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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Creating a readable matrix with a netCDF file

I'm still learning R and I'm having trouble getting R to read and organize data in a way for me to perform analysis on. I have taken data from a free online weather database here: ...
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17 views

Similarity between two 2D matrices

I have two matrices: A= 4000x78 where 78 is the dimension of features and 4000 is the number of samples. B= 1000x78 where 78 is the dimension of features and 1000 is the number of samples again. ...
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13 views

maximizing matrix diagonal elements in R [migrated]

Given a matrix (or table in R ) ...
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22 views

Closed form solution for the diagonals of the symmetric matrix in RAM specification

Question: Is there a closed-form solution to finding the residual variances of endogenous variables using RAM specification (for SEM and Path Analysis)? Problem: Suppose someone wants to represent ...
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24 views

Row maximums in a matrix [migrated]

I have a 10 by 3 matrix (called u_V) and I would like to know in which column I have my row maximum. I know how to do it with which.max for a given row, and I coded ...
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1answer
61 views

Whitening transformation for skewness?

Let $X$ be an $(m,n)$-matrix interpreted as a two dimensional array with each column representing $m$ samples from a random variable, with known covariance matrx $M$ and mean equal to $0$, it is ...
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1answer
47 views

Derivative of $x^T A^Ty$ with respect to $\Sigma$ where $A$ is (an upper triangle matrix and ) Cholesky decomposition of $\Sigma$

I would like to evaluate: $$ \frac{ \partial x^T A^Ty}{\partial \Sigma} $$ where $A$ is a Cholesky decomposition of $\Sigma$ and an upper triangle matrix such that $\Sigma = A^T A$, $x$ and $y$ are a ...
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8 views

Local covariance matrix in Locally Linear Embedding

In Locally Linear Embedding (LLE), when contructing the weight matrix, denote $\mathbf{x}_i$'s neighboring data points centered w.r.t. $\mathbf{x}_i$ by ...
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1answer
44 views

Justification for default contr.poly() polynomial contrasts in R

In R, one can use contr.poly() to create a set of orthogonal contrast codes for testing linear and higher order effects of categorical factors: ...
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21 views

Similarity metric for 2 sets of vectors

I'm trying to determine the similarity between two sentences. I have vectors for each word in a corpus, and using cosine distance of the two vectors, I can get quite a good "similarity" score ...
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26 views

What is the advantage of non-negativity in matrix factorization?

I am wondering why matrix factorization techniques in the machine learning domain almost always expect the provided matrix to be non-negative. What is the advantage of this constraint? Background: I ...
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25 views

Represent decision tree as matrices

Is it possible to use matrix operations to generate node membership for decision trees? In a binary decision tree, each node represents a condition for a single variable. Ignoring the more complicated ...
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1answer
70 views

Linear Algebra (trace): How to pull out $X^T[…]X$?

In fallowing equation - (1) $tr(X^TA^TAX+X^TLX)$ equals to $tr(X^T[A^TA+L]X)$. My question is how about in the following equation (2) $tr(X^TA^TAX+X^TXL)$, can we pull out $tr(X^T[...]X)$ like first ...
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1answer
51 views

R - Constrained optimization for a function taking a matrix

I would like to do constrained optimization for a function which takes a matrix as input. The matrix is sparse, representing a weighted adjacency matrix , and only the weights shall be subject to ...
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13 views

How to get covariance matrix of the coefficient estimates of compound regression model in SPSS

AFter running regression model in SPSS, I get the compound model: ln(diamter)=1.126*height +3.102. I would like to have the covariance matrix of the coefficient estimates of this model and get the ...
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1answer
55 views

machine learning with linear regression algorithm

I'm noob in machine learning, but I'm trying to know more about it. I have a question about a prediction model (predict for every page when the number of click). I try to use kNNimpute to handle with ...
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0answers
15 views

What is the derivative of this? [migrated]

I have a function of the following form: $J = \|W^TW-I\|_F^2$ Where, $W$ is a matrix and $F$ is the Frobenius Norm. How can I find the derivative of $\frac{\partial J}{\partial W}$ ?
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87 views

interpreting PERMANOVA (adonis function) output?

I am trying to look at expression of some genes and relate the dist matrix (Sm) to a number of different factors that I collected on the individuals (e.g., litter size, licking behavior, group housing ...
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1answer
21 views

Difference between recentred and scaled eigenvalues and the Tracy Widom distribution

I have been generating correlation matrices from independent normal data simulated using the MASS package. I do this k times and extract the eigenvalues of the matrices. I was interested in comparing ...
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2answers
48 views

Apply function generating random numbers to a matrix (R) [closed]

I have a function which basically creates a random number. Now I want to apply the function to a matrix for given conditions to replace the value in the matrix with the random number created by the ...
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1answer
51 views

Variance expressed in Quadratic Form

Given a vector $\pmb x$ of length $n$, $\pmb x=\{x_1,...,x_n\}$ the variance is proportional to $\pmb x^\top \pmb x - \frac{1}{n}{\left(\sum_{i=1}^n x_i\right)}^2$ I'm trying to determine $(i,j)$ ...
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35 views

In R: Gravity model; how to handle vectorized data from symmetrical matrix?

I have vectorized data from a symmetrical matrix with collaboration data. So the collaboration between country i and country j is the same as between country j and country i. I deleted the principal ...
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21 views

Is there any matrix operations to find conditional probabilty distribution?

Is there any matrix operations defined in Matlab. Octave, R or Python to work with Joint, Marginal, and Conditional probabilities?For example if I have a probability distribution table which looks ...
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1answer
65 views

Why take transpose of regressor variable in linear regression

I am stuck trying to understand the basic calculation of ordinary least squares. From wikipedia $$y = \beta X^T + \varepsilon$$ where $X$ is the independent variable, $Y$ is the dependent variable ...
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71 views

Generate Symmetric Positive Definite Matrix with a pre-specified Sparsity

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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1answer
86 views

Recommenderlab - Getting the user_id out the RealRatingMatrix containing UBCF recommendations

I'm trying to use recommenderlab (with RSTUDIO) to get recommendations.When I'm using UBCF I can't extract the user id out of the realRatingMatrix containing the predictions, although I can do it with ...
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27 views

Transition probability matrix negative values of an M/M/C in R

I am trying to calculate a transition probability matrix of an M/M/C in R. The information given is the following : An IT support help desk represents a queuing system with five assistants taking ...
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1answer
34 views

Fix dominant columns/rows in symmetric data matrix?

I have a symmetric data matrix $A$, giving co-occurrence of events. That is, $A_{ij}$ is the frequency of occurrence of $i,j$ together. The diagonal elements of $A$ are unknown/indeterminate. I am ...
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58 views

R - system is computationally singular - dealing with small numbers

I'm working with a ~200x200 Markovian transition matrix of non-zero probabilities. Forcibly, these probabilities are, for the large part, going to be very small. I am trying to find the inverse of my ...
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1answer
75 views

Correcting for spatial autocorrelation in dissimilarity datasets

I have a community assembly dataset with 299 species at 15 sites. Im interested in correcting for the effect of spatial autocorrelation on beta-diversity (or species turnover). Dataset here. There is ...
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1answer
27 views

Steady state Markov Chain

is it able to count the steady state of problem with recurrent subchain.. for example if there are A B C D things and they are all recurrent. do they have steady state?? and also.. how to count ...
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2answers
61 views

Maximally reducing the rank of a matrix by removing some rows or columns

I have a $N \times M$ matrix, and the rank of matrix, $r$, is near $\min(M,N)$. I want to minimize the rank by removing some of the rows or columns to get $r \ll \min(M,N)$. The goal is to achieve ...
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159 views

Minimizing numbers along diagonal

Please forgive my ignorance if this isn't the appropriate place to ask this question, I'm by no means an expert in statistics. I'll omit most of the esoteric linguistic details here, but I've run up ...
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1answer
23 views

Why is this matrix code not behaving? [closed]

I'm running this code: ...
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2answers
79 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 few negative eigenvalues. Rest of eigenvalues are quite equal to ideal ...
3
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1answer
106 views

Robust estimates of the covariance matrix in the big data space

I am trying to compute the robust estimates of the covariance matrix (and also the mean) in the big data space. I am aware of FastMVE and FastMCD (Minimum Covariance Determinant and Minimum Volume ...
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35 views

Efficient calculation of selected diagonals (bands) of a covariance matrix?

I'm looking for an algorithm that can calculate a select few diagonals of a covariance matrix. Here's the problem: I have an $m\times n$ data matrix $X$ where $m$ is the number of features, which is ...
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1answer
43 views

Why do some parameters not appear in the matrix equation for an ANOVA model?

Here is the question I have been working on and this is the answer of it I realised $\beta_3$ is not in the $\beta$ matrix. I don't understand why. Can anyone please explain this?
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1answer
72 views

Expected value of least squares estimator $\hat{\beta}$

Given $\hat{\beta} = (X^{T}X)^{-1}(X^{T}Y)$, how do you derive the expected value? I found answers for finding the variance matrix but not the expected value. Thank you kindly.
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26 views

How to find the covariance matrix? [duplicate]

I have some trouble understanding the concept of a covariance matrix. For instance, I'm going over this question that says: assume that we have U1, U2 and U3 as independent zero-mean, unit-variance ...
3
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1answer
79 views

Variance of Beta IV

I'm trying to calculate the variance of the Instrumental Variables (IV) estimator $${\hat \beta _{IV}} = {\left( {{Z^T}X} \right)^{ - 1}}{Z^T}y = \beta + {\left( {{Z^T}X} \right)^{ - 1}}{Z^T}u$$ (or, ...
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1answer
72 views

Determinant of the covariance matrix in a normal distribution

Suppose a $p \times 1$ vector $x \sim N_p(\boldsymbol 0, \boldsymbol \Sigma_1)$. Now, There is another covariance matrix $\boldsymbol \Sigma_2$. We know that $|\boldsymbol \Sigma_2| < |\boldsymbol ...
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37 views

Parametrizing a matrix (and algorithm) by its orthogonal complement

Given a large orthonormal matrix $U$, say $p\times p-k$ (with $k$ much smaller than $p$), is there an effficient way to parametrize $U$ by any matrix orthogonal complement (any orthonormal matrix ...
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1answer
70 views

How to correlate categorical personality and music genre preference scores?

I'm currently a third year Biology student and I've annoyingly screwed myself over by not following the golden rule of stats, always know how to analyze your data prior to conducting the experiment. ...
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13 views

Comparison of two correlation matrix of same dimension in R [duplicate]

I have two correlation matrices(Pearson).For example, metrices of (3 gene X 3 gene) for cancer samples and normal samples,individually. I have got gene-gene correlation for both sample. Now I want to ...
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31 views

What does hat matrix mean? [duplicate]

$$H= X(X'X)^{-1}X'$$ I understand that if we multiply $Y$ matrix by $H$ matrix, then we will have $\hat Y$. That's why we call it $H$ matrix. Can someone please let me know what $h_{ii}$ ($i$-th ...
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23 views

G and R matrices in mixed model and model selection

I have data in which the plants were subjected to four conditions and measured weekly for a month. I would like to incorporate "plot" as a random factor into my linear mixed model using SPSS. I am ...
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1answer
15 views

Generating Regression For Unknown Beta in Matlab

My professor wants me to generate a regression problem based on the following: B is fixed unknown 100,100 matrix, X is random 100,100 matrix and y and noise are a random scalar for every output. He ...
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1answer
114 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
50 views

Standardized regression coefficients

I have a question regarding standardized regression coefficients and the correlation matrix. I have a two part problem that I am working on, and I need to show that the correlation matrix R is equal ...