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I need some guidance on applying PCA analysis to my data. As a novice in statistics I'm not sure if PCA is suitable and profitable in my case. I have daily gridded SST data for a 35 years (1982-2015) in a single file with columns "date","SST at point 1",....,"SST at point n"

These are temporal series for 4248 points through 35 years (daily values). Should I apply PCA to this data? What results should I look for? Well, I'm not sure I would get any profit from PCA cause all my variables (columns) are SST values, I think I don't have components to extract with PCA.

Maybe PCA is not suitable for that data, maybe my approach to PCA is not good. I also have the daily SST data in gridded files (lon,lat,SST) but I don't think I can apply PCA on them.

Any guidance will be welcome. Thanks in advance

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PCA is a method to reduce the dimensionality of your data. If the numerical values constituting your data set represent a cloud of points around a high-dimensional version of a plane, then there is a way of changing this representation of the points - say by rotating and stretching the co-ordinates - such that the order of the amount of variance matches the order of the axes - so in three dimensions, the x-axis of the new representation will have the most variance, the y-axis less than that and so on.

(if you know some basic linear algebra then you are are simply changing the basis of the transformation underlying the covariance matrix to an orthogonal (orthogonality means zero correlation) one consisting of its eigenvectors; the spectrum measures the amount of variance so you select the eigenvectors corresponding to the higher eigenvalues.)

In your case, when you perform such a thing, then the new features that you will get will be a mixture (linear combination) of your SST readings from different locations (assuming your matrix is shaped such that your rows are your SST readings) and will no longer be interpretable as 'temperature at a location'.

A more natural way for you to reduce the dimensionality would be to consider a subset of the locations from which you have collected your SST values based on, well, climatological/geographical reasons.

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  • $\begingroup$ Hi @sntx and thanks for your answer. I am not sure I can't see how can I reduce dimensionality in my case. I have longitude, latitude and time, should I use lon, lat as variables in the analysis? I have made some attempt with just the n SST time series giving a cluster of close points in the new representation. Is it adequate to introduce lon-lat as variables for the PCA analysis? $\endgroup$ – pacomet Mar 29 '17 at 6:32
  • $\begingroup$ About subsetting the locations, I have run a cluster analysis and obtained regional patterns for the monthly data. Mainly two winter/summer modes for SST and transitional patterns in spring and fall. This patterns appear every year in the series with very similar shapes. $\endgroup$ – pacomet Mar 29 '17 at 6:33
  • $\begingroup$ @pcaomet Can I ask why do you want to reduce dimensionality in the first place (I don't mean some general reason like concentration of measure)? $\endgroup$ – sntx Mar 29 '17 at 17:45
  • $\begingroup$ That's the question. I have seen EOF (similar to PCA if I understand) applied to spatio-temporal gridded data series (see [link]menugget.blogspot.com.es/2011/11/… ) and tried to search if it was suitable for my data (daily gridded data) analysis. $\endgroup$ – pacomet Mar 30 '17 at 6:27

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