Censored trajectory data clustering using mixture of semi-Markov models with application to targeted marketing

Abstract A trajectory is a spatio-temporal data instance in which a customer or user moves between a set of discrete states while spending a certain amount of time in each state. Using trajectory data as a proxy for customers’ behavior and performing clustering can help to devise targeted marketing strategies. However, the censoring is often encountered due to the inability to observe the complete trajectories. In addition, the exact number of clusters is often unknown. In this work, we propose a novel mixture model-based clustering methodology to analyze the trajectory data and decipher different user segments based on their behavior. Each cluster is profiled using a semi-Markov model while considering the effect of censoring. Each entity is assigned to a cluster based on its similarity to the cluster’s profile. Entity assignments and cluster profiles are simultaneously inferred using a robust expectation maximization algorithm. In the simulation study, our methodology demonstrates better performance than existing methods. The effectiveness of our methodology is further corroborated using a real data set obtained from an internet music provider, where the obtained clustering results are found to be helpful in devising better marketing strategies to target users in different segments.