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1answer
25 views

Dimension Reduction

I have a n*m matrix, the rank of matrix (r) is near to min(m,n) I want to minimize the rank by removing some of the rows or columns to get r << min(m,n) The goal is to achieve least rank for ...
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1answer
15 views

Independent component analysis with nonnegative mixing matrix

In independent component(s?) analysis, I have the observed signal, $O$, the mixing matrix, $A$, and the source matrix, $S$, with $O ≈ AS$ I've found some literature on ICA with the sources assumed to ...
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0answers
23 views

faster alternatives to solve() in R [migrated]

If chol2inv(chol(matrix)) is not applicable to my matrix (i.e. not positive-definite square matrix), is there any other alternative methods in R to do matrix inversion (or avoiding the inversion). I ...
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1answer
44 views

Oaxaca Decomposition: Unexplained Constant

I am doing an Oaxaca decomposition of the Log Wage Differential between Whites and non-Whites. I would like to find out if there is any interpretation for the constant term under the unexplained ...
2
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1answer
24 views

WH=V matrix decomposition that allows negative values

I'm looking for a matrix factorization method that is able to decompose a matrix: V => W * H V has dimensions ...
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0answers
20 views

Problems with calculation of numerical identification w.r.t. ANOVA smooth for large scale matrices

Suppose we have two (centered) Spline-matrices $\boldsymbol{B_1}$, $\boldsymbol{B_1}$. Then $\boldsymbol{X_1} = [\boldsymbol{B_1},\boldsymbol{B_2}]$ contrains lower order smooths and ...
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2answers
165 views

How to choose an optimal number of latent factors in non-negative matrix factorization?

Given a matrix $\mathbf V^{m \times n}$, Non-negative Matrix Factorization (NMF) finds two non-negative matrices $\mathbf W^{m \times k}$ and $\mathbf H^{k \times n}$ (i.e. with all elements $\ge 0$) ...
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1answer
46 views

Intuition behind matrix factorization formulations?

I'm reading this paper about matrix factorization. In the paper they propose to use this factorization for the adjacency (or similarity) matrix $G$ using the following formulation: $G = U \Lambda U^T$ ...
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1answer
45 views

Matrix Factorization Recommendation Systems with Only “Like Ratings”

I'm trying to build a recommendation system, but I only have data on what my user's have "liked" i.e. all non-missing data has the same numeric value. Is it possible for me to using matrix ...
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0answers
17 views

Help with Euclidean update rule

I'm trying to figure out the derivation of the Euclidean update rule for NMF on page 2 of http://sig.umd.edu/publications/Tjoa_ICASSP2_201003.pdf but can't seem to eke it out. The end result that they ...
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0answers
41 views

Cholesky decomposition and confidence ellipsoid

I'm trying to construct an error ellipsoid from a covariance matrix (which exists for a 3D point) and then sample consistent xyz points in this region. (This question succeeds this one.) What I'm ...
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0answers
110 views

Trying to use Cholesky decomposition of covariance matrix to sample error ellipsoid

I'm trying to construct an error ellipsoid from a covariance matrix (which exists for a 3D point) and then sample consistent xyz points in this region. In a previous question when I asked about this ...
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0answers
25 views

clustering versus projection - what are the best example/scenario to explain their differences

I am dealing with non statistician who know are crunching data but don't have a deep understanding of statistics. I am trying to introduce them to non-matrix factorization methods but it has been ...
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0answers
48 views

Is there a way to perform SVD in a sequential manner?

My neurology experiment has a spike detector outputting 40 sample long spike waveforms. I'm using a dictionary method for sorting the spikes in real time. To ...
1
vote
1answer
78 views

Trying to understand non-negative matrix factorization (NMF)

I'm trying to understand how NMF is derived, and I got the basic idea of NMF, that is, it tries to approximate the original matrix $V$ with $WH$, where $V$ are non-negative, and $W,H$ are constrained ...
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1answer
214 views

Evaluating matrix factorization algorithms for Netflix

I've been trying to implement Simon Funk's movie recommendation algorithm explained here. I understand how the user and item factors are computed. However the evaluation method is not clearly ...
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0answers
126 views

PCA Using prcomp in R

I'm trying to do principal component analysis (PCA) in R using the prcomp function. My input is a large matrix of 1,188 observations (rows) and 15,462 features (cols). I input this to the function ...
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0answers
94 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 ...
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0answers
26 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
399 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 ...
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0answers
42 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
votes
1answer
163 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
89 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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1answer
65 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 ...
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2answers
598 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 $\bf X$ ...
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2answers
99 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
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1answer
330 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 ...
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0answers
74 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
163 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. ...
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0answers
36 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
156 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
votes
1answer
117 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 ...
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0answers
50 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 ...
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2answers
292 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
135 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
118 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
858 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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2answers
187 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
votes
1answer
216 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
310 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
100 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
89 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
158 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
167 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 ...
3
votes
2answers
201 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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1answer
340 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
508 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
4k 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
180 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
613 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 ...