Questions tagged [singular-value-decomposition]
The singular-value-decomposition tag has no usage guidance.
8
questions
0
votes
0
answers
6
views
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 ...
- 111
0
votes
0
answers
17
views
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
0
answers
51
views
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 $A$ ...
- 3,612
1
vote
1
answer
168
views
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 $k-$...
- 3,612
1
vote
0
answers
37
views
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 ...
- 111
1
vote
0
answers
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. ...
- 11
1
vote
0
answers
36
views
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?
- 1,613
3
votes
1
answer
285
views
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 (...
- 149