# Questions tagged [principal-component-analysis]

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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### Help with a PCA procedure.

I'm studying THIS paper which builds an index from a set of observed variables using Principal Component Analysis (PCA). However, the procedure described in Section 3.1 by formulas (6)-(8) confused me....
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### What is the correct formula for the covariance matrix?

I am solving about principal component analysis (PCA) and I stumbled upon a place where I need to calculate the covariance matrix, I am seeing varieties of formula. Here are some that I have found: ...
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### Linear auto-encoders and PCA with unequal input-output

It is a well-known fact that linear auto-encoders are equivalent to PCA, i.e. for the data matrx $X\in {\mathbb R}^{n\times N}$ the task $$\min_{W\in {\mathbb R}^{n\times k}}||X-WW^TX||$$ has a ...
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### How to create separation of "sides"/signs in PCA / eigenvector "directionality of data" analysis?

How to create separation of "sides"/signs in PCA / eigenvector "directionality of data" analysis? Since PCA will only give eigenvectors that show the principal axes, but it does ...
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### Bound for a random matrix and a normal distributed random vector

In the topic of Principal component analysis in high dimensions I have given the following task: Let $X\in\mathbb R^{n\times d}$ and $w\sim\mathcal N(0,\sigma^2I_n)$. Show that for any $\lambda>0$ ...
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### Compare Computation Time of PCA Using SVD of Data Matrix VS Eigen Vectors of Covariance Matrix

I know that principal axises can be computed both using SVD of data matrix and eigen vector decomposition of covariance matrix. I also heared that when dimension of data is larger than the number of ...
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