Activity discovery using Dirichlet multinomial mixture models from discrete sensor data in smart homes

Abstract

To develop smart home technology designed to analyze the activity of residents based on the logs of installed sensors, an activity model tailored to individuals must be constructed from less privacy-invasive sensors to avoid interference in daily life. Unsupervised machine learning techniques are desirable to automatically construct such models without costly data annotation, but their application has not yet been sufficiently successful. In this study, we show that an activity model can be effectively estimated without activity labels via the Dirichlet multinomial mixture (DMM) model. The DMM model assumes that sensor signals are generated according to a Dirichlet multinomial distribution conditioned on a single unobservable activity and can capture the burstiness of sensors, in which even sensors that rarely fire may fire repeatedly after being triggered. We demonstrate the burstiness phenomenon in real data using passive infrared ray motion sensors. For such data, the assumptions of the DMM model are more suitable than the assumptions employed in models used in previous studies. Moreover, we extend the DMM model so that each activity depends on the preceding activity to capture the Markov dependency of activities, and a Gibbs sampler used in the model estimation algorithm is also presented. An empirical study using publicly available data collected in real-life settings shows that the DMM models can discover activities more correctly than the other models and expected to be used as a primitive activity extraction tool in activity analysis.