In exploratory tensor mining, a common problem is how to analyze a set of variables across a set of subjects whose observations do not align naturally. For example, when modeling medical features across a set of patients, the number and duration of treatments may vary widely in time, meaning there is no meaningful way to align their clinical records across time points for analysis purposes. To handle such data, the state-of-the-art tensor model is the so-called PARAFAC2, which yields interpretable and robust output and can naturally handle sparse data. However, its main limitation up to now has been the lack of efficient algorithms that can handle large-scale datasets. In this work, we fill this gap by developing a scalable method to compute the PARAFAC2 decomposition of large and sparse datasets, called SPARTan. Our method exploits special structure within PARAFAC2, leading to a novel algorithmic reformulation that is both fast (in absolute time) and more memory-efficient than prior work. We evaluate SPARTan on both synthetic and real datasets, showing 22X performance gains over the best previous implementation and also handling larger problem instances for which the baseline fails. Furthermore, we are able to apply SPARTan to the mining of temporally-evolving phenotypes on data taken from real and medically complex pediatric patients. The clinical meaningfulness of the phenotypes identified in this process, as well as their temporal evolution over time for several patients, have been endorsed by clinical experts.

通过提出SPARTan方法，我们得以解决PARAFAC2运算大规模、稀疏数据时的效率问题。在通过真实病例进行的评估中，我们发现SPARTan在表现上胜过了过去的实现，并以高效的方式获得了对于复杂医学病例下几位小患者的临床意义刻画及其时间进化路径的结果。

SPARTan: 大规模稀疏数据的可扩展PARAFAC2