Timeline for Making sense of principal component analysis, eigenvectors & eigenvalues
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 7, 2022 at 3:35 | comment | added | David M W Powers | Te-Won Lee (2010). Independent Component Analysis: Theory and Applications | |
| Dec 7, 2022 at 3:29 | comment | added | David M W Powers | Vapnik, Vladimir (2000). The nature of statistical learning theory. New York: Springer-Verlag. ISBN 978-1-4757-3264-1. | |
| Dec 7, 2022 at 3:27 | comment | added | David M W Powers | Conversely, any statistics or statistical learning or signal processing textbook with a discussion of bias, variance and noise should discuss the dependence on the central limit theorem and assumptions of normality, and the related difference independence vs uncorrelated (as distinguished in ICA vs PCA), e.g. | |
| Dec 7, 2022 at 3:22 | comment | added | David M W Powers | Golub, G. and C. Reinsh (1971) ‘Singular Value Decomposition and least squares solutions’, in Handbook for Automatic Computation, Vol 2: 134-151. New York: Springer-Verlag. | |
| Dec 7, 2022 at 3:21 | comment | added | David M W Powers | Any textbook on spectral methods (SVD, PCA, ICA, NMF, FFT, DCT, etc) should discuss this, and in particular in an SVD context will explain how the variance is the sum of squared singular values, so when you drop components to compress the data, the ratio of new to old variance is regarded as the proportion of variance explained. e.g. | |
| Dec 6, 2022 at 1:44 | comment | added | thomaskeefe | @DavidMWPowers Do you know a reference that explains this coincidence that you describe? | |
| S Mar 14, 2019 at 14:02 | history | suggested | Glorfindel | CC BY-SA 4.0 |
broken image fixed (click 'rendered output' or 'side-by-side' to see the difference); for more info, see https://gist.github.com/Glorfindel83/9d954d34385d2ac2597bbe864466259f
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| Mar 14, 2019 at 7:46 | review | Suggested edits | |||
| S Mar 14, 2019 at 14:02 | |||||
| Mar 9, 2017 at 17:30 | history | edited | CommunityBot |
replaced http://25.media.tumblr.com/ with https://25.media.tumblr.com/
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| Apr 15, 2014 at 18:46 | comment | added | isomorphismes | @DavidMWPowers Interesting. I am thinking about rotations from a linear-algebra standpoint. | |
| Apr 15, 2014 at 14:06 | comment | added | David M W Powers | Actually it is kind of coincidental that rotations are linear and so a convenient way of describing what's going on for non-geometric data. The coincidence relates to the quadratic nature of both Cartesian/Euclidean space and the Central Limit Theorem/Gaussians. Viz. sigmas add up quadratically like orthogonal dimensions, which is where our ND rotational/orthogonal terminology originates by analogy with 2D and 3D space. | |
| Jan 16, 2014 at 7:13 | history | edited | isomorphismes | CC BY-SA 3.0 |
added 877 characters in body
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| Jan 16, 2014 at 5:22 | history | answered | isomorphismes | CC BY-SA 3.0 |