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 ...
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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 $A$ ...
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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 $k-$...
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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 ...
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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. ...
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What is the difference between principal component analysis and singular value decomposition in image processing?

What is the difference between principal component analysis and singular value decomposition in image processing? Which one performs better, and why?
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What is $USV^T$ in the context of word embeddings?

Here is an excerpt from the notes of the first lecture of the course CS224n: Natural Language Processing with Deep Learning. 3 SVD Based Methods For this class of methods to find word embeddings (...