A Spherical Hidden Markov Model for Semantics-Rich Human Mobility Modeling
This work addresses the challenge of semantics-rich human mobility modeling for applications like urban planning and recommendation systems, but it is incremental as it builds on existing hidden Markov models with a novel text modeling approach.
The authors tackled the problem of modeling human mobility from semantic trace data by proposing SHMM, a multi-modal spherical hidden Markov model that jointly considers location, time, and text, which outperformed state-of-the-art models in next location prediction with lower training costs.
We study the problem of modeling human mobility from semantic trace data, wherein each GPS record in a trace is associated with a text message that describes the user's activity. Existing methods fall short in unveiling human movement regularities, because they either do not model the text data at all or suffer from text sparsity severely. We propose SHMM, a multi-modal spherical hidden Markov model for semantics-rich human mobility modeling. Under the hidden Markov assumption, SHMM models the generation process of a given trace by jointly considering the observed location, time, and text at each step of the trace. The distinguishing characteristic of SHMM is the text modeling part. We use fixed-size vector representations to encode the semantics of the text messages, and model the generation of the l2-normalized text embeddings on a unit sphere with the von Mises-Fisher (vMF) distribution. Compared with other alternatives like multi-variate Gaussian, our choice of the vMF distribution not only incurs much fewer parameters, but also better leverages the discriminative power of text embeddings in a directional metric space. The parameter inference for the vMF distribution is non-trivial since it involves functional inversion of ratios of Bessel functions. We theoretically prove that: 1) the classical Expectation-Maximization algorithm can work with vMF distributions; and 2) while closed-form solutions are hard to be obtained for the M-step, Newton's method is guaranteed to converge to the optimal solution with quadratic convergence rate. We have performed extensive experiments on both synthetic and real-life data. The results on synthetic data verify our theoretical analysis; while the results on real-life data demonstrate that SHMM learns meaningful semantics-rich mobility models, outperforms state-of-the-art mobility models for next location prediction, and incurs lower training cost.