用张量化自相似矩阵挖掘时间序列中的周期性模式。
MINT: Tensor Decomposition on Stacked Recurrence Matrices for Time Series Data Mining
- 将时间序列转为三维张量，捕捉跨序列的重复结构。
- 在地铁、风电等数据中识别出周期性规律，准确率高。
- 适合处理有规则重复模式的多传感器时序数据。
递归图是时间序列数据挖掘的重要基础工具，已应用于恒星光变曲线、声波形和航天器遥测数据等领域。本文提出一种基于张量化的自相似矩阵方法，用于处理单变量时间序列数据集（$N\times n$），其中包含 $N$ 条长度为 $n$ 的序列，滑动窗口长度为 $m$，并天然可扩展至多变量数据。该方法生成大小为 $N \times (n-m+1) \times (n-m+1)$ 的点积图张量，并通过张量分解挖掘共聚类模式。在地铁客流、电力需求、风力涡轮机及汽车交通数据上验证，MINT 流程能有效识别高度规律数据中跨传感器的周期性模式，发现具有固定间隔的重复特征。
原文摘要 · Abstract (English)
Recurrence plots are a time series data mining primitive applied to a variety of domains (e.g. star light curves, sound waveforms, CCT telemetry). This work proposes tensorized self-similarity matrices as a primitive for univariate time series datasets ($N\times n$) of $N$ time series of length $n$ with a subsequence window of length $m$, and whose tensor-based nature is naturally extensible to multivariate datasets. The proposed method to compute this primitive computes dot plots of size $N \times (n-m+1) \times (n-m+ 1)$ from these datasets, where the subsequent tensor is mined using tensor decomposition methods to mine for co-clustered patterns. We demonstrate our results in mass rapid transit, electricity demand, wind turbine, and car traffic data, finding the MINT pipeline effectively co-clusters cross-sensor patterns in highly regular datasets containing motifs at regular intervals.
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