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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Finding independent “clusters” in a matrix

I've called my question "clustering" but I am not sure if that's the right term. Imagine my matrix looks like this: ...
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8 views

Distribute chips over matrix [closed]

Suppose I have a 2x2 matrix A. Each element in this matrix can have a value between 0 and 1. So for example element A[1,1] can be 0.6 and element A[0,1] can be 1.0 while the other two elements A[0,0] ...
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Calculation the Expectation of an Inverse Wishart matrix

I have $\boldsymbol{A} = \boldsymbol{G}^H \boldsymbol{G}$ is a Wishart matrix, i.e, $\boldsymbol{G}^H \boldsymbol{G} \sim \mathcal{W}_K (M, \boldsymbol{\Lambda})$ with $\boldsymbol{\Lambda} = ...
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1answer
21 views

Is it a Wishart matrix?

We know that an $m \times m$ random matrix $\boldsymbol{A} = \boldsymbol{H} \boldsymbol{H}^H$ is a (central) real/complex Wishart matrix with $n$ degrees of freedom and covariance matrix ...
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25 views

Different results for Singular Value Decomposition (SVD) using different tools

I am currently implementing Latent Semantic Analysis in Java using the EJML library for the preliminary Singular Value Decomposition (SVD). I am testing my code against the original term frequency ...
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25 views

Problem constructing model matrix to generate predicted values to plot Bayesian glmmBUGS output

My goal is to plot the predicted values generated from a Bayesian model using glmmBUGS run through R. I believe my problem stems from a lack of understanding in 1) how to properly construct a model ...
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12 views

Effective ways to display confusion matrices from different predictors in an academic publication?

I want to display the results of two different predictors' performance on a dataset. I have a confusion matrix for each of the predictors' results on the test cases. I want to present these confusion ...
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9 views

Transforming vector elements to element indices [migrated]

Is there a way mathematically transform a vector to another with values of the first one being the indices of the second one? For example Y=[1 0 0 0 1 1 0 0 0] and X=[1 5 6] So X shows the indices ...
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31 views

Matrix completion approaches for healthcare big data

I am working on a prediction problem that leverage sparse clinical datasets. Missing data rate is in the range of 80%. 1- I am wondering if there is any example of application of matrix completion ...
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18 views

Cholesky decomposition and confidence ellipsoid

I'm trying to construct an error ellipsoid from a covariance matrix (which exists for a 3D point) and then sample consistent xyz points in this region. (This question succeeds this one.) What I'm ...
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1answer
39 views

Is the information matrix equality valid for the Poisson distribution?

As far as I know it should, since the support of the Poisson is independent of its lambda parameter. The negative of the expected Hessian equals $\frac{n}{\hat{\lambda}}$, where $\hat{\lambda}$ is ...
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30 views

Build corpus with phrases

I have my documents as: doc1 = beautifull, very good, very bad, you are great doc2 = very bad, good restaurent, nice place to visit I want to make my corpus ...
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39 views

Difference in values of tf-idf matrix using scikit-learn and hand calculation

I am playing with scikit-learn to find the tf-idf values. I have a set of documents like: ...
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46 views

Difference in tf-idf values in R

I am playing around in R to find the tf-idf values. I have a set of documents like: ...
3
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1answer
133 views

Generating a correlated data matrix where both observations and variables are correlated

I am trying to generate a simulated data matrix that is correlated by both observation and variable directions. So far I know how to do this for variable x variable. ...
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13 views

Matrix rank and amount of regressors

A question states: $X$ is the vector of regressors stacked for 30 observations and $Rank(X)=5$. There are no lags of $y_t$ in the set $X_t$. Using the Durbin-Watson statistic, test the null hypothesis ...
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27 views

Which contingency method to use with a 3x3 table yet still account for expected or discrete choice?

Im not sure what test to conduct when I have 3x3 matrix of data and still account for availability. So, in a simple chi square you have an observed observation and then you are often able to ...
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38 views

LDA - Why differents formulas to calculate covariance and pooled covariance matrix

Reading materials from differents sites some questions have risen about covariance and the pooled covariance matrix calculation to implement LDA: Definitions Ci - covariance matrix of group i (C1 and ...
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45 views

Can you use the chi-squared test with tables of real numbers?

Consider a $N \times 2$ matrix (MATLAB notation): M = [1.2, 3; 1.4, 2; 1.8, 1; 2.0, 2]; That is a $4 \times 2$ matrix where the first column ...
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1answer
36 views

can matrix completion work in the presence of many missing values?

I have a matrix with about 550k elements (2500 x 220) with 100k values known and the rest are unknown. Would it make sense to use matrix completion in this case, or are there too many values which ...
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40 views

Is there a way to perform SVD in a sequential manner?

My neurology experiment has a spike detector outputting 40 sample long spike waveforms. I'm using a dictionary method for sorting the spikes in real time. To ...
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2answers
26 views

OLS Coefficient estimator; Transformation from Matrix to sum of matrices form

I do not understand why the following equality holds (taken from Cameron & Trivedi 2005: Microeconomtrics): ...
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1answer
26 views
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117 views

Removing structure with a known functional form from the covariance matrix

I have a set of timeseries data $X^B = \begin{bmatrix} {X^B_1},{X^B_2},\dots, X^B_n \end{bmatrix}$ consisting of observations recorded at different spatial locations. There is crosstalk between the ...
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61 views

PCA Using prcomp in R

I'm trying to do principal component analysis (PCA) in R using the prcomp function. My input is a large matrix of 1,188 observations (rows) and 15,462 features (cols). I input this to the function ...
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51 views

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
133 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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1answer
36 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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20 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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60 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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35 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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9 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
51 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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11 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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28 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 ...
2
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1answer
183 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
69 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
39 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
38 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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19 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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28 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
23 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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37 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
93 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 ...
3
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1answer
51 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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0answers
54 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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26 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 ...