R help - Oct 2014 - Using PCA to filter a series

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?




Jonathan B. Thayn
	[[alternative HTML version deleted]]

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