# Evaluating time series clustering through EM/GMM

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?
• In fact..based on this paper you can cluster time series with GMM/EM. I am working on how to implement with the well-known scikit-learn tools however. For an evaluation of hte optimal number of clusters, BIC/AIC are what you want to observe. These are also in the library for convenience. The link contains a great summary of how to use GMM/EM on certain data but not time series unfortunately. I'd like to hear of your updates as well. – HSL Mar 11 '18 at 15:29

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.