SamBaTen: Sampling-based Batch Incremental Tensor Decomposition

TL;DR

SaMbaTen is a sampling-based incremental tensor decomposition algorithm that efficiently updates decompositions for evolving datasets, scaling to very large tensors while maintaining accuracy and significantly reducing computation time.

Contribution

It introduces a novel sampling-based approach for incremental tensor decomposition that scales to larger datasets than existing methods.

Findings

Achieves comparable accuracy to state-of-the-art methods.

Operates 25-30 times faster than existing techniques.

Scales to tensors of size up to 100K x 100K x 100K.

Abstract

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.