How does soil pollution affect a plant's circadian clock? Are there anydifferences between how the clock reacts when exposed to differentconcentrations of elements of the periodic table? If so, can we characterisethese differences? We approach these questions by analysing and modelling circadian plant data,where the levels of expression of a luciferase reporter gene were measured atregular intervals over a number of days after exposure to differentconcentrations of lithium. A key aspect of circadian data analysis is to determine whether a time series(derived from experimental data) is `rhythmic' and, if so, to determine theunderlying period. However, our dataset displays nonstationary traits such aschanges in amplitude, gradual changes in period and phase-shifts. In this paper, we develop clustering methods using a wavelet transform.Wavelets are chosen as they are ideally suited to identifying discriminantlocal time and scale features. Furthermore, we propose treating the observedtime series as realisations of locally stationary wavelet processes. Thisallows us to define and estimate the evolutionary wavelet spectrum. We can thencompare, in a quantitative way, using a functional principal componentsanalysis, the time-frequency patterns of the time series. Our approach uses aclustering algorithm to group the data according to their time-frequencypatterns. We demonstrate the advantages of our methodology over alternativeapproaches and show that it successfully clusters our data.
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