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I applied EOF (Empirical Orthogonal Function, a type of Principal Component Analysis, PCA) analysis to a dataset(geopotential height at 925hpa from ECMWF-interim reanalysis data) that contains 3 coordinates (time, longitude, latitude). Moreover, spatial field data at each time level was defined as sample or origin pattern. The results of the EOF showed that the first 4 PCs can explain 95% of the variance. How can I classify the sample or origin patterns into different PCs? In other words, which PC is similar to the origin patterns mostly?

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    $\begingroup$ I'm voting to close this question as off-topic because it should be on cross validated se $\endgroup$ – Gimelist May 15 '18 at 0:51
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    $\begingroup$ I think the question can be answered here $\endgroup$ – arkaia May 15 '18 at 1:00
  • $\begingroup$ I'm ambivalent as to whether it's on topic (I think it depends what the data is about, which isn't explained), but I think it really needs to explain at least what EOF is, and possibly what PC and PCA stand for. (I think I figured out the latter, but it took a while). Voting to close until we understand why it's related to earth science. $\endgroup$ – Semidiurnal Simon May 15 '18 at 13:22
  • $\begingroup$ Li Ziming, can you please describe the dataset you are using EOF for, so that it is a better fit for this stack exchange site? $\endgroup$ – arkaia May 15 '18 at 16:44
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    $\begingroup$ @arkaia, thank you. I use EOF for the daily mean gh at 925hpa. In my knowledge, science of meteorological or atmosphere doesn't belong to earth science? $\endgroup$ – Li Ziming May 16 '18 at 14:06
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I recommend you read Monahan et al. (1990) for a thorough explanation of Empirical Orthogonal Functions. I suggest you pay attention to the way the principal components are extracted. Ultimately, there is no guarantee that a sample belongs to a specific component. What you are working with is eigenvalues/eigenvectors and thus a specific data point can have influences from multiple components. The EOF provides a time series of eigenvalues for each component. The larger the eigenvalue for that component at a specific time, the more that component explains the data point.

If what you need is to assign a data point to a component, I would recommend a cluster analysis instead. For instance Smith & Aretxabaleta (2007) present an improved methodology to separate regimes that outperforms the EOF analysis in an ENSO-influenced dataset.

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  • $\begingroup$ Thanks, in other word, how to find the most similar PC for each sample? I found the function of pattern cor in NCL. Was that function can help to achieve my goal. $\endgroup$ – Li Ziming May 15 '18 at 1:33
  • $\begingroup$ The EOF provides a time series of eigenvalues for each component. The larger the eigenvalue for that component at a specific time, the more that component explains the data point. $\endgroup$ – arkaia May 15 '18 at 1:37
  • $\begingroup$ Yeah, I understand. Thank you very much! The eigenvalue can be negative or positive value, Could I use the absolute eigenvalue for comparison? $\endgroup$ – Li Ziming May 15 '18 at 3:22
  • $\begingroup$ Ultimately, it represents the magnitude at that point, so changing the sign of the eigenvalue, you need to also consider a change in the sign of the eigenvector at that location. The change in sign will affect any reconstruction from the truncated set of PC's, but the absolute value of the eigenvalues does provide information of the relative size of the component at that time. $\endgroup$ – arkaia May 15 '18 at 16:38
  • $\begingroup$ I saw some articles show that they classify the sample to which PC. Maybe they were wrong from the start. $\endgroup$ – Li Ziming May 16 '18 at 14:12

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