# Tagged Questions

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### How to project test data onto the principal vectors produced by kpca?

So I have a dataset of dimension 6395x15 and when I apply kernel-PCA on this dataset, I get a rotated matrix of dimesion 6395x596. pcv() gives me the matrix of column-wise eigen-vectors and this ...
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### covariance projected data

I am sorry if the question sounds dumb, but statistics among other things is not my stongest subject. In "Principal Component Analysis" (PCA), the idea is to project the data on the orthonormal basis ...
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### 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.
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1answer
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### Why do R function eigen()' and Armadillo's eig_sym()` give different results

I am trying to compute eigenvalues in C++ using the Armadillo function eig_sym via RcppArmadillo. The results are not entirely ...
1answer
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### Regression Estimation difficulties

My regression problem is properly formulated, but is encountering serious computational difficulties. Dependent: $Y$ = multinomial Independent: $X_1, \dots, X_{90}$ = linearly independent set of ...
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### Eigenvectors of a shuffled correlation matrix

A question about a shuffled vs. unshuffled correlation matrix I took the correlation matrix and shuffled between its values symmetrically. (shuffled only the left lower triangle of the matrix and ...
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### Why are the eigenvalues of a covariance matrix corresponding to the data's variance? [duplicate]

For multi-dimensional data, we can compute its covariance matrix, and then the eigenvalues and eigenvectors. It turns out that the eigenvector with the largest eigenvalue corresonds to the direction ...
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### Distribution of eigenvalues given one is known

I'm familiar with using insights from Random Matrix Theory to determine the number of principal components from the PCA of a covariance/correlation matrix to use to form factors. If the eigenvalue ...
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277 views

### Exploratory factor analysis and eigenvalues

I have reviewed a number of questions regarding this issue and just want to throw this one in the mix - so I apologize for its redundancy. So, I ran an EFA on 60 items. Analysis resulted in 19 ...
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278 views

### How do I convert the variances explained by a principal component into an eigenvalue?

I'm using SigmaPlot to run PCA on various measurements that should all correspond to size of an animal. Running PCA using a covariance matrix (instead of a correlation matrix, since all of the ...
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### Adversarial noise in PCA

PCA is known to be quite sensitive to outlier noise (and this is why several Robust PCA techniques exists.) However, I am looking for a concrete example of sensitivity of PCA to adversarial noise that ...
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### Dimensionality Reduction using PCA, with SVD of correlation matrix

I have computed a correlation matrix from certain data set of dimension 6 The correlation matrix is: ...
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### PCA matrix-decomposition in image recognition

I am implementing an image recognition program as an exercise but I am comfused in the following point.I have a data set M with dimensions $NxD$ where $N<<D$ so I have used dimension reduction ...
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### PCA eigenvectors with dimensionality reduction

I want to understand how I can compute the eigenvectors and the eigenvalues of a matrix using dimensional reduction.I have a Matrix $M$ of dimensions $n$ x $d$ using dimension reduction I can compute ...
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### Determining eigenvalues and eigenvectors in R

x<-model.matrix(d) [,-1] e<-eigen(t(x) %*% x) e values [1] 1174600.548 21261.741 16133.842 6206.181 1856.894 First my $\alpha_1=1174600.548$, but ...
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153 views

### What is the relationship between the 1st PC & the mean pairwise correlation?

What is the relationship between (first) principal component(s) and the correlation matrix or the average correlation of the data. For example, in an empirical application I observe that the average ...
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### Show that all the characteristic roots of a dispersion matrix of a random variable are non-negative

Show that all the characteristic roots of a dispersion matrix of a random variable are non-negative. \begin{vmatrix} \sigma_{11}-\lambda & \sigma_{12} & \cdots & \sigma_{1p}\\ ...
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902 views

### What is the correct way to calculate the explained variance of each EOF as calculated from a gappy data set?

I am trying to determine the correct amount of variance explained by each mode of an Empirical Orthogonal Function (EOF) analysis (similar to "PCA") as applied to a gappy data set. (i.e., containing ...
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### Why are eigen and svd decompositions of a covariance matrix based on sparse data yielding different results?

I am trying to decompose a covariance matrix based on a sparse / gappy data set. I'm noticing that the sum of lambda (explained variance), as calculated with svd, ...
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206 views

### Eigenvalues nearly all 1 in canonical correlation analysis

I ran a Canonical Correlation Analysis on about 845 cases with 1000 variables each. (It originally started with 1000 cases and 400 variables but by using a kernel I got a 1000x1000 matrix) As a ...
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148 views

### Estimated distribution of eigenvalues for i.i.d. (uniform or normal) data

Assuming I have a data set with $d$ dimensions (e.g. $d=20$) so that each dimension is i.i.d. $X_i \sim U[0;1]$ (alternatively, each dimension $X_i \sim \mathcal N[0;1]$) and independent of each ...