# Questions tagged [pca]

Principal component analysis (PCA) is a linear dimensionality reduction technique. It reduces a multivariate dataset to a smaller set of constructed variables preserving as much information (as much variance) as possible. These variables, called principal components, are linear combinations of the input variables.

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### Blind source separation of convex mixture?

Suppose I have $n$ independent sources, $X_1, X_2, ..., X_n$ and I observe $m$ convex mixtures: \begin{align} Y_1 &= a_{11}X_1 + a_{12}X_2 + \cdots + a_{1n}X_n\\ ...&\\ Y_m &= a_{m1}X_1 + ...
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### Can I use optimally scaled variables for a factor analysis to account for rotation? If I can then how?

I have discussed this issue several times in this site, but I am asking it again for a final justification from the experts of our community. I wanted to extract four factors (I should call dimensions ...
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I’m using Stata 12.0, and I’ve downloaded the polychoricpca command written by Stas Kolenikov, which I wanted to use with data that includes a mix of categorical ...
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### What is the precise relation between the eigenvalues of a covariance *function* and the eigenvalues of a covariance *matrix*?

Assume we have a temporal Gaussian Process $\mathcal{GP}(t;\ m,k)$ (GP) with mean $m$ and covariance function (aka. kernel) $k$ on some compact time interval $[0,T]$. Then, the eigenvalues $\lambda$ ...
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### Principal components: Can I interpret PCA as essentially a change of basis

I was hoping that someone could simply validate or correct my interpretation of Principal Components Analysis. There are a lot of questions on this site about Principal Components analysis--some ...
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### Interpretation of biplot in PCA

Blue points all appear in the lower right-hand quadrant in the plane formed by the first two principal components. Is it a good interpretation of the biplot (right panel) to say that blue points are ...
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### What, if any, dissimilarity is preserved in partial least squares (PLS)?

When we perform a principal components analysis (PCA) on a multivariate data set we are interested in finding orthogonal components that explain maximal variance in the data set. We can form a biplot ...
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### How does NIPALS algorithm work?

I'm working on NIPALS algorithm and I found this procedure from here: I'm just confused with the 4th step which stated, "using the $k$th scores, re-estimate the eigenvalues". As I understand, ...
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### Distributions of eigenvalues of random matrices: what can they be used for in data mining?

I've accidentally come across some papers discussing distributions of principal components of the sample covariance matrices. An example of such a paper is Johnstone, 2001, On the distribution of the ...
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### Kernel PCA vs principal curve analysis

Both principal curve analysis and kernel PCA provide the ability to find nonlinear PCA. Kernel PCA does this by finding principal components in a higher dimensional space. Principal curve analysis is ...
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### What is the rationale behind the "eigenvalue > 1" criterion in factor analysis or PCA?

What is the meaning of "eigenvalue > 1" criterion? I understand what eigenvalues and eigenvectors are. This question is w.r.t. this link and this statement there: By default, VARCLUS stops ...
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### How to compute component or factor scores when the analysis is based on polychoric/tetrachoric correlations?

[This question is modified based on suggestion from @ttnphns] I am doing linear principal component analysis (PCA) based on polychoric correlations between the variables (rather than on native Pearson ...
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### Reducing size of dataset to a fixed size - retaining maximum information in all dimensions

I was wondering about about the following problem: I have a set of $N=10^5$ observations with dimensionality $D=2$, and I would like to reduce it to a set of size with $M=10^3$, or some other \$(M \ll ...