What algorithms are available to cluster sequences of data? I have a data set containing points through time, generated by multiple Markov processes (each point in time contains N points).  I know the statistical nature of the Markov processes (same for all), but my task is to determine which points go together (from the same process).  Are there developed algorithms that address this type of problem?  I should say my more general problem has missing data and an unknown number of processes, but I'd be interested in approaches to the "easy" version too, where there are no missing points and N is known.
 A: A few ideas...
K-means clustering
K-means clustering is a supervised learning technique in which you can

partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean.

However, this will require you to determine the number of clusters before hand. There are a few techniques that can assist you in this.
Model-based Clustering
Many coding environments have built in packages that algorithmically divide your data into the optimum size and number of clusters based on their common characteristics. For instance, this can be done in R using the mclust package. 
This applies maximum likelihood estimators and Bayesian information criteria (BIC) to determine the size, shape, location, and number of clusters. This answer to this question has a worthwhile explanation of the mechanics. I have found using these techniques to be the most fruitful for large data projects.
Convex Hull (somewhat different than clustering, but could be useful to you)
Similar to your ant hill example in the comment discussion, I have done some similar spatial work with player location in sports. For soccer players it is common to want to find the location in which a player is when a certain event takes place. One technique discussed by Applied Mathematics Professor David Sumpter in Sweden is taking the average of each player's locations (ant's location at a given time) and then building a convex hull around all the points that are within 1 standard deviation of the average location.
