I have a similar problem area as mentioned Trajectory Clustering: Which Clustering Method? . As per suggestion to use dynamic time warping for aligning the time series, are there any differences in performance when a data is clustered with k means and Gaussian mixture model (GMM) or in general when to employ k means and GMM for clustering?Under what circumstances should k means and GMM be chosen for clustering? Also, in the response mentioned how is the centroid calculated from (x,y) ?
Both k-means and GMM need to be able to compute a sensible mean of the cluster, and are designed for Euclidean distance.
This is not really trivial for trajectories; you may need to do a lot of interpolation.
Instead, use a distance based clustering that can handle DTW distances; such as DBSCAN, OPTICS and good old hierarchical linkage clustering.