I have 100 participants performing the same activity (picking up a box from the ground) in their preferable way, and for every participant I have recorded time series of all trajectories and angles of their joints. I wish to cluster participants based on the way they performed the activity. I can use factor analysis to identify which trajectory/angle time series are important for the analysis but how do I proceed with clustering the time series?
Standard time series solutions are very well-developed for continuously distributed information, are moment-based, focused on the analysis of HAC residuals and, obviously, include the variants of Holt-Winters decompositions, exponential smoothing, Box-Jenkins, ARCH, GARCH, HARCH functional forms, spectral decompositions, and so on. Take your pick.
Nonstandard approaches to longitudinal clustering of principal components originated in the 70s with guys working in the (then) hot area of multidimensional scaling and were based on higher order tensor ranks and SVD decompositions such as CANDECOMP and PARAFAC or Pieter Kroonenberg's three-mode approaches:
Time series clustering has been getting a lot of attention in recent years. One excellent overview is Aggarwal and Reddy's book, Data Clustering..However, temporal clustering of aperiodic and qualitative constructs is not a well developed topic in their collection of essays.
Andreas Brandmaier's Permutation Distribution Cluster (PDC) approach to clustering aperiodic time series is well developed conceptually as well as offering routines that can be run in R. This method is not based on analyzing the moments of the empirical distribution of the time series, much less on deriving HAC residuals. Rather, PDC is an information-theoretic and complexity-based algorithm that leverages a dissimilarity concept (motivated by Kullback-Leibler divergence) drawn from the complexity of time series of differing lengths. His approach might be ideal for your purposes as it can easily be adapted to the patterning of the nonmetric or qualitative shapes in your raw data.
Much of this response was lifted from an answer to this thread as written by myself: