You might be interested in NNMF (Non-negative Matrix Factorisation) algorithm where there are tons of Matlab codes available on the internet on NNMF. There are also tons of freely available papers on NNMF on the internet. NNMF is different from SVD (or PCA) factorisation in that it factorises a positive matrix (all elements), say ‘A’ into factor matrices which are also both positives. NNMF was originally developed for face-recognition but now it has exploded into other areas in signal processing, finance, search engine algorithm, image processing, recommendation engines (Amazon type, such as ‘Customer who bought item Q also look at item Z’), etc,…

PCA have got negative eigenvalues (hard to physically interpret) which are inappropriate for Mann’s temperature reconstruction. NNMF can help there, which it does not have negative factors.

]]>If you want to compare time series similarities, that is given a test target time series, say ‘A’, rank a collection of 4 time-series from the database (say, ‘B’, ‘C’, ‘D’, ‘E’) from the most similar ones to the most dis-similar ones. The popular algorithm for this is called ‘Dynamic Time Warping’ or DTW for short. DTW had been used in speech processing and signal processing in the past 20 years or so. So, if you want to rank your time-series from your graphs above and see which one is more similar to other ones, then look for DTW codes on the internet, which are freely available in Java, Matlab, etc…

]]>It might be; but I don’t think 8 years of noisy decline is enough of a trend to conclude “divergence”. Also, that the decline is happening in the late 1970s, and not the late 1990s, suggests it is not nearly as divergent from the temperature record as some of the other cases that have been reported. But you’re right: this divergence problem is a devil. If tree ring responses to temperature are nonlinear, then that might lead to MWP temperature reconstructions that are biased low. ]]>

AIG News will be publishing some articles on historical measured CO2 from air and sampling problems with ice-cores in Issue 86 due out in November 2006 plus some 11th hour French data on sampling methods

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