Sequential clustering withparticle filters - Estimating the numberofclusters fromdata

Inthis paper wedevelop aparticle filtering approach forgrouping observations into anunspecified number ofclusters. Eachcluster corresponds toapotential target fromwhich the observations originate. Apotential clustering with aspecified number ofclusters isrepresented byanassociation hypothesis. Whenever anewreport arrives, aposterior distribution overall hypotheses isiteratively calculated fromaprior distribution, an update model andalikelihood function. Theupdate modelis basedonanassociation probability forclusters giventhe probability offalse detection andaderived probability ofan unobserved target. Thelikelihood ofeachhypothesis isderived from a costvalue ofassociating thecurrent report withits corresponding cluster according tothehypothesis. A setof hypotheses ismaintained byMonteCarlo sampling. Inthis case, thestate-space, i.e., thespace ofall hypotheses, isdiscrete with a linearly growing dimensionality overtime.Tolowerthe complexity further, hypotheses arecombined iftheir clusters are close toeachother intheobservation space. Finally, foreach time-step, theposterior distribution isprojected intoa distribution overthenumber ofclusters. Compared toearlier information theoretic approaches forfinding thenumberof clusters this approach doesnotrequire alarge number oftrial clusterings, since itmaintains anestimate ofthenumber of clusters along with thecluster configuration.