Timeline for PCA on correlation or covariance: does PCA on correlation ever make sense? [closed]
Current License: CC BY-SA 3.0
25 events
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| Jul 16, 2018 at 19:39 | history | edited | ttnphns |
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| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Dec 15, 2014 at 14:33 | review | Reopen votes | |||
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| Dec 15, 2014 at 14:10 | history | edited | amoeba | CC BY-SA 3.0 |
Improved the readability of this question. Rewrote the title to represent what is being asked. Provided explicit link to the "main" question.
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| Jul 1, 2013 at 14:32 | history | closed |
Nick Cox Glen_b gung - Reinstate Monica Scortchi♦ whuber♦ |
Opinion-based | |
| Jun 28, 2013 at 21:37 | answer | added | mark | timeline score: 6 | |
| Jun 28, 2013 at 19:29 | answer | added | Lucozade | timeline score: -1 | |
| Jun 28, 2013 at 9:58 | history | edited | Lucozade | CC BY-SA 3.0 |
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| Jun 27, 2013 at 20:54 | comment | added | Gala | PCA does not “claim” anything. People make claims about PCA and in fact use it very differently depending on the field. Some of these uses might be silly or questionable but it does not seem very enlightening to assume that a single variant of the technique must be the “algebraically correct” one with no reference to the context or goal of the analysis. | |
| Jun 27, 2013 at 14:36 | comment | added | whuber♦ | The crux of this matter appears to rest on a misunderstanding of what standardization does and how PCA works. This is understandable, because a good grasp of PCA requires visualization of higher-dimensional shapes. I would maintain that this question, like many other questions based on some sort of misapprehension, is thereby a good one and ought to remain open, because its answer(s) can reveal truths that many people might not have fully appreciated before. | |
| Jun 27, 2013 at 11:37 | comment | added | Scortchi♦ | Perhaps you're thinking of PCA in the wrong way: it's just a transformation, so there's no question of its being correct or incorrect, or relying on assumptions about the data model - unlike, say, regression or factor analysis. | |
| Jun 27, 2013 at 11:17 | comment | added | Lucozade | @ Gael: Because both approaches claim to solve the same problem (see pt. 1 of my answer to ttnphs). Moreover, in e.g. linear regression, there are a set of specific conditions that must be satisfied to be able to use the method. Between cov-PCA and corr-PCA, I have not yet seen (a) clear rule(s) or division when each of these should/should not be applied, how both methods diverge/converge under which conditions, etc. PS: I did not intend any agression; on the contrary. Perhaps this rather applies to anyone who writes "I quit reading your question", but still comments nevertheless. | |
| Jun 27, 2013 at 9:55 | comment | added | Gala | But that's the case with many other techniques as well and I think Patrick's point is reasonable. Also it was merely a comment, no need to become aggressive. Generally speaking, why would you assume that there should be one true “algebraically” correct way to approach the problem? | |
| Jun 27, 2013 at 9:23 | comment | added | Lucozade | @ Patrick: (1) please read the full question before answering, as a courtesy & generally sensible approach. (2) Your example illustrates the point: if I convert the [0,1000] interval to dBA or any log scale, the data now range from -\infty to 30, i.e., the values originally close to zero (say, 0.001) are stretched and get much further away from the new (log) center than does the original 1000. Scaling (including dividing by individual s.d) enables data points -- particularly outliers -- to be moved to almost anywhere. This is the case even of all variables are measured on the same scale. | |
| Jun 27, 2013 at 7:09 | comment | added | Gala | I changed the title, to mark the difference with previous questions on the topic. I hope the new title is OK. | |
| Jun 27, 2013 at 7:08 | history | edited | Gala | CC BY-SA 3.0 |
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| Jun 27, 2013 at 6:55 | history | edited | ttnphns | CC BY-SA 3.0 |
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| Jun 27, 2013 at 6:52 | answer | added | ttnphns | timeline score: 38 | |
| Jun 27, 2013 at 0:30 | comment | added | Patrick | I'm going to be honest and tell you I quit reading your question at some point. PCA makes sense. Yes, the results may be different depending on whether you choose to use the correlation or variance/covariance matrix. Correlation based PCA is preferred if your variables are measured on different scales, but you don't want this to dominate the outcome. Imagine if you have a series of variables that range from 0 to 1 and then some that have very large values (relatively speaking, like 0 to 1000), the large variance associated with the second group of variables will dominate. | |
| Jun 26, 2013 at 23:47 | review | Close votes | |||
| Jun 27, 2013 at 14:41 | |||||
| Jun 26, 2013 at 22:31 | history | asked | Lucozade | CC BY-SA 3.0 |