dim(S)=d$ for a given $d$ so as to minimize the sum of the squared distances ...
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### calculate correlation coefficient with singular values of covariance matrix

Given a normal distribution where the covariance matrix $\Sigma$ has known singular values $s_1$, $s_2$, ... $s_m$, what are the Pearson's correlation coefficient values?
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### How to calculate RMSE with missing values except filling them with zeros? [duplicate]

I have a real and predicted matrix of the form np.array and I calculate the RMSE using Sklearn: ...
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### Dot product and linear combination of Basis

I am currently going through the SVD intuition provided here. In the section "From intuition to definition", It says that, First, note that any vector $\textbf{x}$ can be described using ...
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### what is the difference between factor analysis and SVD? factanal() vs svd()

I am doing factor analysis. Some sources tell me that I should use factanal() to do (exploratory) factor analysis; my goal is to find common sources of latent ...
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### Use K-means clustering on SVD/PCA of data

In an assignment I was suppose to perform K-means clustering on the MNIST dataset (just the 0's and the 1's) and then use SVD/PCA to visualize the data in two dimensions. I missunderstood this and ...
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