[R] Using PCA to filter a series

[Don McKenzie]

On Oct 2, 2014, at 2:29 PM, Jonathan Thayn <jthayn at ilstu.edu> wrote:

> Hi Don. I would like to "de-rotate” the first component back to its original state so that it aligns with the original time-series. My goal is to create a “cleaned”, or a “model” time-series from which noise has been removed. 

Please cc the list with replies. It’s considered courtesy plus you’ll get more help that way than just from me.

Your goal sounds almost metaphorical, at least to me.  Your first axis “aligns” with the original time series already in that it captures the dominant variation
across all four. Beyond that, there are many approaches to signal/noise relations within time-series analysis. I am not a good source of help on these, and you probably need a statistical consult (locally?), which is not the function of this list.

> 
> 
> Jonathan Thayn
> 
> 
> 
> On Oct 2, 2014, at 2:33 PM, Don McKenzie <dmck at u.washington.edu> wrote:
> 
>> 
>> On Oct 2, 2014, at 12:18 PM, Jonathan Thayn <jthayn at ilstu.edu> wrote:
>> 
>>> I have four time-series of similar data. I would  like to combine these into a single, clean time-series. I could simply find the mean of each time period, but I think that using principal components analysis should extract the most salient pattern and ignore some of the noise. I can compute components using princomp
>>> 
>>> 
>>> d1 <- c(113, 108, 105, 103, 109, 115, 115, 102, 102, 111, 122, 122, 110, 110, 104, 121, 121, 120, 120, 137, 137, 138, 138, 136, 172, 172, 157, 165, 173, 173, 174, 174, 119, 167, 167, 144, 170, 173, 173, 169, 155, 116, 101, 114, 114, 107, 108, 108, 131, 131, 117, 113)
>>> d2 <- c(138, 115, 127, 127, 119, 126, 126, 124, 124, 119, 119, 120, 120, 115, 109, 137, 142, 142, 143, 145, 145, 163, 169, 169, 180, 180, 174, 181, 181, 179, 173, 185, 185, 183, 183, 178, 182, 182, 181, 178, 171, 154, 145, 147, 147, 124, 124, 120, 128, 141, 141, 138)
>>> d3 <- c(138, 120, 129, 129, 120, 126, 126, 125, 125, 119, 119, 122, 122, 115, 109, 141, 144, 144, 148, 149, 149, 163, 172, 172, 183, 183, 180, 181, 181, 181, 173, 185, 185, 183, 183, 184, 182, 182, 181, 179, 172, 154, 149, 156, 156, 125, 125, 115, 139, 140, 140, 138)
>>> d4 <- c(134, 115, 120, 120, 117, 123, 123, 128, 128, 119, 119, 121, 121, 114, 114, 142, 145, 145, 144, 145, 145, 167, 172, 172, 179, 179, 179, 182, 182, 182, 182, 182, 184, 184, 182, 184, 183, 183, 181, 179, 172, 149, 149, 149, 149, 124, 124, 119, 131, 135, 135, 134)
>>> 
>>> 
>>> pca <- princomp(cbind(d1,d2,d3,d4))
>>> plot(pca$scores[,1])
>>> 
>>> This seems to have created the clean pattern I want, but I would like to project the first component back into the original axes? Is there a simple way to do that?
>> 
>> Do you mean that you want to scale the scores on Axis 1 to the mean and range of your raw data?  Or their mean and variance?
>> 
>> See
>> 
>> ?scale
>>> 
>>> 
>>> 
>>> 
>>> Jonathan B. Thayn
>>> 	
>>> 
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>> 
>> Don McKenzie
>> Research Ecologist
>> Pacific WIldland Fire Sciences Lab
>> US Forest Service
>> 
>> Affiliate Professor
>> School of Environmental and Forest Sciences 
>> College of the Environment
>> University of Washington
>> dmck at uw.edu
> 

Don McKenzie
Research Ecologist
Pacific WIldland Fire Sciences Lab
US Forest Service

Affiliate Professor
School of Environmental and Forest Sciences 
College of the Environment
University of Washington
dmck at uw.edu


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