# Questions tagged [matrix-decomposition]

Matrix decomposition refers to the process of factorizing a matrix into a product of smaller matrices. By decomposing a large matrix, one can efficiently perform many matrix algorithms.

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• 101
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### Decomposing Distance Matrix D for approximating Original Matrix A

Let's say we have a matrix $A \in R^{n \times d}$ where n is the number of elements and d is the dimension size. And we calculate the pairwise distances between each elements; say cosine for instance ...
• 103
227 views

### Matrix dimensions in Linear Algebra vs Time series Analysis

I am confused or may misunderstand the dimensions of a Matrix when I was reading about time series analysis. From what I understand in linear Algebra, if we have a Matrix $A \in \mathbf{R}^{m*n}$, ...
• 23
536 views

### Funk SVD for binary data - product like or dislike

Assume the following situation: you have a user-item sparse matrix. However, instead of the usual 1 to 5 rating scale, items can only receive a positive (1) or negative (-1) feedback. Thus, the matrix ...
• 143
1 vote
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### CP Tensor Decomposition and Correlating Sample Magnitudes with Variables of Interest

I am learning about tensor decomposition, specifically CP, and am trying to understand if I can use it for my research. To give a bit more detail, I have brain imaging data from 10 participants, with ...
• 335
139 views

### Constrained Matrix Decomposition

I am working on a structural vector autoregression that requires imposing constraints on a matrix factorization. In particular, I have an N-dimensional positive definite matrix $\Sigma$ that I need to ...
• 2,287
1 vote
100 views

### How to decompose a random walk (array) into its Markov Chain transition matrix?

The algorithm, PageRank, receives a Markov Chain transition matrix (page links from one to another.) Either by random walk, or more efficiently, eigenvectors, the stationary distribution of the Markov ...
• 3,386
65 views

### Is the first independent component of independent component analysis always important?

I was looking at a neuroscience paper that used ICA to reduce dimensionality of calcium signaling profiles in 20 randomly selected neurons of a zebrafish brain. I presume that in Figure 2, ICA was ...
• 21
1 vote
27 views

### Relation between low-rank approximation, nuclear norm of a matrix and Singular Value Decomposition

I'm reading the following paper https://arxiv.org/pdf/2005.10203.pdf which proposes improvements on robustness of large graphs to defend against adversarial attacks that are nothing but slight ...
• 647
1 vote
67 views

### Latent factors are the same in both decomposed matrices?

This question is in the context of recommendation systems. We can use matrix factorization techniques to decompose a user-product explicit/implicit matrix(R) into two matrices(U, P). Let's say R is a ...
• 1,007
1 vote
892 views

### Why absolute value of eigenvalues are used in PCA or LDA?

In PCA and LDA techniques, eigenvectors with the $k$ largest eigenvalues give principal components. However, when selecting these eigenvalues, are they to be sorted by the absolute value (regardless ...
• 11
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### Drawing samples from matrix normal

I have to generate $n \times m$ sample ($A$) from a matrix normal distribution, given two covariance matrices: $n \times n$ row covariance matrix (matrix $B$) (defines the covariance between the rows ...
• 51
1 vote
322 views

### Are principal component analysis (PCA) and empirical orthogonal function (EOF) methods the same?

As far as I've seen, EOF is just PCA but instead of thinking about the data matrix X as (number of samples, number of features), you consider it as (number of time points, number of different spatial ...
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### Matrix Factorization and Linear Regression

Which matrix factorization algorithm is used in LinearRegression() function of scikit-learn?
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• 111
1 vote
96 views

### Fastest way to find Leading singular value and vector (power iteration, rsvd etc)

I want to know the fastest way to find out the leading singular value and vector of a large rectangular matrix. I have seen 2 suggestions and have questions on both of them : Power Method : For this ...
292 views

### How to explain the numerical discrepancy between FactoMineR::PCA() and the svd() in their output of the U matrix?

I am comparing the output of two functions in R to do Principal Component Analysis (PCA), the FactoMineR::PCA() and the ...
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