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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Item-based collaborative filtering – Can you add demographic information to initial user×item matrix?

I am building an item-based collaborative filter recommendation system. I have a matrix of users and items, which in this case, are products that were either bought or not (i.e., binary: ...
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2answers
101 views

Why is the Pearson correlation 1 when only two data values are available?

I am trying to obtain a Pearson correlation between 6 different variables (represented by columns in the matrix below) with two datapoints each (rows). This is the matrix: ...
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Least squares / residual sum of squares in closed form [migrated]

In finding the Residual Sum of Squares (RSS) We have: \begin{equation} \hat{Y} = X^T\hat{\beta} \end{equation} where the parameter $\hat{\beta}$ will be used in estimating the output value of input ...
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17 views

What is the limit of variables that can be used in R to create matrix scatter diagrams? [closed]

R crashes after trying to create a matrix scatter diagram with 47 variables that are in a CSV file being read by my R workspace. I have already set my limit number to NA by using limitNo=NA which ...
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39 views

Linear programming problem [closed]

You're given 3 puncts of producery $A_1=138$, $A_2=102$, and $A_3=120$, and 4 puncts of consumery $B_1= 120$, $B_2=105$, $B_3=90$, $B_4=135$. Sort the stocks in a way that the necessity of $B_1$ to be ...
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how to transfer/export output of rcorr(matrix) into excel table? [migrated]

I use correlation test using code "rcorr", and here it is my script: ...
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11 views

JAGS array indexing

I have a relatively simple multivariate response problem that seems to causing me problems with array indexing. I've scraped/rewworked the model program down to the bare essentials and hopefully ...
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15 views

Derivation of a fixed effects estimator

I've come across parts of a derivation of a fixed effects estimator in a paper i don't understand. The log likelihood function is where $Y_i=(Y_{i1},...,Y_{iT})'$, and $X_i$ is a $T\times k$ ...
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24 views

Iterative solving of ML estimators

I have derived this likelihood function \begin{equation} \begin{split} &-\frac{1}{N}\log L(\eta,\beta,\mathit{\Omega})\\ &=\frac{1}{2}\log ...
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56 views

Understanding the derivation of a ML-estimator

I have the following likelihood function: I'm given this information about the $\Omega$ matrix ($\boldsymbol{1}$ is a $T \times 1$ vector of ones): I would like to be able to show that the ...
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32 views

Convergence of a matrix product

Let $A=o_{a.s.}(1)$; $A:k\times k$ matrix and $Vu=O_p(1)$; $V:k\times k$; $u: k\times 1$. Specifically, $Vu$ converges in distribution to $\mathcal N(0,I_k)$. Can we show that $VAu=o_p(1)$ or ...
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7 views

Too Large Values with Assembled Distance Transform

I am trying to apply ADT as a distance between two images or their DCT coefficents. The ADT is given as (image taken from "Bidirectional PCA with assembled matrix distance metric for image recognition ...
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1answer
33 views

Linearly dependent features

I have a matrix A of 1000 observations (rows) and 100 features (cols). I would like to find: Linearly dependent features so that I can remove them and simplify the problem. rank(A) gives me 88, ...
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10 views

Question on Matrix Operation Notation

I have confused myself in attempt to express a 2-step operation in matrix notation-- The data consists of 2 "chunks" of information--quantity of identical items sold in different stores and their ...
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18 views

Condition number of covariance matrix

I am interested in generating a covariance matrix of dimension say 100. I managed to get a correlation matrix with finite condition number. To construct a covariance matrix I need to have standard ...
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1answer
52 views

Plotting error ellipsoid from 3x3 covariance matrix in R?

I'm hoping to be able to take a 3x3 covariance matrix and turn this into an error ellipsoid but so far I haven't been able to achieve this. I'm very new to R (in fact turned to it to attempt to solve ...
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1answer
25 views

Normalize row or column while each row is an observation

Suppose I have a matrix compose of row as each observation, column as each property and I want to calculate the distance between each observation. In this case I think I should normalize each column, ...
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2answers
28 views

Padding a matrix - effect on statistical analyses

I have the time-series data for a lot of stocks from their specific groups (market indices), and I would like to perform some quantitative tests on them as a group. Let's say for example I have 30 ...
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1answer
36 views

Name of this simple descriptive method for showing crosstable combination typicalities?

This might be a basic question, but I have no clue what this descriptive method could be named. Simplified, I have a cross-table with Occupations (e.g., doctor, lawyer, engineer) as rows, and Hobbies ...
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17 views

Conditional distribution of Inverse Wishart

Suppose $\begin{bmatrix} K_{11} K_{12}\\K_{12}^T K_{22} \end{bmatrix}\sim\mathcal{IW}\left(\eta,\begin{bmatrix} \Sigma_{11} \Sigma_{12}\\\Sigma_{12}^T \Sigma_{22} \end{bmatrix}\right)$. What is the ...
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0answers
26 views

How to compare 37 dichotomous variables (lab tests) to 31 dichotomous variables (diagnosis)

I've constructed a database based on chart review of patients. Patients had a variety of tests performed (37 different types, which were either positive, negative, or not performed aka 1/0/blank - I ...
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5 views

Modeling data using matrices

I have multiple square matrices represent the relations between members of a club. Is there any statistical method to represent these metrices as one matrix.
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1answer
20 views

how can I concatenate these mixtures

I have a matrix. for each row of this matrix I made a Gaussian mixture, how can I concatenate these mixtures.
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32 views

How to complete matrix multiplication with an index that runs across all nodes?

Not sure if this would be the right place to ask...but I am attempting to calculate a topological overlap measure (TOM) matrix using R. I'm running into a problem with a likely simple solution. ...
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1answer
90 views

What are the 2nd derivatives of the log multivariate normal density?

I develop open-source statistical software (http://openmx.psyc.virginia.edu/), but matrix calculus is not my strong point. I need the 1st and 2nd derivatives of the log multivariate normal density. I ...
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1answer
49 views

Problem related to OLS estimators

The problem is: Suppose we fit a model Y = XA βA + ε. However, the true model is Y = XA βA + XB βB + ε. A is kA x 1 and B is kB x 1. Show that the OLS estimates of βA will still be equal if ...
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39 views

Lipschitz constant for a matrix completion problem? (frob loss)

For regression (squared loss) I know it's something like the largest eigen value of the matrix X'*X, or something. Where X is the data matrix. Matrix completion is basically: ...
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22 views

Symbolic matrix algebra software [closed]

just wondering is there a symbolic matrix algebra software like Mathematica that would solve complicated matrix expressions? Many thanks!
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25 views

Reading and interpreting the scatter matrix [duplicate]

The scatter matrix is defined as $$S = \sum_{j=1}^n (\mathbf{x}_j-\overline{\mathbf{x}})(\mathbf{x}_j-\overline{\mathbf{x}})^T$$ The trace (sum of the diagonal elements) of this matrix is ...
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79 views

Summing up two matrices of distances among centroids

I am ecologist, using mainly the 'vegan' R package. I want to combine ('cbind') 2 matrices (sample x species) but samples (row) are different. I sampled within 24 sites, by using 2 distinct methods, ...
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1answer
31 views

In non-negative matrix tri-factorization, initialization not possible because matrix is singular

I have implemented the non-negative matrix tri-factorization algorithm (link to paper). If is similar to the more widely known NMF (non-negative matrix factorization), but incorporates prior knowledge ...
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24 views

Identifying the Distributon from a Distance Matrix

I have a number of distance matrices that I want to associate their members with a probability distribution. Is there a method which can affiliate each distance matrix with a distribution? EDIT: Lets ...
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1answer
96 views

For PCA prove that covariance matrix is diagonal?

For $z=W^\mathbf{\intercal}(x-m)$ where $k$ columns of $W$ are the top $k$ principal components of a given dataset $x$ and $m$ is the mean, how can I prove that $z$ is diagonal? $x$ is the original ...
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77 views

Training Restricted Boltzmann Machines with Bias Units

I have written some code that basically does the following:- 1: creates a matrix of binary features and a matrix of scaled features ( in the range 0 to 1 ) 2: RBM trains separately on each of the ...
2
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56 views

Appropriate measure to find smallest covariance matrix

In the textbook I am reading they use positive definiteness (semi-positive definiteness) to compare two covariance matrices. The idea being that is A-B is pd then B is smaller than A. But I'm ...
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49 views

Covariance matrix explanation OLS and correcting residuals

I have been wondering, in a couple of books on econometrics I have discovered that they explain many things in regards to the distribution of beta. I therefore have an example and a couple of question ...
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34 views

Newey-West standard errors computation further explanation

I am trying to calculate the Newey-West standard errors but I get stuck with the E value of (X'X)^-1. What is E actually doing? If it is the mean how would you compute it? Please give a short example ...
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9 views

What are methods/software packages to create temporal matrices for agricultural practices?

I would like to create a temporal model showing the likelihood (I am sure this is not used in the correct context) that certain size avocados grow from smallest, small, bigger, biggest. I have ...
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1answer
38 views

How to make similarity matrix from two distributions?

My domain expertise is not in statistics, therefore my question might sound stupid to you. I have two different distributions, first has studentIDs as columns and features in row. First Distribution ...
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45 views

How to extract covariance (error) matrix of independent parameters x,y from covariance matrix of dependent parameters x,y,z?

Suppose I have a covariance (error) matrix C_xyz for system with 3 parameters: x, y, z. Then it appears that ...
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26 views

Region comparability over a matrix sample

We are given a list of rows R, with elements R_i, i=1..n, and a list of columns ...
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37 views

Correlation structures in Linear mixed models

The linear mixed model I want to fit to my data shows some major correlations. Z.transformation already reduced the correlations but not as much as I had hoped. I calculated the variance inflation ...
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0answers
38 views

tensor cross covariance calculation

I have an $N \times P$ matrix $X$ (with $\Sigma$ variance covariance matrix $P \times P$) and I am using R to calculate the tensor product $E\{(X-\mu)(X-\mu)' \otimes (X-\mu)(X-\mu)'\}$ (tensor ...
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27 views

nearPD function in Matrix package

Does anyone know how the eigenvalues are adjusted to make a non-positive definite matrix into a positive definite matrix in Matrix package? I mean in nearPD function.
2
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What is the distribution of an outer product of random values mod P?

I haven't been able to answer this daunting question for days now and I am not able to find the right resource for it, so maybe someone here might help me out. Consider an outer product of two ...
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51 views

Decomposing a correlation matrix

I'm doing some work on a model implementation. The specific model is the Multi-factor concentration risk model This Paper. Although I don't think the context is necessary for the specific problem I'm ...
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1answer
104 views

how to Normalize data(with noise) into 0-1 range good scale in mean and variance?

i have a matrix data. Perhaps some data in one cluster and another in some cluster. data scale is between [0-1000](just example). and i want to normalize into [0-1] and good in mean and variance. it ...
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72 views

Multivariate Data into VAR model in the vars package

I have been trying to use the vars package in r for my multivariate time series data. I am having some problems. Do I have to do something to my multivariate data before using the vars package? Can ...
3
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2answers
727 views

What does the inverse of covariance matrix says about data? (Intuitively)

I'm curious about the nature of $\Sigma^{-1}$. Can anybody tell something intuitive about "What does $\Sigma^{-1}$ say about data?"
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79 views

Use matrix feature for machine learning or cluster analysis

I have a bunch of features that I would like to use for classification/machine learning and cluster analysis. Normally I use single point values or transformations of values for features and ...