A weighted combination similarity measure for mobility patterns in wireless networks

The similarity between trajectory patterns in clustering has played an important role in discovering movement behaviour of different groups of mobile objects. Several approaches have been proposed to measure the similarity between sequences in trajectory data. Most of these measures are based on Euclidean space or on spatial network and some of them have been concerned with temporal aspect or ordering types. However, they are not appropriate to characteristics of spatiotemporal mobility patterns in wireless networks. In this paper, we propose a new similarity measure for mobility patterns in cellular space of wireless network. The framework for constructing our measure is composed of two phases as follows. First, we present formal definitions to capture mathematically two spatial and temporal similarity measures for mobility patterns. And then, we define the total similarity measure by means of a weighted combination of these similarities. The truth of the partial and total similarity measures are proved in mathematics. Furthermore, instead of the time interval or ordering, our work makes use of the timestamp at which two mobility patterns share the same cell. A case study is also described to give a comparison of the combination measure with other ones.