Efficient CoxianDuration Modelling forActivity Recognition in SmartEnvironments withthe Hidden semi-MarkovModel

Inthis paper, weexploit thediscrete Coxian distribution and propose a novel formofstochastic model, termed asthe Coxian hidden semi-Makov model(Cox-HSMM), andapply ittothetask ofrecognising activities ofdaily living (ADLs) in asmart house environment. TheuseoftheCoxian hasseveral advantages overtraditional parameterization (e.g. multinomial orcontinuous distributions) including thelownumberof free parameters needed, itscomputational efficiency, andthe existing ofclosed-form solution. Tofurther enrich themodel inreal-world applications, wealsoaddress theproblem of handling missing observation fortheproposed Cox-HSMM. Inthedomain ofADLs,weemphasize theimportance ofthe duration information andmodelitviatheCox-HSMM. Our experimental results haveshownthesuperiority oftheCoxHSMM inallcases whencompared withthestandard HMM. Ourresults havefurther shownthatoutstanding recognition accuracy canbeachieved withrelatively lownumberof phases required intheCoxian, thusmaking theCox-HSMM particularly suitable inrecognizing ADLswhosemovement trajectories aretypicallv very long innature.