# Questions tagged [singular-value-decomposition]

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### Dimensionality Reduction of a matrix preserving number of rows

Let A ($d \times k$) be a matrix such that k < d. How to reduce the dimension of the matrix A to another lower dimension matrix B ($d \times l$ ) such that $l < k$. Note that, while reducing ...
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### Approximate weight matrices of pretrained models

I am looking for a guide on matrix approximation of pretrained models. My idea is related to transfer learning: I want to use a pretrained model, take the weights and biases of one of its layers, ...
1 vote
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### What is the role of left singular vectors in SVD?

SVD decomposition of a data matrix $A$ of order $n \times d$ and rank $r$ can be expressed as follows $$A_{n\times d} = U_{n\times r}D_{r \times r}V^{T}_{r \times d}$$ The rows of the data matrix $A$ ...
1 vote
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### How many singular vectors do we need to calculate for SVD?

In the geometrical interpretation of SVD, the data points that we have need to be imagined as points in high dimensional space (say $d$-dimensional space). But we need to find a hyperplane in $k-$...
1 vote
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### Human intuition behind SVD in case of recommendation system

This does not answer my question. I struggled very hard to understand the SVD from a linear-algebra point of view. But in some cases I failed to connect the dots. So, I started to see all the ...
1 vote
134 views

### Applications of polar decomposition in Machine Learning

Assume there exists a new and very efficient algorithm for calculating the polar decomposition of a matrix $A=UP$, where $U$ is a unitary matrix and $P$ is a positive-semidefinite Hermitian matrix. ...
1 vote