How can we efficiently and accurately analyze an irregular tensor in a dual-way streaming setting where the sizes of two dimensions of the tensor increase over time? What types of anomalies are there in the dual-way streaming setting? An irregular tensor is a collection of matrices whose column lengths are the same while their row lengths are different. In a dual-way streaming setting, both new rows of existing matrices and new matrices arrive over time. PARAFAC2 decomposition is a crucial tool for analyzing irregular tensors. Although real-time analysis is necessary in the dual-way streaming, static PARAFAC2 decomposition methods fail to efficiently work in this setting since they perform PARAFAC2 decomposition for accumulated tensors whenever new data arrive. Existing streaming PARAFAC2 decomposition methods work in a limited setting and fail to handle new rows of matrices efficiently. In this paper, we propose Dash, an efficient and accurate PARAFAC2 decomposition method working in the dual-way streaming setting. When new data are given, Dash efficiently performs PARAFAC2 decomposition by carefully dividing the terms related to old and new data and avoiding naive computations involved with old data. Furthermore, applying a forgetting factor makes Dash follow recent movements. Extensive experiments show that Dash achieves up to 14.0x faster speed than existing PARAFAC2 decomposition methods for newly arrived data. We also provide discoveries for detecting anomalies in real-world datasets, including Subprime Mortgage Crisis and COVID-19.

翻译：如何在张量两个维度随时间增长的双向流式设置中高效准确地分析不规则张量？双向流式设置中存在哪些类型的异常？不规则张量是一组列长度相同但行长度不同的矩阵集合。在双向流式设置中，既有现有矩阵的新增行，也有新矩阵随时间到达。PARAFAC2分解是分析不规则张量的关键工具。尽管双向流式场景需要实时分析，但静态PARAFAC2分解方法无法高效工作——因为每当新数据到达时，它们会对累积张量重新进行完整分解。现有流式PARAFAC2分解方法仅在有限场景下适用，且无法高效处理矩阵的新增行。本文提出Dash——一种在双向流式设置中高效准确的PARAFAC2分解方法。当新数据到达时，Dash通过精细划分新旧数据相关项并避免涉及旧数据的朴素计算，实现高效PARAFAC2分解。此外，引入遗忘因子使Dash能够跟踪最近变化。大量实验表明，Dash对新增数据的处理速度相比现有PARAFAC2分解方法提升可达14.0倍。我们还提供了真实世界数据集（包括次贷危机和COVID-19）中异常检测的发现。