The matrix-decomposition tag has no wiki summary.
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13 views
Fast distributed parallel Cholesky Decomposition algorithm or implementation for dense matrices?
What is a fast distributed parallel Cholesky Decomposition algorithm or implementation, for dense matrices?
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18 views
Step detection segment
Is it possible to identify a segment (not point) of structure change within a time series? Ideally, I want something similar to a way to look at a time series and use the breakpoint function within ...
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0answers
31 views
Harmonic or dummy seasonal model
Within the BFAST package in R, one of the parameters that it gives is the choice of seasonal model parameter (harmonic, dummy, or none). I understand what none does; However, I didn't really ...
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1answer
73 views
Time series deseasonalization
How do you know when deseasonalization is not necessary? That is, from what I understand, if you want to just look at the trend and irregular components of a time series, then you just need to remove ...
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87 views
Adding content information to matrix factorization-based recommender
I'm currently using a matrix factorization method to generate recommendations (for info on this, check: Matrix Factorization Techniques for Recommender Systems). At the moment, my rating estimate is ...
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1answer
76 views
Why sparse QR decomposition yield different results from dense QR decomposition in R?
A simple example is given below:
mat <- diag(1:6)
qr.R(qr(as(mat,"Matrix")))
qr.R(qr(dd))
the diagnal values are of opposite signs. There is a warning message ...
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0answers
137 views
Matrix factorization and gradient descent for recommender systems; user bias?
I've been reading about using Matrix Factorization techniques to do collaborative filtering. A popular thing to do seems to be to add user and item biases into the ratings prediction. What I don't ...
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0answers
57 views
recommender system implicit rating to ordinal scale
There are 4 ways a user can show preference for an article within my news app: number of times an article was viewed; for how long was the article viewed; whether it was favorited or not; and number ...
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0answers
50 views
How to sample from a multivariate normal given the $P^T LDL^T P$ decomposition of $\Sigma$?
How to sample from a multivariate normal given the $P^TLDL^TP$ decomposition of $\Sigma$, and $\mu$?
Here, $P$ is a permutation matrix, $L$ is lower-triangular, and $D$ is diagonal
Given the ...
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0answers
94 views
Slope Derivation for the variance of a least square problem via Matrix notation
I have a question to solve the following matrix problem:
$$E[( (X'X)^{-1}X \epsilon )^T ((X'X)^{-1}X \epsilon )]$$
into the solution
$$= \Sigma^{2} (X'X)^{-1}.$$
Where $\Sigma$ is the covariance ...
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0answers
92 views
Matrix factorization vs random walk with restart for recommender systems
Suppose I want to handle "friend recommendation" problem on a large social network graph. I came across random-walk-with-restart as one technique used. I was thinking of using matrix factorization as ...
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110 views
R- replace values in a matrix with the average value of its group? Q2 [closed]
I realised I should have been more specific in my question so let me re phrase.
how would you do this when the number of columns and rows in each group (and indded in each mxtrix) is unknown and ...
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0answers
55 views
Collaborative filtering through matrix factorization with logistic loss function
Consider collaborative filtering problem. We have matrix $M$ of size #users * #items. $M_{i,j} = 1$ if user i likes item j, $M_{i,j} = 0$ if user i dislikes item j and $M_{i,j}=?$ if there is no data ...
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89 views
PCA matrix-decomposition in image recognition
I am implementing an image recognition program as an exercise but I am comfused in the following point.I have a data set M with dimensions $NxD$ where $N<<D$ so I have used dimension reduction ...
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1answer
147 views
PCA eigenvectors with dimensionality reduction
I want to understand how I can compute the eigenvectors and the eigenvalues of a matrix using dimensional reduction.I have a Matrix $M$ of dimensions $n$ x $d$ using dimension reduction I can compute ...
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0answers
250 views
Getting positive definite matrix for chol update
I am making a square-root UKF implementation. I also use cholupdate function in Matlab. However cholupdate needs a positive ...
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1answer
960 views
Dimensionality reduction (SVD or PCA) on a large, sparse matrix
I have a large, sparse Matrix of features I would like to use in a machine learning algorithm:
...
2
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1answer
124 views
Does the product of two p.s.d kernel matrices result in a kernel matrix?
In a ML setting, where $a_1,..., a_n$ are a set of training points. A kernel function is a function $κ$ that gives the inner product between two vectors
in the feature space:
$κ(a_i, a_j ) = ψ(a_i) · ...
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1answer
254 views
Eigenvectors for the sum of two symmetric matrices
$R = S + xx^t$
where $x \in \mathbb{R}^n$ and $R$ and $S$ are $n \times n$ covariance matrices.
Is there anything I can say about the eigenvectors of $R$ and $S$? Or at least the largest ...
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1answer
1k views
SVAR, Cholesky decomposition and impulse-response function in R
I have two sets of data from the FRED database: real GDP (y) and GDP deflator (p) and I want to be able to use R in order to estimate a VAR(p) (p determined by AIC) process and generate the sets of ...
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0answers
139 views
Singularity issues when fitting an ARIMAX model
When I want to apply an ARIMA model like this:
arimax(dataMat, order=c(7,0,0), xreg=xreg)
it raises an error
"singular and could not compute QR ...
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2answers
2k views
Finding matrix eigenvectors using QR decomposition
First, a general linear algebra question: Can a matrix have more than one set of (unit size) eigenvectors? From a different angle: Is it possible that different decomposition methods/algorithms (QR, ...
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1answer
192 views
How do I propagate error values through a matrix diagonalization?
In the general case, if I have a symmetric, invertible (real-valued) matrix where each entry in the matrix has a separate error associated with it (or, in the more general case, where each value has a ...
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145 views
How can I perform joint Schur decomposition or joint spectral decomposition?
I have a collection of matrices $A_1,\ldots,A_n$, and I want to do joint Schur decomposition on them (they all have the same unitary matrices in their decomposition). I couldn't find any ...
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1answer
2k views
How do you calculate eigenvector/value of a non-square matrix in R?
I have been wanting to calculate eigenvalues and eigenvectors for a non-square matrix and I know that svd method is used.
But, given my poor background, I don't ...
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4answers
1k views
Testing for linear dependence among the columns of a matrix
I have a correlation matrix of security returns whose determinant is zero. (This is a bit surprising since the sample correlation matrix and the corresponding covariance matrix should theoretically be ...
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1answer
2k views
Efficient calculation of matrix inverse in R
I need to calculate matrix inverse and have been using solve function. While it works well on small matrices, solve tends to be ...
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1answer
483 views
Eigenvectors corresponding to eigenvalues
In R, the eigen() returns descending sorted eigenvalues. However, the eigenvectors do not correspond to these sorted eigenvalues. How do I identify the eigenvector corresponding to the ith sorted ...
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1answer
352 views
Eigenfunctions of an adjacency matrix of a time series?
Consider a simple time series:
> tp <- seq_len(10)
> tp
[1] 1 2 3 4 5 6 7 8 9 10
we can compute an adjacency matrix for this time series ...
2
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1answer
69 views
Bounds on entries of Cholesky factors?
Motivated by the problem of covariance estimation.
Let $\Sigma$ be a positive-definite matrix whose diagonal entries are identically 1. (i.e. $\Sigma$ is a correlation matrix.)
If $L$ is an ...
3
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1answer
127 views
Efficient parametrization of the covariance matrix with some covariances constrained to zero
I'm trying to estimate the unknown 8x8 covariance matrix X in R using the maximum likehood, but I have problems of figuring out the efficient way of parametrization of X when some of the covariances ...
9
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1answer
234 views
Fast computation/estimation of a low-rank linear system
Linear systems of equations are pervasive in computational statistics. One special system I have encountered (e.g., in factor analysis) is the system
$$Ax=b$$
where $$A=D+ B \Omega B^T$$
Here $D$ is ...
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1answer
216 views
Solving a regression problem
I wanted to solve such a regression problem:
$$Y = Xb + e$$
where $X$ is a $m$ by $n$ matrix, resulting in: b = (X'X)-1X'Y as a solution. Since $n$ is quite large (2400), I can't use the ...
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1answer
154 views
QR factorization: floating-point issues
I've implemented QR factorization based on Householder reflections (for the purposes of computing the OLS fit). Mathematically, the $R$ matrix is upper triangular. However, due to floating-point ...
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2answers
6k views
How to plot an ellipse from eigenvalues and eigenvectors in R?
Could someone come up with R code to plot an ellipse from the eigenvalues and the eigenvectors of the following matrix
$\begin{equation*}
\mathbf{A} = \left(
\begin{array} {cc}
2.2 & 0.4\\
...
5
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4answers
778 views
How to diagonalize a large sparse symmetric matrix, to get the eigen values and eigenvectors?
The matrix could be as large as $2500\times 2500$, what is the best algorithm to do that, is there some algorithm that is easy to write a program, is there any convenient packages for that?
4
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2answers
603 views
Randomized SVD and singular values
Randomized SVD decomposes a matrix by extracting the first k singular values/vectors using k+p random projections. This works surprisingly well for large matrices.
My question concerns the singular ...
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4answers
644 views
How can one extract meaningful factors from a sparse matrix?
I am interested in finding some practical (and reasonably well accepted) techniques for finding the underlying factors of a sparse matrix.
Specifically, I have a very large sparse matrix whose ...
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5answers
894 views
Essential papers on matrix decompositions
I recently read Skillicorn's book on matrix decompositions, and was a bit disappointed, as it was targeted to an undergraduate audience. I would like to compile (for myself and others) a short ...
