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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How to find factor that is making matrix singular

I have a 300+ column data.frame, and no matter how I break it up I get this error every time: ...
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45 views

How to summarise information in a correlation matrix? [closed]

I have ten variables, which I have correlated against each other. I get a correlation matrix of size $10\times10$, where the correlations are relatively high on average. I would like to somehow sum ...
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23 views

how to do a t-test in matlab of 2 data(matrix of 3 ex: 180*820*23) [closed]

how to do a t-test in matlab of 2 data(X and Y) and X and Y have each 9 signals those signals are matrix of 3 ex: 180*820*23 or 180*820*30 etc..) and which i have to take the peak from each signal, so ...
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34 views

What is this theorem used in proving canonical correlation model?

I am watching a video about canonical correlation that proves the canonical correlation model. In the prof's proof of the canonical correlation model, a theorem from matrix analysis is used. That is ...
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7 views

R Shiny Matrix Multiplication [migrated]

I am currently developing an Monte Carlo Simulation with R's shiny. Unfortunately, I am stuck at some and can't see the error right now. I tested the code for the simulation before and it works. What ...
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2answers
22 views

reasons for a non-invertible matrix

I am trying to factor analyze a matrix in R and I keep getting errors that lead me to believe my matrix is non-invertible. What are the reasons a matrix could be non-invertible? The only one I found ...
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37 views

Does rank of observation matrix tell anything useful when applying machine learning?

Suppose I have an observation matrix of size $N \times M$ where $N$ is the number of samples and $M$ is the number of variables. If the rank of the observation matrix is $R<M$, does it tell ...
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41 views

Generating a matrix for regression from long form data

I'm having some difficulty interpreting how to correctly create a matrix input for regression from a long form data source. I have table containing marketing data where each row represents a view of ...
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10 views

commonalities and differences among groups in a matrix (based on features)

I have a (rather sparse) matrix with 7 columns and 66 rows. Each column represents a user group, each row represents a feature, and each cell represents a weighted value (see note below). I'd like to ...
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3 views

3D Array value assignment ruins the structure of array [migrated]

Here is how to reproduce my problem. I want to create a 3D array > g=array(0,dim=c(3,31,31)) > dim(g) [1] 3 31 31 > dim(g[1,,]) [1] 31 31 This is x with ...
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31 views

Correlation operations in R

I need som help using correlation matrix in R. Let's assume I have simulated 10 year of forecasted rental income for a property. The simulation parametar is accumulated income growth and my R code ...
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1answer
117 views

What is the intuitive (geometric?) meaning of minimizing the log determinant of a matrix?

I have come across optimization problems which seek a positive semi-definite matrix $A$ that minimizes some possibly non-convex function that includes the addition of $1/(\text{dimension}) * \log \det ...
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21 views

Calculating correlation between two different gene set of different size using R

From my previous post, I got the idea of generating correlation matrix and subsequent filtering the values for an input matrix. A problem arise is :I have a list of 8000 genes and would like to ...
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18 views

Looking for a principled/systematic procedure for discarding features

I have a collection of $M_i \times N$ matrices $X_i$ whose rows are (raw) feature vectors (from a common $N$-dimensional feature space). MATLAB reports that most of the covariance matrices $C_i := ...
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1answer
69 views

Matrix Multiplication to find Correlation Matrix

In this book on matrix factorizations: http://lnfm1.sai.msu.ru/~rastor/Books/Skillicorn-Understanding_complex_datasets_data_mining_with_matrix_decompositions.pdf The author states the following ...
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10 views

Finding possible interval for correlation coefficient under a certain correlation structure

I want to determine the interval for possible values of the correlation coefficient under certain correlation structures (eg. Compound Symmetry, Autoregressive and Banded Toeplitz). I can do it by ...
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1answer
34 views

Rewriting RegressionSS

I am having troubles in deriving the RHS of this formula: $$RSS= \hat{\beta}^{T}Z^{T}y-n\bar{y}^{2}$$ where $Z$ is the design matrix I am given ${y}^{T}y$ (what exactly does ${y}^{T}y$ stand for and ...
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17 views

Least Angle Regression - How do I extract the coefficients from the prediction vector?

I am a biologist trying to make sense of least angle regression. It is not going swimmingly. The paper I am looking at can be found here: statweb.stanford.edu/~tibs/ftp/lars.pdf I have a very ...
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1answer
31 views

Ordinal Logistic Regression Predicted Probabilities

I'm looking for a way to produce a matrix of predicted probabilities on data that went through SPSS's logistic regression test. I only use two ordinal variables with a range of 1-4 and 1-10 ...
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30 views

Posterior Conditional on Beta in Bayesian Linear Regression with Factor Analysis

This should be an easy question if you're familiar with the terms involved. I am performing some research using a hierarchical Bayesian regression model that incorporates factor analysis into the Beta ...
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37 views

How to figure out whether PCA can be performed on a data set or not?

I do have idea on the way PCA works but I do not know how to figure out whether a high dimensional data set is suited for PCA compression. I googled for some algorithms but could find any. Are there ...
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200 views

Textbooks on Matrix Calculus?

See this question on Math SE. Short story: I read The Elements of Statistical Learning and got frustrated when I was trying to verify some of the results, e.g., given $$\text{RSS}(\beta) = ...
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1answer
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Is a covariance matrix composed of matrixes derived from separate samples guaranteed to be positive definitive?

I have two samples that partially overlap on the variables they describe. The samples are taken from more or less the same population, and show similar values on the overlapping variables. Based on ...
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40 views

Markov Process-Variance of time until jump

A Markov process on E = {1, 2} is constructed according to holding time parameters λ1 = 2 and λ2 = 4; the defining Markov chain has transition probabilities p11 = p12 = 0.5 and p21 = 1. How do I ...
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1answer
26 views

I need a matrix in order to calculate g-inverse of it [closed]

I want to calculate g-inverse of a matrix, which has 4 rows and not a square matrix and has no inverse. Please help me find such a sound (good) matrix. I only need a matrix. You can suggest a book or ...
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34 views

Correlation between two quadratic forms of Gaussian random vectors

I want to approximately calculate the correlation between two quadratic forms of two Gaussian random vecotrs (of course these are in fact non-Gaussian densities). Does anyone know the derivation of ...
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29 views

Prove that minimum of the matrix norm is achieved on certain parameters

Given matrix $A\in R^{n\times m}$ prove that minimum of the $||A-xy^T||$, $||B||=tr(B^TB)$, is achieved when $x$ is an eigenvector of $AA^T$, corresponding to its greatest eigenvalue, and $y$ is an ...
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21 views

Linear form arising in expected value of empirical variance of non-independent variables

Consider a normal vector $Y \sim \mathcal N(\mu, V)$ with $\mu \in\mathbb R^n$ and $V\in\mathbb R^{n\times n}$. I am interested in the expected value of $$ {1\over n-1} \left( Y'Y - {1\over n} ...
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18 views

Matrices F and c for F test?

In $\mathcal{F}$ test, the hypotheses involve multiple regression coefficients with the $\mathcal{F}_{0}$ test statistic: \begin{equation} z_{j} = \beta_{0} + \beta_{1} x_{1} + \beta_{2} x_{2} + ... + ...
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23 views

List of statistical test where correlation matrix is an important part

I wondered where all the correlation matrix forms an integral part of statistical test. Standalone also it is important (though there is no correlation-matrix tag for posts on this forum). It is ...
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46 views

Why the principal components correspond to the eigenvalues? [duplicate]

Suppose ${\bf{X}} = ({X_1},{X_2},\ldots,{X_n})$ are the original components (also random variables) and ${{\bf{w}}_j} = ({\omega _1},{\omega _2},\ldots,{\omega _n})$ are loadings for the $j$th ...
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33 views

Validating Neural Network

I have a relatively large set of labelled data which I am using to verify how well-trained a neural-network I wrote is. The network uses a competitive learning technique. It has N output neurons, each ...
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1answer
72 views

Correlation matrix is not positive definite… But why?

As part of an analysis I am conducting (Structural Equation Modeling) the estimated correlation matrix among some variables ended up looking like this: ...
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1answer
113 views

F-test and Rank test for underidentification

I've been performing a manual 2sls regression and I've come with the following results and that I find a bit suspicious. I've done the F-test of the first-stage regression and I've obtained a score ...
4
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1answer
77 views

How to generate uniformly random orthogonal matrices of positive determinant?

I've got probably a silly question about which, I must confess, I'm confused. Imagine repeated generating of uniformly distributed random orthogonal (orthonormal) matrix of some size $p$. Sometimes ...
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1answer
63 views

Understanding the marginal distribution of multivariate normal distribution

I am trying to better understand the multivariate normal distribution. Here I try to refer to the conditional distribution part of wiki also the fifth page of this tutorial. I do not quite ...
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22 views

Find repetitive patterns in matrices below

How can I identify the repetitive patterns from the matrices below? My problem is that the patterns in the matrix are different from matrix to matrix (dependent on the input data). I need some machine ...
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0answers
26 views

Difficulties in interpreting the Equations in Parameter estimation for linear dynamical system

I have implemented the Kalman Smoothing with Expectation Maximization based on the Paper Parameter Estimation for Linear dynamical system. All notations are based on this paper. The model is an IIR ...
2
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1answer
54 views

Clustering Matrices

Suppose I have a set of 100 $n \times 2$ matrices that all have the following format: Bid Profit [5.00 7.10] [3.14 6.04] [2.9 10.08] Where the numbers ...
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62 views

How to create a QQ plot of azimuths to test rotational symmetry of a spherical point dataset?

I am trying to do some Q-Q plots and the Kuiper test for rotational symmetry about the mean direction. These are unit vector, spherical data. What I am struggling to understand is the rotation from ...
2
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1answer
59 views

Can $x'x$ be written as correlation matrix?

$x'x=$ $$ \begin{bmatrix} \sum_{i=1}^{n}(X_{1i}-\bar X_1)^2&\sum_{i=1}^{n}(X_{1i}-\bar X_1)(X_{2i}-\bar X_1)\cdots & \sum_{i=1}^{n}(X_{1i}-\bar X_1)(X_{ki}-\bar X_k) \\ ...
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1answer
21 views

log multivariate normal differentiation (MLE)

I've come across a lot of explanations of how to differentiate the multivariate normal, but they all appear to skip the step that I'm stuck on. Here's what I've got so far. By logging and removing ...
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35 views

Matrix manipulation (weighted error term)

I have a question about matrix manipulation. I start off with a weighted error term. $$E_{D}(w) = \frac{1}{2}\sum_{n = 1}r_n (t_n - w^T \phi(x_n))^2$$ I differentiate, and set to zero to minimize ...
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19 views

How to run ANOVA on multiple groups of samples, each composed by different variables

I have a $m$ x $n$ matrix, where the $n$ columns are split into multiple classes. If I had only a $1$ x $n$ vector, I would have used ANOVA to evaluate if all subset of columns had the same ...
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48 views

Relation between raw and central moments

This question arose when reading Johansen's likelihood-based inference in cointegrated VAR models, the 2009 reprint, page 146. I will do my best to make my post self-contained. Let $Z_{0t}=\Delta ...
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1answer
27 views

Is this a valid method for unipartite projection of a bipartite graph?

I would like to know if a given method of projecting a bipartite graph exists, and if yes, if there is a formula for transforming the weight matrix. Given a bipartite graph with edges' weights ...
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31 views

Markov Process w/ a non-stochastic matrix?

I've come across a problem which at first appeared to be a markov process however the transition matrix of the graph is non-stochastic. That is, the probabilities among edges leaving a node do not sum ...
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10 views

How to evaluate enrichment of features in groups of samples?

I have a matrix composed by features on rows and samples on columns. Each value in the matrix correspond to a value of activation of the feature $i$ in the sample $j$. I want to evaluate enrichment ...
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30 views

Correlation of Distance Matrix

I have a matrix with 15 samples and ~10,000 data points (all z-scores). I calculated a distance matrix with euclidean distances using R. Is it valid to calculate and present a correlation on this ...
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1answer
49 views

R t-test, 1 response, multiple independent variables

I'd like to perform a t-test between groups 'A' and 'B'. The difficulty is that although there is only one response variable, there are many observations, and the grouping (A or B) differs with each ...