Autoregressive model-based fuzzy clustering and its application for detecting information redundancy in air pollution monitoring networks

Fuzzy clustering enables the simultaneous membership of objects in two or more clusters. This is particularly pertinent where time series are concerned, because very often patterns of time series change over time. Thus, a time series might belong to different clusters over different periods of time, in which case, crisp clustering is unable to capture this multi-cluster membership. In this paper, we adopt a Fuzzy C-Medoids approach to clustering time series based on autoregressive estimates of models fitted to the time series. We illustrate very good performance of this approach in a range of simulation studies. By means of two applications, we also show the usefulness of this clustering approach in the air pollution monitoring, by considering air pollution time series, i.e., CO time series, CO₂ time series and NO time series monitored on world and urban scales. In particular, we show that, by considering in the clustering process, the autoregressive representation of these air pollution time series, we are able to detect possible information redundancy in the monitoring networks and then, decreasing the number of monitoring stations, to reduce the monitoring costs and then to increase the monitoring efficiency of the networks.