Unsupervised learning to identify most common basketball plays from spatial data The NBA has a system called Sports VU that tracks x-y coordinates of every player and the ball every 1/10th of a second for every game of the 2013-2014 and 2014-2015 seasons. With some fancy web scraping I now have access to this data and -- because I'm such an avid fan of the NBA -- I would like to identify each team's most common plays. Assume I don't have any knowledge about each team's plays beforehand (so I don't think supervised learning would work here). What would be the best unsupervised learning techniques to use? 

If I could trace each player's path over the course of the play, I imagine the problem would be similar to what you would see with image recognition/classification. Anyways, should I use PCA, some kind of neural  network? I understand this is a very broad question -- I don't need to know how to code it (I'm a proficient coder and machine learning practitioner); I'm just looking for high level unsupervised machine learning details.
This is a really interesting problem! Like most really interesting problems, you're unlikely to find an out-of-box solution for this, but I think the field of graph/subgraph similarity has some promise here. I'll go into more detail, but, at a high level, I think you can view players' paths during a play as a collection of five traversals through x,y space, with a vertex being any x,y point you have available (presumably there's some level of time granularity here), and an edge describing a player's movement from one point in x,y space to the next over time. It should be possible to cluster your data using a similarity metric (e.g., see Koutra et al., 2011 for a nice overview). Then, using your own domain expertise, you should be able to identify whether the clusters you've derived have some real-world meaning in basketball.