1. Multi-Agent Behaviour Segmentation via Spectral Clustering Dr Bálint Takács, Simon Butler, Dr Yiannis Demiris Intelligent Systems and Networks Group Electrical and Electronic Engineering Imperial College, London http://www.iis.ee.ic.ac.uk/~y.demiris/ AAAI 2007 PAIR Workshop

2. Clustering Unsupervised classification “The goal of clustering is to separate a finite unlabeled data set into a finite and discrete set of ‘natural’, hidden data structures, rather than provide an accurate characterization of unobserved samples generated from the same probability distribution.”

3. Spectral clustering Shi & Malik, 1999 Some successful applications: –Image segmentation –Subgoal selection in learning systems –Underconstrained blind source separation (one microphone, two speakers) Related to non-linear dimensionality reduction methods and manifold learning (ISOMAP, LLE, kernel-PCA, diffusion maps, etc.)

4. Examples (from Zelnik-Manor & Perona, 2004)

5. Algorithm overview 1.Define a similarity (or affinity) measure over the points to be clustered (gives how similar two points are) –Usually derived from the distance between any u and v points: 2.Form an affinity matrix from these over all point-point pairs 3.Determine the eigenvector decomposition of this matrix 4.Keep some of the eigenvectors with the highest eigenvalues (reduce dimension) 5.Cluster the points formed by the remaining eigenvectors with some other method (e.g. k-means) or directly estimate the clusters from the eigendecomposition structure

6. Clustering for multi-agent behaviour May generate clusters for –automatic plan primitive extraction –preprocessing for plan recognition –subgoal selection in learning tasks Not a probabilistic model –may work even on a single example of behaviour!

7. Our approach Clustering spatio-temporal positions of individual agents in multi-agent systems Non-homogenous dimensions –how to extend the similarity metric into time? Non-spatial events –how to treat these in the similarities?

8. Simplest: Has undesired consequences: –Cluster boundaries in time will become indefinitely weak as more time is spent  No arbitrary long temporal clusters Temporal extension

9. and be equivalent to the original if no temporal attribute is present Proposed temporal extension

10. Proven in the paper: –Temporal cluster boundaries become stabilized versus spatial cluster boundaries –The parameter  can be used for balancing spatial and temporal cluster boundaries agents are far enough to be clustered as a separate group when they are further away than  /2 Two-agents approximation

11. Increase the similarity of those points which are participants of the same event Strength of similarity may reflect event importance Importance can be scaled with regards to the spatio-temporal measure No new points introduced but existing connections are modified When more events, simply add importance Adding events

12. MAS: real-time strategy game

13. Recorded human-controlled games Spatio-temporal points were assigned to each agent by 1 update/sec frequency 4 events were defined: –SEE: a unit becomes visible to an other one (2) –HIDE: a unit becomes invisible to an other one (2) –FIRE: a unit fires (4) –HURT: a unit’s health is decreased by a hit (4) Number of clusters was automatically selected Experiments

14. Example I. 4 2 1 1 1 3

15. Example II. 8 5

16. Tolerance regarding event removal

17. Spectral clustering was proposed as a tool for segmentation of behaviour in multi-agent systems Suggested a new affinity measure which extends spectral clustering into the temporal domain in a plausible manner Proposed a technique to incorporate events with different importance The output of the algorithm coincides with the human- provided segmentations in our examples Conclusions