On Thu, 14 Sep 2006 17:18:37 +0100, Tony Mathew <[EMAIL PROTECTED]> wrote:
>List > >Got a few questions on standardised principal components (SPCA). I hasten to add that I am not an ecologist. I use remotely sensed images (e.g., NDVI) for the analysis of vegetation changes and hence my presence in the list. Happened to see a discussion on PCA here and I realise that the ideas are applicable to remote sensing as well. Tony, Standardised PCA....I assume that this is PCA applied on the correlation matrix? > >Once you do SPCA and you have your individual components, how is it that you go about interpreting them? There are a couple of things you can do to simplify the loadings and scores. See Jolliffe (2002) or Zuur et al (2007) at www.springer.com/0-387- 45967-7 for various methods and examples (one such is: SCoTLASS) > >PC1 is said to show characteristic variability over the time period and the other PCs will show variability as caused by different factors like flood, drought, fire etc. On to the questions: > >1. How can I be sure that the variability is caused by one single (or dominant) factor and not by a combination of two or more factors - e.g., rainfall and grazing? You cannot do this. If the first few axes are determined by a series of variables then this is due to the nature in the variability of your data. All you can do is to try and apply one of these simplification/rotation methods like a varimax or SCoTLASS methods. But your question is against the principle of PCA. If each axes would be dominated by only one variable you may as well plot the original data. A biplot may help interpretation. >2. If the number of images going in to the time series are increased isn't the chance of me isolating factors to component (individual) images increasing? >3. Is it realistic to expect that seasonality will come out in one component? If seasonality is the most important source of variation in your data, then certainly it will be dominating the first axis (or even the first few axes) >4. Is it sensible to do this kind of time-series analysis with only 4 images as against the published literature which talks about analysis using NDVI images for every month of the year for e.g., 20 years? > PCA is not a time series analysis method! And you have not provided enough info to answer this question. >Literature also talk about the area-weightedness of PCA. Basically this mean that if you are taking the African continent as a whole and doing SPCA and then comparing it with the SPCA done for only South Africa, the results will be different not only because of the difference in vegetation but also because of the area involved. Anyone out there who can give provide me further information on this? I don't understand the issue. You apply PCA on data from a whole continent, and then only on a subset...of course you may get different results.....it all depends how different the correlation matrix is. > >The area that I am focussing on is Kruger National Park, in South Africa and there is clear distinction in vegetation activity across summer and winter. To add to the trouble the images come from both summer and winter. Is there any other method to isolate seasonality from a time series of vegetation intensity? There are different options. But keep in mind that PCA is not really designed to analyse time series! Change the order of the observations and you still get the same results. You could de-seasonalise the data....or apply any of the time series analysis methods described in for example www.springer.com/0-387-45967-7 Jolliffe (2002) also has a couple of sections on remote sensing data. Hope this helps. Alain www.highstat.com > >Advance thanks for any input. > >Tony > > >This message has been checked for viruses but the contents of an attachment >may still contain software viruses, which could damage your computer system: >you are advised to perform your own checks. Email communications with the >University of Nottingham may be monitored as permitted by UK legislation. >=========================================================================
