Principal components analysis for functional data

For many reasons, principal components analysis (PCA) of functional data is a key technique to consider. First, our own experience is that, after the preliminary steps of registering and displaying the data, the user wants to explore that data to see the features characterizing typical functions. Some of these features are expected to be there, for example the sinusoidal nature of temperature curves, but other aspects may be surprising. Some indication of the complexity of the data is also required, in the sense of how many types of curves and characteristics are to be found. Principal components analysis serves these ends admirably, and it is perhaps also for these reasons that it was the first method to be considered in the early literature on FDA.