A matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. The individual items in a matrix are called its elements or entries.

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Create an arbitrary covariance matrix for MASS::mvrnorm()'s Sigma argument in R [on hold]

MASS::mvrnorm() takes a mandatory Sigma argument which is a symmetric matrix specifying the covariance matrix of the variables. ...
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26 views

Understanding Matrix and Vector Notation

I am trying to understand the Matrix and Vector Notations on page 2 here: (the page is also pasted below, to make it easier to explain the problem). Problem: For equation (2), I think it should be ...
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9 views

Bounds on spectral radius of convergence matrix for EM algorithm

The following comes from Dempster, Laird and Rubin (1977) - Maximum likelihood from incomplete data via the EM algorithm: where $L(\phi)$ is the log-likelihood function for the observed data, ...
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10 views

Recursive function that operates on its own preceding output [on hold]

I have the price for a particular baseline year (in this case for 1993), and the multiplication factor for all the years. Using these known multiplication factor, I want to compute (project) price for ...
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5 views

Tunable sparsity parameter in sparse matrix approximation

I'm mostly casting around for what terms I should be looking for in the literature, but specific recommendations are also welcome. I have a sparse binary matrix in a collaborative filtering scenario. ...
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9 views

Correlate two matrix representing different variables

I've two matrix containing informations from 50 samples and 20000 genes. Matrix A contains the gene expression; Matrix B the methylation state of these genes. My first idea was to compute the ...
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46 views

What can I do with NA values in my second-order Markov chain?

I have states A, B, C, I have developed both a 1st and 2nd Order Markov Chain for them. Each state represents a status that an individual can be in, and the transitions represents the probability of ...
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2answers
25 views

Which of the 3 cases should my data matrix belong to ideally?

I found this question, and while useful, I wanted to ask something more spcific: I am trying to get a good handle/intuition for the two types of data dimensionalities (number of data samples, and the ...
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1answer
28 views

Distribution of the product of a Wishart matrix

If $\mathbf{M} \sim W_2(\Sigma, 3)$ is a Wishart matrix and $\Sigma =\begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}$ then what is the distribution of $(3, 1) \mathbf{M}^{-1}(3,1)^T$ ? Thank ...
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12 views

Creating a Radial basis function kernel matrix in matlab

I never used matlab, and I have this code about kernalized locality sensitive functions. I think that the following code is trying to create the kernalized matrix of a RBF kernel function: ...
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2answers
21 views

Find out a huge number of coordinates is uniformly distributed or not

Assume that we have a huge number of locations like $10^{6}$ locations in two-dimensional space. The coordinates are generated randomly. what I want to do is to make sure that the data distributed ...
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44 views

What is the difference between the anti-image covariance and the anti-image correlation?

What is the difference between the anti-image covariance and the anti-image correlation? How are the matrices of these coefficients computed, and what is the meaning of their elements?
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matrix signal deconvolution

I measured the dietary habits of thousands of animals throughout the world, giving me the following matrix: X = (M x N), where Xij = measurement of food j in animal i M = number of animals N = ...
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3 views

How to design a contrast matrix with a continuous variable

I was wondering if someone could help me designing a contrast matrix when you have a continuous variable. My model looks like this: ...
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18 views

What is the most efficient algorithm for online Non- negative Matrix Factorization (NMF)?

What is the most efficient algorithm for online Non- negative Matrix Factorization (NMF) in recent study? Thanks.
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1answer
11 views

constructing random effects design matrices for lassop{MMS}

I'd like to use elastic net regression for coefficient estimate and parameter selection on a data set that includes nested structure. I've been experimenting with lassop{MMS} to do so. I'm not a ...
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3 views

Storing hierarchical data as a list of matrices in R [migrated]

Noob R question here from a Matlab/Python user. I have a dataset with hundreds of different users, each of whom has a unique number of rows of data, and would like to store the data as a list of ...
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1answer
16 views

generating random matrix

My problem is this: I have a matrix with three columns. I created a second matrix with only two columns where column1 is the first column (col1) from the first matrix and column2 = ...
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22 views

Using a change detection error matrix approach for raster aggregation

I am assessing annual land use change along a 10 year period and have rasterized a vector land use dataset to base resolution 'n' metres to do so (vector data is taken as ground truth, errors in it ...
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6 views

Simultaneously Diagonalizable matrices

I'm interested in partitioning matrices into groups which are almost simultaneously diagonalizable. I'm aware that if matrices commute and one of them has no multiple eigenvalues then the matrices are ...
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11 views

Interpreting the psych::cor.smoother function in R

I've tried to contact William Revelle (the package creator) about this but he isn't responding. In the psych package there is a function called cor.smoother, which determines whether or not a ...
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41 views

Neural Net Matrix Multiplication

I'm trying to figure out the matrix multiplications for the implementation of a single hidden layer neural net for MNIST digit recognition in Python. Like the following: ...
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1answer
19 views

$LDL^T$ decomposition from Cholesky decomposition

Suppose we have a covariance matrix $\Sigma$. I know that the Cholesky decomposition $A^T A$ can be found from the LDL decomposition using $$ \Sigma = LDL^T = (LD^{\frac 1 2})(LD^{ \frac 1 2 })^T = ...
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3answers
131 views

Decrease of $(X'X)^{-1}$ as n increases

Let $X$ be a $n \times p$ matrix, filled with iid draws, with $n \geq p$ (like a conventional data matrix). I would like to show that, in a sloppy notation, $(X'X)^{-1} \rightarrow 0$ as $n ...
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12 views

Several variables in correlation matrix output

I'd like to improve a big correlation matrix output correla, because I want to see significante values (p<0.05) but with my code is very dificult to find ...
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28 views

How does Guttman's image analysis work?

Could anyone explain to me how Guttman's image matrix works? Is extracting variables a reiterative process? Are all variables extracted? What's the meaning of the formula? What happens to the diagonal ...
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39 views

Variance of a multivariate AR(1) process

I have a multivariate AR(1) process (first-order vector autoregression, VAR(1)) of the form $$ \pmb X_{t+1} = A \pmb X_t + \zeta_t $$ where $\pmb X_t$ is a vector, $A$ is a matrix and $\zeta_t \sim ...
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125 views

Codification of Matrix $X$ in $Y=XB+\epsilon$

The variables for the data below is age, group (treatment 1,2,3), Y response variable. ...
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31 views

Recommenderlab not working with highly sparse binary data?

The data used is a ratings matrix generated from simple 0-1 yes/no click data based on whether or not a user visited a section of a website. This is implicit voting since if a user is interested in a ...
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1answer
71 views

Differentiating the RSS w.r.t. $\beta$ in Linear Model

I am reading the book "The Elements of Statistical Learning". The book says But when I try to prove it, I get the following: $$RSS(\beta) = (y - X\beta)^T(y-X\beta)$$ $$RSS(\beta) = y^Ty ...
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42 views

How to obtain the inverse of a matrix while solving an equation?

Given a matrix $A$, let us assume there is a equation: $Ax = b$ To solve for $x$, we can write: $x = A^{-1} b$ One way to obtain the inverse of A is by single value decomposition: Decomposition ...
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15 views

R-programming limma design matrices

I have a really basic understanding of how the package limma works in that it fits a linear model to each row/sample in a micro-array dataset. What I do not understand is how to use a design matrix to ...
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33 views

How to provide input to TSNE

I am using TSNE for the first time for dimension reduction. I have around 12 million records with 5000 distinct values. I want to perform dimension reduction (DR) so that I visualized those distinct ...
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24 views

When using loss matrix in rpart in R, xerror does not start at 1 [closed]

I am trying to use a loss matrix in rpart penalizing false positives 10 times as much as false negatives, but when I fit my data and then use printcp, my xerror values start at 10 and not 1. I am ...
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8 views

How to find the generalized inverse of a matrix in SageMath?

Given a matrix $A_{m\times n}$, a matrix $G_{n\times m}$ is said to be a generalized inverse of $A$, if it satisfies, $$AGA=A$$ Now, since for a matrix $A$, generalized inverse of $A$ is plenty if ...
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30 views

Question about idempotent matrix: how can M(I-M) equal zero?

Let me assume that M is an idempotent matrix (MM=M) and (I-M) is not zero (I is identity matrix with the same dimensions as M). If I multiply (I-M) by M, (M-MM)=(M-M)=0. How could it be possible that ...
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1answer
38 views

Get distance matrix directly condensed

I am developing a content-recommender Python system and most of my items (~8 millions) are static so I have thought about pre-computing the top 150 similar items for each item. This way, when a user ...
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11 views

Confusion Matrix in FCM

I have written code of FCM(Fuzzy c-mean) in java for centroid and membership matrix generation as well as object function. How can i generate confusion matrix any idea in this FCM program.
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36 views

Application of Givens rotation to two matrices

I am reading this paper on Multiresolution Matrix Fatorization, http://arxiv.org/pdf/1507.04396v1.pdf, and have come across something that seems like an error to me. In Algorithm 2, the authors take ...
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13 views

Input matrix construction for time series

I am having problems constructing the input matrix for a data analysis / machine learning task. The data set consists of ~300 data points, each one in form of a matrix where rows are time steps, ...
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1answer
33 views

How to reduce dimensionality of audio data that comes in form of matrices and vectors?

I'm working on a project involved with identifying different types of sounds (such as screams, singing, and bangs) from each other. We've got our data a reasonable number of different transformations ...
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20 views

Metric from a positive definite matrix

I'm trying to prove that the Mahalanobis distance is an actual distance, more in general Given B symmetric and positive definite matrix set d(x,y)=(x-y)'B(x-y) ( ...
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16 views

Primal and dual problem in simplex algorithm [closed]

I know that the primal problem \begin{equation} \begin{aligned} & \text{maximize} & & \textbf{c}^T \textbf{x} \\ & \text{subject to} & & \textbf{A} \textbf{x} \leq \textbf{b} ...
3
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1answer
48 views

Determinant of a block matrix with sparse elements

I have a positive definite symmetric matrix that looks like $$\pmatrix{A & 0 & 0 & E \\ 0 & B & 0 & F \\ 0 & 0 & C & G \\ E^\prime & F^\prime & G^\prime ...
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9 views

help me understand the proof in the paper “restricted ridge estimation”

I'm reading the paper "restricted ridge estimation" by Grob(2003). I can not understand the proof of theorem 1 in this paper. I don't know how this estimator $\hat{\beta}_{r}(k) = ...
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1answer
24 views

R unfold a list into a matrix [closed]

I have a list in which each element inside it is a matrix. How can I unfold this list to get a matrix. Example: List[[1]]=matrix A List[[2]]=matrix B List[[3]]=matrix C and I want directly to get a ...
3
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1answer
155 views

Sampling a random binary matrix with “Gaussian” probability distribution

Let $A_{ij}$ be a $n\times n$ random binary matrix with probability mass function $P(A)$ given by $$ \log P(A)=-\frac 12 \mathrm{tr}\left[\left(A-M\right)^TV\left(A-M\right)\right] + C, $$ where $M$ ...
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9 views

Create Optimal Matrix based on Given Constraints

I would like to construct a 0-1 matrix which satisfies certain constraints and allocates either 1 or 0 to the value in order to optimize the objective function. The following constraints should be ...
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13 views

Coherence matrices

I'm analyzing ECoG data that were recorded during a working memory task. There are 6 different subjects and they all have about 100 trials. Each subject has different electrode coverage (so not in the ...
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19 views

How is this gradient derived?

I am reading this paper, http://math.ucla.edu/~dakuang/pub/sdm0125.pdf, and came across this function, $f(x) = ||A-H^TH||_F^2$. Later, the authors take the gradient of this function, $\nabla f$, but ...