SamBaTen: Sampling-based Batch Incremental Tensor Decomposition

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

A Unified Optimization Approach for Sparse Tensor Operations on GPUs

Sparse tensors appear in many large-scale applications with multidimensional and sparse data. While multidimensional sparse data often need to be processed on manycore processors, attempts to develop highly-optimized GPU-based implementations of sparse tensor operations are rare. The irregular computation patterns and sparsity structures as well as the large memory footprints of sparse tensor operations make such implementations challenging. We leverage the fact that sparse tensor operations share similar computation patterns to propose a unified tensor representation called F-COO. Combined with GPU-specific optimizations, F-COO provides highly-optimized implementations of sparse tensor computations on GPUs. The performance of the proposed unified approach is demonstrated for tensor-based kernels such as the Sparse Matricized Tensor- Times-Khatri-Rao Product (SpMTTKRP) and the Sparse Tensor- Times-Matrix Multiply (SpTTM) and is used in tensor decomposition algorithms. Compared to state-of-the-art work we improve the performance of SpTTM and SpMTTKRP up to 3.7 and 30.6 times respectively on NVIDIA Titan-X GPUs. We implement a CANDECOMP/PARAFAC (CP) decomposition and achieve up to 14.9 times speedup using the unified method over state-of-the-art libraries on NVIDIA Titan-X GPUs

Identifying and Alleviating Concept Drift in Streaming Tensor Decomposition

Tensor decompositions are used in various data mining applications from social network to medical applications and are extremely useful in discovering latent structures or concepts in the data. Many real-world applications are dynamic in nature and so are their data. To deal with this dynamic nature of data, there exist a variety of online tensor decomposition algorithms. A central assumption in all those algorithms is that the number of latent concepts remains fixed throughout the entire stream. However, this need not be the case. Every incoming batch in the stream may have a different number of latent concepts, and the difference in latent concepts from one tensor batch to another can provide insights into how our findings in a particular application behave and deviate over time. In this paper, we define "concept" and "concept drift" in the context of streaming tensor decomposition, as the manifestation of the variability of latent concepts throughout the stream. Furthermore, we introduce SeekAndDestroy, an algorithm that detects concept drift in streaming tensor decomposition and is able to produce results robust to that drift. To the best of our knowledge, this is the first work that investigates concept drift in streaming tensor decomposition. We extensively evaluate SeekAndDestroy on synthetic datasets, which exhibit a wide variety of realistic drift. Our experiments demonstrate the effectiveness of SeekAndDestroy, both in the detection of concept drift and in the alleviation of its effects, producing results with similar quality to decomposing the entire tensor in one shot. Additionally, in real datasets, SeekAndDestroy outperforms other streaming baselines, while discovering novel useful components.Comment: 16 Pages, Accepted at ECML-PKDD 201