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2
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0answers
79 views

Matrix decomposition

I have a symmetric matrix $V$ of order 10. I want to decompose $V$ in such a way that $$V=SS'$$ with $S$ being non triangular. The matrix $S$ has some restrictions that 45 cells have ‘0’ values and ...
0
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0answers
17 views

Collaborative Filtering, matrix decomposition, and incorporate various kinds of data

Just about every matrix factorization (e.g., SVD++) has some matrix that includes a n users and m (e.g.,) ratings. Here is my question, how do you include information like demographic information, ...
2
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1answer
52 views

Plotting error ellipsoid from 3x3 covariance matrix in R?

I'm hoping to be able to take a 3x3 covariance matrix and turn this into an error ellipsoid but so far I haven't been able to achieve this. I'm very new to R (in fact turned to it to attempt to solve ...
0
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0answers
29 views

How to re-construct a matrix from SVD

I have a Audio time-series, to which I'm trying to detect the most significant parts of the signal, i.e. the voiced parts and forget the unvoiced parts. $$ T = [0, 0, 1, 1, .....n] $$ I then ...
2
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1answer
62 views

QR factorization and linear regression

I have been reading "Generalized Additive Models an Introduction with R" by Simon Wood and have come across a section I'm having trouble with. On page 13 it is stated that the model or design matrix ...
2
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0answers
46 views

Confused about Cholesky and eigen decomposition

I'm looking to generate correlated random variables. I have a symmetric, positive definite matrix. So I know that you can use the Cholesky decomposition, however I keep being told that this only works ...
1
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0answers
56 views

Stata Oaxaca Blinder decomposition two-fold or three-fold

I have to use Oaxaca Blinder decomposition where my outcome is the wage (logged) and my predictors the level of education and the age. It's related to a company's data. I've seen that Ben Jann ...
1
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1answer
31 views

In non-negative matrix tri-factorization, initialization not possible because matrix is singular

I have implemented the non-negative matrix tri-factorization algorithm (link to paper). If is similar to the more widely known NMF (non-negative matrix factorization), but incorporates prior knowledge ...
6
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2answers
223 views

Why PCA of data by means of SVD of the data?

This question is about an efficient way to compute principal components. Many texts on linear PCA advocate using singular-value decomposition of the casewise data. That is, if we have data $\bf X$ ...
1
vote
1answer
72 views

IV estimator: efficient implementation?

I would like to implement (in R) an instrumental variable (IV) estimator, that takes the most general form (here not 2SLS or GMM!): $$ \beta_{IV} = (Z'X)^{-1}Z'Y $$ I could code this in the naive ...
1
vote
1answer
122 views

Matrix Factorization Model for recommender systems how to determine number of latent features?

I am trying to design a matrix factorization technique for a simple user-item, rating recommender system. I have 2 questions about this. First in a simple implementation that I saw of matrix ...
0
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0answers
51 views

Decomposing a correlation matrix

I'm doing some work on a model implementation. The specific model is the Multi-factor concentration risk model This Paper. Although I don't think the context is necessary for the specific problem I'm ...
2
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0answers
54 views

Why do PCA and Factor Analysis return different results in this example?

The following question is about an example from "The Elements of Statistical Learning" by Hastie, Friedman and Tibshirani $X_1 = Z_1 $ $X_2 = X_1 + 0.001 * Z_2 $ $X_3 = 10 * Z_3 $ Where $ Z_1, ...
2
votes
1answer
126 views

What are the differences between two kinds of PCA?

The book "Elements of Statistical Learning" describes Principal Components Analysis through SVD as follows: $ X = UDV^T $ Then $ UD $ are the Principal Components and $ V $ are the directions. ...
0
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0answers
26 views

Creating a bound for response variable using softImpute?

I'm working on the Netflix challenge in R and was I'm curious if there is a way to create a bound for the possible responses that the softImpute algorithm can predict. It doesn't look like there is a ...
0
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0answers
134 views

Invalid parent values, Adaptation incomplete, and print problem in Jags

I am trying to fit a GLMM for binary responses and I want to model the covariance matrix of random effects, say bigE, with some covariates. To do this, we decomposed the bigE into two different ...
0
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0answers
38 views

Finding random vector from its covariance matrix

I'm having difficulty solving the following problem: Given the covariance matrix Rxx = [1 0.2 ;0.2 1] for a zero-mean random vector X, find two different transformations of the form Y = AX ...
0
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0answers
33 views

Reducing data size to cross correlate with another data set?

I have three matrices A, B, C. A is a matrix of 200 X 32. There are 2000 such different A matrices which make up the B matrix. B is a matrix of 2000 x A. That is there are 2000 x 200 rows in matrix B ...
1
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1answer
99 views

Non-Orthogonality in PCA?

i) What is the main role of "only" trying to find orthogonal components in PCA? I can understand, that we would not want a zero-solution as well as find directions that are orthogonal in order to ...
0
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1answer
94 views

Truncated SVD matrix reconstruction: what is the meaning of the real values?

Im my algorithm, I am working with Singular Value Decomposition (SVD). I have an input matrix $A_{in} \in \{0,1\}^{(m * n)} $, made by $n$ rows and $m$ colums. All the entries are 0 or 1. I ...
1
vote
0answers
42 views

How to visualize the low-rank visualization result?

In a numerical low rank decomposition, whether it is non-negative matrix factorization(NMF), or binary matrix factorization(BMF), or non-negative sparse PCA, we have two low-rank matrices to ...
0
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2answers
176 views

Cholesky decomposition in error covariance [closed]

I try to implement Unscented Kalman Filter. Everything seems to be done correctly but I do receive an error about Cholesky decomposition ...
2
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1answer
117 views

Physical significance: multiplying matrix by outer product of its eigenvector

I stumbled around this piece of code: v1 <- eigen(X.center %*% t(X.center))$vectors[,1] X.0 <- v1 %*% t(v1) %*% X.center while v1 is the eigenvector ...
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0answers
23 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?
0
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0answers
84 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 ...
1
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0answers
90 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 ...
0
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1answer
551 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 ...
0
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2answers
157 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 ...
0
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1answer
158 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 ...
2
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0answers
228 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 ...
1
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0answers
88 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 ...
1
vote
0answers
64 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 ...
1
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0answers
130 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 ...
1
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0answers
125 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 ...
2
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0answers
115 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 ...
0
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0answers
105 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 ...
1
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1answer
246 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
409 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 ...
13
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1answer
2k 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
157 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) · ...
1
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1answer
398 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 ...
1
vote
1answer
2k 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 ...
0
votes
0answers
161 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 ...
0
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2answers
3k 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, ...
2
votes
1answer
267 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 ...
3
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0answers
175 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 ...
2
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1answer
3k 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 ...
4
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4answers
2k 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 ...
9
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1answer
4k 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 ...
1
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1answer
661 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 ...