Abstract
Tensor decomposition has been demonstrated to be successful in a wide
range of applications, from neuroscience and wireless communications to
social networks. In an online setting, factorizing tensors derived from
multidimensional data streams is however non-trivial due to several
inherent problems of real-time stream processing. In recent years, many
research efforts have been dedicated to developing online techniques for
decomposing such tensors, resulting in significant advances in streaming
tensor decomposition or tensor tracking. This topic is emerging and
enriches the literature on tensor decomposition, particularly from the
data stream analystics perspective. Thus, it is imperative to carry out
an overview of tensor tracking to help researchers and practitioners
understand its development and achievements, summarise the current
trends and advances, and identify challenging problems. In this article,
we provide a contemporary and comprehensive survey on different types of
tensor tracking techniques. We particularly categorize the
state-of-the-art methods into three main groups: streaming CP
decompositions, streaming Tucker decompositions, and streaming
decompositions under other tensor formats (i.e., tensor-train, t-SVD,
and BTD). In each group, we further divide the existing algorithms into
sub-categories based on their main optimization framework and model
architectures. Finally, we present several research challenges, open
problems, and potential directions of tensor tracking in the future.