<p>I recommend you read <a href="https://journals.ametsoc.org/doi/pdf/10.1175/2009JCLI3062.1" rel="nofollow noreferrer">Monahan et al. (1990)</a> 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.</p>

<p>If what you need is to assign a data point to a component, I would recommend a cluster analysis instead. For instance <a href="https://www.nonlin-processes-geophys.net/14/73/2007/npg-14-73-2007.pdf" rel="nofollow noreferrer">Smith &amp; Aretxabaleta (2007)</a> present an improved methodology to separate regimes that outperforms the EOF analysis in an ENSO-influenced dataset.</p>

CC BY-SA 4.0
2018-05-15T01:33:27.500Z
Thanks, in other word, how to find the most similar PC for each sample? I found the function of [pattern cor](http://www.ncl.ucar.edu/Document/Functions/Contributed/pattern_cor.shtml) in NCL. Was that function can help to achieve my goal.
Li Ziming
CC BY-SA 4.0
2018-05-15T01:37:21.670Z
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.
arkaia
CC BY-SA 4.0
2018-05-15T03:22:26.947Z
Yeah, I understand. Thank you very much! The eigenvalue can be negative or positive value, Could I use the absolute eigenvalue for comparison?
Li Ziming
CC BY-SA 4.0
2018-05-15T16:38:35.027Z
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.
arkaia
CC BY-SA 4.0
2018-05-16T14:12:34.310Z
I saw some articles show that they classify the sample to which PC. Maybe they were wrong from the start.
Li Ziming
CC BY-SA 4.0
2019-06-21T06:48:58.003Z
do you know the project of cost733?
Li Ziming
CC BY-SA 4.0
2019-06-21T11:01:52.823Z
@LiZiming, I thought that project ended a long time ago. Interesting results, though.
arkaia
CC BY-SA 4.0
2019-12-17T22:57:41.980Z
Yes, but I see some paper use the cost733 to classify the samples belong to which PC.
Li Ziming
CC BY-SA 4.0
2018-05-15T01:01:17.203Z
2018-05-15T01:37:18.687Z
2018-05-15T01:37:18.687Z
arkaia
<p>I applied EOF (<a href="https://en.wikipedia.org/wiki/Empirical_orthogonal_functions" rel="nofollow noreferrer">Empirical Orthogonal Function</a>, a type of Principal Component Analysis, <a href="https://en.wikipedia.org/wiki/Principal_component_analysis" rel="nofollow noreferrer">PCA</a>) 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?</p>

CC BY-SA 4.0
2018-05-15T00:51:23.787Z
I'm voting to close this question as off-topic because it should be on cross validated se
Gimelist
CC BY-SA 4.0
2018-05-15T01:00:58.383Z
I think the question can be answered here
arkaia
CC BY-SA 4.0
2018-05-15T13:22:18.480Z
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.
Semidiurnal Simon
CC BY-SA 4.0
2018-05-15T16:44:06.443Z
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?
arkaia
CC BY-SA 4.0
2018-05-16T14:06:43.840Z
@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?
Li Ziming
CC BY-SA 4.0
2018-05-17T13:12:59.633Z
@LiZiming meteorology and atmospheric science *definitely* belong here. Earth science means "about the planet Earth", rather than "about the ground".
Semidiurnal Simon
<meteorology><statistics>
How to know to which PC (Principal Component) a sample belongs in EOF/PCA
Li Ziming
# How to know to which PC (Principal Component) a sample belongs in EOF/PCA

(Asked by: username_0 on 2018-05-14)

I applied EOF ([Empirical Orthogonal Function](https://en.wikipedia.org/wiki/Empirical_orthogonal_functions), a type of Principal Component Analysis, [PCA](https://en.wikipedia.org/wiki/Principal_component_analysis)) 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?

**Tags:** meteorology, statistics

> **Comments:**
> **username_1**: I'm voting to close this question as off-topic because it should be on cross validated se  
> **username_2**: I think the question can be answered here  
> **username_3**: 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.  
> **username_2**: username_0, can you please describe the dataset you are using EOF for, so that it is a better fit for this stack exchange site?  
> **username_0**: @username_2, 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?  
> **username_3**: @username_0 meteorology and atmospheric science *definitely* belong here. Earth science means "about the planet Earth", rather than "about the ground".  

---

## 1 answers

### Answer by username_2 on 2018-05-15. Score: 3 | Accepted answer

I recommend you read [Monahan et al. (1990)](https://journals.ametsoc.org/doi/pdf/10.1175/2009JCLI3062.1) 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)](https://www.nonlin-processes-geophys.net/14/73/2007/npg-14-73-2007.pdf) present an improved methodology to separate regimes that outperforms the EOF analysis in an ENSO-influenced dataset.

> **Comments:**
> **username_0**: Thanks, in other word, how to find the most similar PC for each sample? I found the function of [pattern cor](http://www.ncl.ucar.edu/Document/Functions/Contributed/pattern_cor.shtml) in NCL. Was that function can help to achieve my goal.  
> **username_2**: 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.  
> **username_0**: Yeah, I understand. Thank you very much! The eigenvalue can be negative or positive value, Could I use the absolute eigenvalue for comparison?  
> **username_2**: 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.  
> **username_0**: I saw some articles show that they classify the sample to which PC. Maybe they were wrong from the start.  
> **username_0**: do you know the project of cost733?  
> **username_2**: @username_0, I thought that project ended a long time ago. Interesting results, though.  
> **username_0**: Yes, but I see some paper use the cost733 to classify the samples belong to which PC.  

---

