Evaluating time series clustering through EM/GMM

Question

I perform clustering of time series into k=[2,N] number of clusters by using either DTW+kmedoids or DTW+single linkage+hierarchical clustering (HC), as advised in a previous post: Dynamic Time Warping Clustering

Regarding the evaluation of optimum number of clusters, I want to use expectation–maximization (EM) Gaussian Mixture Models (GMM) and determine the k that maximizes the log-likelihood for each approach.

My questions are:

• What should be the input dataset in EM/GMM? The DTW similarity distance or the raw dataset?
• Can the initializations in EM/GMM be the clusters centers of either the kmedoids or randomly selected seeds from the HC clusters?
• Should I run k-fold cross-validation of the input dataset with the EM/GMM and return the average log-likelihood value?

Answer 1

Gaussian Mixture Modeling assumes ypur input data are coordinates in $R^d$ and contain Gaussian-shaped clusters. I don't think you can use this on time series. Also, GMM is a clustering approach on its own, and I don't see how you could use that to evaluate other clusterings.