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.

learn more… | top users | synonyms

0
votes
0answers
4 views

Handle random orthogonal matrix 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 ...
0
votes
0answers
22 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 ...
0
votes
0answers
19 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 ...
2
votes
0answers
17 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
votes
1answer
51 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 ...
6
votes
1answer
42 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
votes
1answer
52 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) \\ ...
0
votes
1answer
15 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 ...
0
votes
0answers
34 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 ...
0
votes
0answers
14 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 ...
0
votes
0answers
16 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 ...
0
votes
0answers
13 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 ...
0
votes
0answers
19 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 ...
0
votes
0answers
7 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 ...
0
votes
0answers
23 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 ...
0
votes
0answers
6 views

what is the derivative of following notation? [migrated]

Could you help me to find the derivative of following function with respect to $x_i$ $f = \sum_{j=1}^{n}{}A_{i,j}(x_i-x_j)(x_i-x_j)^T$, where $x_i$ and $x_j$ are vectors, and $A_{i,j}$ is affinity ...
0
votes
1answer
31 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 ...
0
votes
0answers
4 views

Error in Coocur matrix: 'x' must be numeric [migrated]

I am trying to determine species co-occurrence using cooccur package in R. My data appears to be formatted just like the example data, finches, except I keep getting a "non numeric" error when I run ...
0
votes
0answers
9 views

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: ...
0
votes
1answer
27 views

Similarity between two samples (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. ...
0
votes
0answers
13 views

maximizing matrix diagonal elements in R [migrated]

Given a matrix (or table in R ) ...
1
vote
0answers
33 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 ...
1
vote
1answer
63 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 ...
1
vote
1answer
49 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 ...
0
votes
0answers
11 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 ...
3
votes
1answer
60 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: ...
1
vote
0answers
24 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 ...
1
vote
0answers
34 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 ...
1
vote
0answers
28 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 ...
0
votes
1answer
87 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 ...
0
votes
1answer
60 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 ...
0
votes
0answers
18 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 ...
0
votes
1answer
57 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 ...
1
vote
0answers
149 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 ...
1
vote
1answer
26 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 ...
0
votes
2answers
65 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 ...
2
votes
1answer
54 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 $(i,j)$ ...
1
vote
0answers
50 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 ...
0
votes
0answers
24 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 ...
2
votes
1answer
69 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 ...
3
votes
0answers
73 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 ...
0
votes
1answer
104 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 ...
0
votes
0answers
28 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 ...
1
vote
1answer
35 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 ...
1
vote
0answers
74 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 ...
2
votes
1answer
90 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 ...
1
vote
1answer
34 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 ...
1
vote
2answers
67 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 ...
5
votes
1answer
164 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 ...
-1
votes
1answer
23 views

Why is this matrix code not behaving? [closed]

I'm running this code: ...