# Questions tagged [singular-value-decomposition]

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### Recommendation and prediction system for learning performance of students

I would like to start my master's thesis soon. The topic is "the use of collaborative filtering for creating recommendations and predictions of learning performance". I have a dataset that ...
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
90 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