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.
297 questions
0 votes
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41 views
Efficient inversion and/or decomposition of block Toeplitz matrix in R (or else)?
I am working with a multivariate stationary Gaussian process characterized by a block Toeplitz covariance matrix. I often need to invert the matrix to calculate conditional expectations and variances ...
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1 vote
0 answers
59 views
Is there a standard method to construct stochastic representations for random matrices? [closed]
As the title says, I would like to know how to construct stochastic representations of random matrices whose distribution is known. Since it may not exists a general method, I would quite appreciate ...
- 111
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64 views
Should Data Be Weighted Differently for PCA vs. SVD ($\cos(\text{latitude})$ or $ \sqrt{\cos(\text{latitude})}$)
Background I am analyzing data on a latitude-longitude grid and want to account for geographic distortions caused by the Earth's curvature (higher data density near the poles). To correct this, I plan ...
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1 vote
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55 views
INDSCAL as a special case of CANDELINC
Here is my attempt to show that INDSCAL as a special case of CANDELINC. I am using the following paper as my reference for definitions. Kolda, Tamara G., and Brett W. Bader. "Tensor ...
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3 votes
2 answers
117 views
Why does UV matrix factorization for recommender systems work?
In recommender systems research one approach is to make a UV matrix factorization. $M' = U\cdot V$ where the number of columns of $U$ equals the number of rows of $V$ and "$\cdot$" is the ...
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1 vote
1 answer
71 views
Sequential sum of squares with svd
I am studying some methods to determine the coefficients of a linear regression and I am wondering how to find the sequential sum of squares, or the second column of the ANOVA table which shows ...
- 311
3 votes
1 answer
173 views
The Math Behind the Conditional Probability of a Probabilistic PCA
I am trying to understand how to calculate the conditional distribution of probabilistic principal component analysis. This is explained in the book "Pattern Recognition and Machine Learning"...
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0 votes
1 answer
75 views
Decomposition of VAR(1) coefficient matrix
Consider the VAR(1) process $X_t = \Phi X_{t-1} + \epsilon_t.$ Is there a generally accepted decomposition for the coefficient matrix $\Phi$ that would decrease the degrees of freedom? My initial ...
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2 votes
1 answer
190 views
Passing a cholesky decomposition for a matrix with constrained variances to an objective function
I am trying to optimize an objective function $L(\theta)$ in which some parameters that I aim to recover belong to a covariance matrix, $\Sigma$. $\Sigma$ has a unique structure, which includes ones ...
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0 votes
2 answers
136 views
The Impact of Vector Magnitudes in Recommendation Systems Matrix Factorization Models
I'm currently exploring latent factor models in recommendation systems, specifically focusing on the interaction between vector magnitudes and the angles between these vectors. While it's clear that ...
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1 vote
1 answer
70 views
Efficient construction of correlation matrix—serial correlation
Given $\rho$, is there a way to efficiently construct this matrix (i.e., as a product of matrices, rather than using a for loop)? $$ \Sigma = \begin{pmatrix} 1 & \rho & \rho^2 &\cdots &...
4 votes
0 answers
333 views
Fast Cholesky decomposition of a Toepllitz matrix via embedding in a circulant & fft
As I understand it, the Cholesky decomposition of a Toeplitz matrix can be computed more efficiently by first embedding it in a circulant matrix then using FFT, but I'm having trouble finding any ...
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2 votes
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Is spiked tensor decomposition a special case of INDSCAL decomposition?
I understand that "Spiked" often refers to the presence of a dominant component (or a few dominant components) in a tensor decomposition. Spiked tensor decomposition is applied to multi-way ...
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1 vote
1 answer
168 views
Method of least squares, first order condition and QR decomposition
When you use the method of least squares you estimate the parameters in the following way: $$\min_{\mathbf{b}} (\mathbf{y} - \mathbf{X}\mathbf{b})^T(\mathbf{y} - \mathbf{X}\mathbf{b})$$ Where $\mathbf{...
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0 votes
0 answers
48 views
Matrix Factorization with SGD gets na results
I'm trying to implement MF with SGD to my sample data following thru https://nbviewer.org/github/albertauyeung/matrix-factorization-in-python/blob/master/mf.ipynb. And, it's hard to figure out why the ...
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