  Tensor decompositions are invaluable tools in analyzing multimodal datasets.
In many real-world scenarios, such datasets are far from being static, to the
contrary they tend to grow over time. For instance, in an online social network
setting, as we observe new interactions over time, our dataset gets updated in
its "time" mode. How can we maintain a valid and accurate tensor decomposition
of such a dynamically evolving multimodal dataset, without having to re-compute
the entire decomposition after every single update? In this paper we introduce
SaMbaTen, a Sampling-based Batch Incremental Tensor Decomposition algorithm,
which incrementally maintains the decomposition given new updates to the tensor
dataset. SaMbaTen is able to scale to datasets that the state-of-the-art in
incremental tensor decomposition is unable to operate on, due to its ability to
effectively summarize the existing tensor and the incoming updates, and perform
all computations in the reduced summary space. We extensively evaluate SaMbaTen
using synthetic and real datasets. Indicatively, SaMbaTen achieves comparable
accuracy to state-of-the-art incremental and non-incremental techniques, while
being 25-30 times faster. Furthermore, SaMbaTen scales to very large sparse and
dense dynamically evolving tensors of dimensions up to 100K x 100K x 100K where
state-of-the-art incremental approaches were not able to operate.
