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.

💡 Research Summary

The paper addresses the problem of measuring similarity between mobility patterns in cellular wireless networks, where each pattern is a sequence of visited cells together with timestamps. Existing similarity measures—most of which are based on Euclidean distances, continuous spatial networks, or temporal ordering—do not adequately capture the discrete, cell‑centric nature of wireless logs. To fill this gap, the authors propose a two‑phase framework. In the first phase they formally define a spatial similarity component and a temporal similarity component. The spatial component is based on the Jaccard index of the sets of cells visited by two patterns, augmented with a normalized distance term that accounts for the relative positions of shared cells. The temporal component focuses on exact timestamp matches: for every cell that appears in both patterns, the method checks whether the two patterns visited that cell at the same time, encoding the result in a binary matrix and computing a Jaccard‑like similarity. Both components are normalized to the interval