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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Using a change detection error matrix approach for raster aggregation

I am assessing annual land use change along a 10 year period and have rasterized a vector land use dataset to base resolution 'n' metres to do so (vector data is taken as ground truth, errors in it ...
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6 views

Simultaneously Diagonalizable matrices

I'm interested in partitioning matrices into groups which are almost simultaneously diagonalizable. I'm aware that if matrices commute and one of them has no multiple eigenvalues then the matrices are ...
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9 views

Interpreting the psych::cor.smoother function in R

I've tried to contact William Revelle (the package creator) about this but he isn't responding. In the psych package there is a function called cor.smoother, which determines whether or not a ...
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10 views

Reading Centroid extracted factor matrix into SPSS for rotation, analysis [migrated]

I've been struggling with this for the last 4 days. I have concluded that I'm not smart enough to sort this out on my own, and I want to do this right. Desired Outcome: I want to instruct SPSS to ...
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1answer
26 views

Neural Net Matrix Multiplication

I'm trying to figure out the matrix multiplications for the implementation of a single hidden layer neural net for MNIST digit recognition in Python. Like the following: ...
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1answer
17 views

$LDL^T$ decomposition from Cholesky decomposition

Suppose we have a covariance matrix $\Sigma$. I know that the Cholesky decomposition $A^T A$ can be found from the LDL decomposition using $$ \Sigma = LDL^T = (LD^{\frac 1 2})(LD^{ \frac 1 2 })^T = ...
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3answers
125 views

Decrease of $(X'X)^{-1}$ as n increases

Let $X$ be a $n \times p$ matrix, filled with iid draws, with $n \geq p$ (like a conventional data matrix). I would like to show that, in a sloppy notation, $(X'X)^{-1} \rightarrow 0$ as $n ...
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0answers
12 views

Several variables in correlation matrix output

I'd like to improve a big correlation matrix output correla, because I want to see significante values (p<0.05) but with my code is very dificult to find ...
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25 views

How does Guttman's image analysis work?

Could anyone explain to me how Guttman's image matrix works? Is extracting variables a reiterative process? Are all variables extracted? What's the meaning of the formula? What happens to the diagonal ...
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1answer
35 views

Variance of a multivariate AR(1) process

I have a multivariate AR(1) process (first-order vector autoregression, VAR(1)) of the form $$ \pmb X_{t+1} = A \pmb X_t + \zeta_t $$ where $\pmb X_t$ is a vector, $A$ is a matrix and $\zeta_t \sim ...
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1answer
123 views

Codification of Matrix $X$ in $Y=XB+\epsilon$

The variables for the data below is age, group (treatment 1,2,3), Y response variable. ...
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1answer
19 views

Recommenderlab not working with highly sparse binary data?

The data used is a ratings matrix generated from simple 0-1 yes/no click data based on whether or not a user visited a section of a website. This is implicit voting since if a user is interested in a ...
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1answer
64 views

Differentiating the RSS w.r.t. $\beta$ in Linear Model

I am reading the book "The Elements of Statistical Learning". The book says But when I try to prove it, I get the following: $$RSS(\beta) = (y - X\beta)^T(y-X\beta)$$ $$RSS(\beta) = y^Ty ...
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1answer
39 views

How to obtain the inverse of a matrix while solving an equation?

Given a matrix $A$, let us assume there is a equation: $Ax = b$ To solve for $x$, we can write: $x = A^{-1} b$ One way to obtain the inverse of A is by single value decomposition: Decomposition ...
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0answers
12 views

R-programming limma design matrices

I have a really basic understanding of how the package limma works in that it fits a linear model to each row/sample in a micro-array dataset. What I do not understand is how to use a design matrix to ...
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23 views

How to provide input to TSNE

I am using TSNE for the first time for dimension reduction. I have around 12 million records with 5000 distinct values. I want to perform dimension reduction (DR) so that I visualized those distinct ...
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0answers
14 views

When using loss matrix in rpart in R, xerror does not start at 1 [closed]

I am trying to use a loss matrix in rpart penalizing false positives 10 times as much as false negatives, but when I fit my data and then use printcp, my xerror values start at 10 and not 1. I am ...
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6 views

How to find the generalized inverse of a matrix in SageMath?

Given a matrix $A_{m\times n}$, a matrix $G_{n\times m}$ is said to be a generalized inverse of $A$, if it satisfies, $$AGA=A$$ Now, since for a matrix $A$, generalized inverse of $A$ is plenty if ...
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1answer
27 views

Question about idempotent matrix: how can M(I-M) equal zero?

Let me assume that M is an idempotent matrix (MM=M) and (I-M) is not zero (I is identity matrix with the same dimensions as M). If I multiply (I-M) by M, (M-MM)=(M-M)=0. How could it be possible that ...
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1answer
32 views

Get distance matrix directly condensed

I am developing a content-recommender Python system and most of my items (~8 millions) are static so I have thought about pre-computing the top 150 similar items for each item. This way, when a user ...
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0answers
9 views

Confusion Matrix in FCM

I have written code of FCM(Fuzzy c-mean) in java for centroid and membership matrix generation as well as object function. How can i generate confusion matrix any idea in this FCM program.
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35 views

Application of Givens rotation to two matrices

I am reading this paper on Multiresolution Matrix Fatorization, http://arxiv.org/pdf/1507.04396v1.pdf, and have come across something that seems like an error to me. In Algorithm 2, the authors take ...
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13 views

Input matrix construction for time series

I am having problems constructing the input matrix for a data analysis / machine learning task. The data set consists of ~300 data points, each one in form of a matrix where rows are time steps, ...
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1answer
32 views

How to reduce dimensionality of audio data that comes in form of matrices and vectors?

I'm working on a project involved with identifying different types of sounds (such as screams, singing, and bangs) from each other. We've got our data a reasonable number of different transformations ...
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18 views

Metric from a positive definite matrix

I'm trying to prove that the Mahalanobis distance is an actual distance, more in general Given B symmetric and positive definite matrix set d(x,y)=(x-y)'B(x-y) ( ...
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16 views

Primal and dual problem in simplex algorithm [closed]

I know that the primal problem \begin{equation} \begin{aligned} & \text{maximize} & & \textbf{c}^T \textbf{x} \\ & \text{subject to} & & \textbf{A} \textbf{x} \leq \textbf{b} ...
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1answer
45 views

Determinant of a block matrix with sparse elements

I have a positive definite symmetric matrix that looks like $$\pmatrix{A & 0 & 0 & E \\ 0 & B & 0 & F \\ 0 & 0 & C & G \\ E^\prime & F^\prime & G^\prime ...
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9 views

help me understand the proof in the paper “restricted ridge estimation”

I'm reading the paper "restricted ridge estimation" by Grob(2003). I can not understand the proof of theorem 1 in this paper. I don't know how this estimator $\hat{\beta}_{r}(k) = ...
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1answer
22 views

R unfold a list into a matrix [closed]

I have a list in which each element inside it is a matrix. How can I unfold this list to get a matrix. Example: List[[1]]=matrix A List[[2]]=matrix B List[[3]]=matrix C and I want directly to get a ...
3
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1answer
152 views

Sampling a random binary matrix with “Gaussian” probability distribution

Let $A_{ij}$ be a $n\times n$ random binary matrix with probability mass function $P(A)$ given by $$ \log P(A)=-\frac 12 \mathrm{tr}\left[\left(A-M\right)^TV\left(A-M\right)\right] + C, $$ where $M$ ...
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0answers
6 views

Create Optimal Matrix based on Given Constraints

I would like to construct a 0-1 matrix which satisfies certain constraints and allocates either 1 or 0 to the value in order to optimize the objective function. The following constraints should be ...
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13 views

Coherence matrices

I'm analyzing ECoG data that were recorded during a working memory task. There are 6 different subjects and they all have about 100 trials. Each subject has different electrode coverage (so not in the ...
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19 views

How is this gradient derived?

I am reading this paper, http://math.ucla.edu/~dakuang/pub/sdm0125.pdf, and came across this function, $f(x) = ||A-H^TH||_F^2$. Later, the authors take the gradient of this function, $\nabla f$, but ...
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7 views

How can I add one continue variable without computing its interaction using factorization machines?

I have an input data which consist of 1) User, 2) Item, and 3) a continuous variable. It is a regression problem. So the input can be as below: ...
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30 views

User defined contrast coding with 2 categorical and 1 continuous predictor

I would really appreciate if someone could confirm that the contrast matrix that I defined with the glht package for my model is correct and that the continous ...
5
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1answer
375 views

How To quickly do derivatives with respect to matrices

Whats a quick way to work the below (and problems similar) out? For me to take this derivative it involves a lot of time and boring calculation, there has to be a better way. This is taken from ...
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4answers
9k views

Why the sudden fascination with tensors?

I've noticed lately that a lot of people are developing tensor equivalents of many methods (tensor factorization, tensor kernels, tensors for topic modeling, etc) I'm wondering, why is the world ...
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1answer
48 views

reverse a data frame in R [closed]

data<-read.csv(file="blabla.csv",row.names=1) data<-t(data) data<-as.data.frame(data) sapply(data,class) #check the type of data I have a big dataset and ...
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2answers
185 views

Prove that $(A^{-1} + B^{-1})^{-1}=A(A+B)^{-1}B$

I have this equality $$(A^{-1} + B^{-1})^{-1}=A(A+B)^{-1}B$$ where $A$ and $B$ are square symmetric matrices. I have done many test of R and Matlab that show that this holds, however I do not know ...
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1answer
31 views

What should be the correct result of this product $(Y-XW)^T(Y-XW)$

i usually come across this equation and I am not able to understand it entirely, here X, W and Y are matrices of size N*D, D*1, and N*1 resp. $(Y-XW)^T(Y-XW)$. As per me it should be equal to ...
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0answers
6 views

4x4 matrix of 4 time series is singular up to certain, why? [duplicate]

why is a covariance matrix which is calculated from 4 time series, so it is 4x4, singular up to time point i=5? I need to calculate with the determinant which is not availble until i=5 so my ...
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0answers
31 views

how to normalize demand/availability matrix for Citibike data

I am not a statistician but would appreciate an outside perspective on my current project analyzing citibike data. This is a bit complicated so please bear with me. My goal is to determine to what ...
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44 views

Mean subtraction and addition purpose

I read Efficient and Accurate Approximations of Nonlinear Convolutional Networks paper. I have this point I don't understand in section 2.1. But may be, my question will be more general. it is known ...
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0answers
11 views

SSCP vs correlation matrix [duplicate]

Lets say I have a matrix X, where each row is a subject and each column is a variable. I have a few questions about manipulating this matrix, and what the result is: If I calculate X'X, am I correct ...
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24 views

Average distance in distance matrix

I have a set of many longitude and latitude points within a city. I constructed the nxn euclidean distance matrix. My goal is to know which is the average distance ...
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1answer
27 views

Design matrix with intersec 0 or 1

I am constructing a model matrix for a repeated meassurments experiment with three individuals per group and three treatments per individual. ...
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1answer
57 views

How to identify if parameters are estimable, after defining a design matrix

I need to define a design matrix $X$ so that it fits this scenario: For $1\leq i< j \leq 5$, where $i$ are competitors and $j$ are different competitors. Their score is $y_{ij} =$ score of player ...
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24 views

Linear models with Matrix notation - eigenvalues, eigenvectors and geometric meaning

Find the eigenvalues and the eigenvectors: 1) $ C=\alpha I_n - (1-\alpha)J $, where $J=ii'$, such that $i=(1,1,...,1)' \in \mathbb{R}^n$, and $\alpha \in (0,1)$. 2) $B=I_n - \frac{1}{n}J$. So, ...
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1answer
41 views

Analysing data from multiple matrices

I have created a function which produces 1000 different matrices simulating the ranking of football teams. The 1000th matrix produced is as so: ...
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15 views

“weigh” different variance covarance matrixes

so my question if I have a set of weights which sums to 1 (say: [0.2,0.2,0.6]) which would represent my states of the world and I have forecasted 3 different variance covariance matrixes (all of which ...