Questions tagged [correlation-matrix]
A $k\times k$ matrix of correlations between all pairs of $k$ random variables. All its diagonal elements are equal to one.
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SPSS correlation matrix from multiple imputation dataset, p-values and df
I use a multiple imputation dataset to create a matrix of correlations between a few variables of interest. The pooled correlation matrix does not show significance or df, unlike the original matrix ...
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1answer
27 views
How to determine mse of estimate from correlation matrix of estimate error?
I have a model of an information transmission system Y = XH + N, where X is a diagonal matrix with the transmitted "symbols" (known), H is a column vector which distorts the transmitted symbols and N ...
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1answer
183 views
Eigenvectors for correlation and covariance matrix PCA
I know the generally reasons of using correlation matrix vs a covariance matrix when doing PCA (and visa versa) however when thinking about the eigenvectors (principal components of the data) of each ...
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62 views
Change in eigenvalues due to perturbation to a correlation matrix
Let $A$ be a $m \times n$ matrix defined as
$ A = \Big[\frac{a_1}{\|a_1\|} \cdots \frac{a_n}{\|a_n\|}\Big]$ and $a_k \in \mathbb{R}^{m\times 1}$ where $k \in [1,\dots,n]$.
Now, we define a ...
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30 views
How to simulate random correlation matrix containing off diagonal structures
I want to simulate a correlation matrix which has some off-diagonal structures and also should have some hierarchical structures. For simulating correlation matrices which contain hierarchical ...
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0answers
87 views
Simulate correlation matrix using a given structure
I want to generate correlation matrix such that it follows the below structure $$\Sigma = B \Lambda B^T $$
where $\Lambda$ is a diagonal matrix containing positive elements, $\Sigma \in R^{n \times n}...
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1answer
107 views
How do I simulate a random valid correlation matrix of ordinal variables given a list of marginal probabilities?
I am trying to use R to simulate random variations in a real dataset with a known number of categorical and continuous predictor variables, as well as known marginal probabilities for each ordinal/...
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4answers
2k views
Is it possible that 3 vectors have all negative pairwise correlations?
Given three vectors $a$, $b$, and $c$, is it possible that correlations between $a$ and $b$, $a$ and $c$, and $b$ and $c$ are all negative? I.e. is this possible?
\begin{align}
\text{corr}(a,b) < ...
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What is the best way to Show a Correlation Matrix as a Cluster/Network Graph in Python? [closed]
I'm struggling because while I want to show the interrelationship of correlation between my fields, I realize that trying to plot nodes in terms of distance away from each other based on correlation ...
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111 views
Method to generate random correlation matrices with specified structure.
Within the social sciences there is a popular technique called Factor Analysis and I am interested in generating random correlation matrices that uniformly sample all the space parameterized by one ...
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1answer
468 views
Help needed with intuition of eigenvalue spectrum of correlation matrix
I wish to get a better understanding of the meaning of the eigenvalues of a correlation matrix I am studying.
I have a correlation matrix of noise levels for 10 cells in a wireless network over time....
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0answers
47 views
How to generate a set of random variables with specific correlations and correlational distributions
I apologize if this question is a bit confusing.
Suppose we get to generate an $n \times n$ matrix, $M$, whose values are all between 0 and 1.
How can we generate a set of $n$ random variables, $\{...
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1answer
2k views
Do the Determinants of Covariance and Correlation Matrices and/or Their Inverses Have Useful Interpretations?
While learning to calculate covariance and correlation matrices and their inverses in VB and T-SQL a few years ago, I learned that the various entries have interesting properties that can make them ...
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1answer
119 views
Cluster analysis using the posterior distribution of a Bayesian correlation matrix
Background and Problem
I recently ran a Bayesian multivariate epidemiological meta-analysis on prevalence estimates for several disorders. This analysis included a probit-based model to deal with the ...
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2answers
849 views
Does using a covariance matrix of scaled and centered variables compare with using a correlation matrix?
I have some data with features which have different units of measurements. Here, by data, I'm trying to say that the row represents the observations and column the features. There are correlations ...
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1answer
91 views
Correlation matrix for biostatistics [closed]
I want to convert the expression of the genes from an array to a gene correlation matrix, to know the correlation of each gene with the other genes.
I have 6 samples, 3 controls and 3 test, is it ...
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255 views
correlation matrix test: is this code correct or is it missing a multiple comparisons correction?
I have $m$ variables $x_1,\dots,x_m$, measured in $N$ independent tests $\{x_{i1},\dots,x_{im}\}_{i=1}^N$, leading to the design matrix $X$. I noted that the demo function ...
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0answers
36 views
Check whether a sample correlation matrix is valid [duplicate]
Is it possible to have the following sample correlation matrix for $x$, $y$, $z$?
$\begin{pmatrix} 1 & 0.8 & 0.2 \\ 0.8 & 1 & 0.7\\ 0.2 & 0.7 & 1\end{pmatrix}$
Where a 3 by 3 ...
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1answer
696 views
Reporting Fisher-transformed Pearson's correlations when the magnitude of difference is relevant
My field regularly demonstrates a certain type of result with pairwise Pearson's correlation matrices between predicted and measured data. As soon as such correlations become high, Fisher-transforming ...
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3answers
2k views
Is there a serious problem with dropping observations with missing values when computing correlation matrix?
I have this huge data set with like 2500 variables and like 142 observations.
I want to run a correlation between Variable X and the rest of the variables. But for many columns, there are entries ...
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0answers
308 views
How to compare diagonal elements of precision matrix (the inverted correlation matrix)?
Let $$C=\begin{pmatrix}C_{11} & C_{12}\\ C_{21} & C_{22}\end{pmatrix}$$ be a $p\times p$ correlation matrix with positive entries, where $C_{11}$ is a $q\times q$ matrix. Define $D=C^{-1}=(d_{...
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1answer
114 views
How to randomly generate a positive semidefinite matrix subject to Loewner constraint?
For real, symmetric, positive semidefinite matrices $A$ and $B$, let $\leq_L$ denote the Loewner partial order: $A \leq_L B$ iff $B-A$ is positive semidefinite. Suppose $A$ and $B$ are fixed PSD ...
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6answers
3k views
Completing a 3x3 correlation matrix: two coefficients of the three given
I was asked this question in an interview.
Lets say we have a correlation matrix of the form
\begin{bmatrix}1&0.6&0.8\\0.6&1&\gamma\\0.8&\gamma&1\end{bmatrix}
I was asked to ...
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2answers
405 views
With an R function that expects a covariance matrix, can I give it a correlation matrix?
The R function mvrnorm from the MASS package generates random numbers from a multivariate normal distribution. It expects a ...
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1answer
195 views
Is there a way to reconstitute the unit of measurement in PCA?
I have a data set composed of changes in financial asset prices. Because they are on different levels, e.g., one asset is trading in the 100s, the other in the 5s, the change their prices have vastly ...
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1answer
271 views
Exact meaning of correlation coefficient
What is the exact meaning of the entries of a correlation coefficients matrix?
I have spent time researching this, but could find only approximate interpretations which give me no good understanding ...
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0answers
639 views
How the Correlation Matrix is built for PCA in Weka?
Just to give a context, I want to use PCA (Principal Component Analysis) to identify which attributes are similar to others, so I can use just one (or a subset) of them.
The correlation matrix of n ...
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0answers
332 views
Covariance Matrix and Correlation Matrix - Singularity
If a covariance matrix is non-singular, does this implies that correlation matrix is also non-singular.
My guess is it depends on mean vector in
$K_{X} = R_{X} - m_X.{m_X}^H$
Not sure though.
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0answers
176 views
Correlation Matrix from given R output of Factor Analysis
I carried out a factor analysis of 5 variables using a single factor. How do I estimate the correlation matrix assuming the one factor model holds? The R output is:
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1answer
949 views
Does it make sense to use PCA when the determinant of the correlation matrix is (almost) zero?
I'm running a PCA over a data set of $N \times p$ size ($N\approx 1000$ being the number of measurements and $p\approx 200$ being the number of dimensions/predictors).
I expect many of the predictors ...
3
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1answer
908 views
Off-diagonal elements of a correlation matrix after removing the first principal component
I have some data with more variables than observations, that I'd like to subject to a principal components analysis.
For didactic reasons (to give an intuition for factor retention criteria under ...
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3answers
7k views
Is every correlation matrix positive definite?
I'm talking here about matrices of Pearson correlations.
I've often heard it said that all correlation matrices must be positive semidefinite. My understanding is that positive definite matrices must ...
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1answer
579 views
Fisher z-transformation and normality
I have 100 50x50 correlation matrices, which I have all Fisher z-transformed. I understood that this results in the all the entries of one matrix being approximately normally distributed.
Questions
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1answer
2k views
Matrix multiplication to find correlation matrix
In this book on matrix factorizations, the author states the following, which I don't find to be true empirically. Is it true and under what conditions?
ADD: Trying to recreate the answer in R, what ...
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2answers
2k views
Does a correlation matrix of two variables always have the same eigenvectors? [duplicate]
I wanted to conduct a total least squares regression on two variables. My statistical programme does not provide TLS, but TLS luckily equals Principal Component Analysis, as far as I know. Since all ...
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2answers
737 views
Generate symmetric positive definite matrix with a pre-specified sparsity pattern
I am trying to generate a correlation matrix $p\times p$ (symmetric p.s.d) with a pre-specified sparsity structure (specified by a graph on $p$ nodes). The nodes that are connected in the graph have ...
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2answers
1k views
Is a weighted average of two correlation matrices again a correlation matrix?
Let $R$ and $Q$ be two correlation matrices of the same size and let $p\in[0,1]$. I'm trying to show that $pR+(1-p)Q$ is still a correlation matrix.
I claim that $\sqrt pX+\sqrt{1-p}Y$ is a random ...
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3answers
2k views
Is every correlation matrix positive semi-definite?
I am generating correlation matrix by some new algorithm. Generated matrix is non positive semi-definite matrix.
I'm getting a few negative eigenvalues. The rest of eigenvalues are quite equal to the ...
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5answers
10k views
How to generate a large full-rank random correlation matrix with some strong correlations present?
I would like to generate a random correlation matrix $\mathbf C$ of $n \times n$ size such that there are some moderately strong correlations present:
square real symmetric matrix of $n \times n$ ...
6
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1answer
766 views
Diagonal elements of the inverted correlation matrix
Is it true that the diagonal elements of the inverted correlation matrix will always be larger than 1? Why?
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1answer
873 views
Quantifying how much “more correlation” a correlation matrix A contains compared to a correlation matrix B
I have 2 correlation matrices $A$ and $B$ (using the Pearson's linear correlation coefficient through Matlab's corrcoef()). I would like to quantify how much "more correlation" $A$ contains compared ...
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2answers
799 views
Permutation tests of correlation matrix in R , which correlations are significant?
As in the title, I have a correlation matrix available with cor() function:
corMatrix <- cor(mydata)
...
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4answers
11k views
Bound for the correlation of three random variables
There are three random variables, $x,y,z$. The three correlations between the three variables are the same. That is,
$$\rho=\textrm{cor}(x,y)=\textrm{cor}(x,z)=\textrm{cor}(y,z)$$
What is the ...
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3answers
36k views
Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite?
I have been researching the meaning of positive semi-definite property of correlation or covariance matrices.
I am looking for any information on
Definition of positive semi-definiteness;
Its ...
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3answers
19k views
How can I generate data with a prespecified correlation matrix?
I’m trying to generate correlated random sequence with mean = $0$, variance = $1$, correlation coefficient = $0.8$. In the code below, I use s1 & ...
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6answers
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Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical ...
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4answers
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How to generate random correlation matrix that has approximately normally distributed off-diagonal entries with given standard deviation?
I would like to generate a random correlation matrix such that the distribution of its off-diagonal elements looks approximately like normal. How can I do it?
The motivation is this. For a set of $n$ ...
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2answers
19k views
Clustering variables based on correlations between them
Questions:
I have a large correlation matrix. Instead of clustering individual correlations, I want to cluster variables based on their correlations to each other, ie if variable A and variable B ...
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8answers
11k views
How to efficiently generate random positive-semidefinite correlation matrices?
I would like to be able to efficiently generate positive-semidefinite (PSD) correlation matrices. My method slows down dramatically as I increase the size of matrices to be generated.
Could you ...
