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Initially appearing as an abstract object frequently used in math and physics, tensors have been attracting increasing interest in a broad range of research fields, such as engineering and data science. However, a few studies have addressed their application in wireless scenarios. In this paper, we investigate the wide applications of tensor techniques with an emphasis on the tensor voting method, which serves as an artificial intelligence approach for automatic inference and perceptual grouping. To illustrate the efficiency of the tensor voting approach, we tackle the tracking problem of inferring human mobility traces, which can provide key location information of networking objects. The trace inferring problem is considered under the circumstance that the recorded location information exhibits missing data and noise. Based on the tensor voting theory, we propose a sparse tensor voting algorithm and an implementation scheme with computational efficiency. The model is constructed based on the geometric connections between the input signals and encodes the structure information in the tensor matrix. The missing location information and noise can be distinguished via tensor decomposition. Once the trace information has been completed, further analysis of the inferred trace can be performed based on feature extraction to differentiate different objects. Moreover, we propose several feature extraction methods to characterize the inferred trace, including the scale invariant feature obtained from the fractal analysis. The proposed methods for trace completion and pattern analysis are applied to real human mobility traces. The results show that our proposed approach effectively recovers human mobility trace from the incomplete and noisy data input, and discovers meaningful patterns of inferred traces from various objects.

Tensor Voting Techniques and Applications in Mobile Trace Inference