astamm
commented
1 week ago Hi @alexpghayes. When you say trajectories of different states, are you referring to time series?
In this case, you can of course use clustering methods from time series analysis and, if you want to disentangle amplitude and phase variability, you can use the so-called dynamic time warping metric. See the dtw package for instance.
The view adopted by the fdacluster cluster here is functional data. You never really observe a curve but rather an evaluation of the desired curve on a grid of points. Time series analysis proposes statistical methods to analyse such points viewed as a sequence of ordered points with probable autocorrelation (points close to each other on the grid should be somehow more correlated that points that are farther apart on the grid). Functional data analysis further assume that what happened between two observed points on the grid is also known. It is in fact the first step of the analysis which pertains to converting the observed time series in a functional data object with the desired regularity. This is achieved via basis representations (usually splines or Fourier or wavelets). The advantage over the viewpoint of time series analysis is that you can access curve derivatives and use them in your analyses. Also you better achieve amplitude and phase variability separation.
Anyway I got carried away :-) I hope I answered the original question. Feel free to insist though if not.
Hey! I'm very new to functional data, and have a naive question: can these methods be used to model longitudinal trajectories of discrete states? If not, are they other better methods for clustering trajectories through a sequence of discrete states?