Questions tagged [singular-value-decomposition]
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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 (otherwise known
as word vectors), we first loop over…
Daschin
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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 $A$ are the data points in $d$ dimensional space.…
hanugm
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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 $k-$dimensional subspace that best fits the given data…
hanugm
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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 application of SVD. Like movie recommendation system,…
F.C. Akhi
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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. Would there be any interesting applications in…
Samuel
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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?
DRV
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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, approximate the matrix using a matrix of a different…
postnubilaphoebus
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