arXiv:2603.08803cs.LGstat.ML2026-03

将时间序列分段建模,让动态变化更清晰地体现在图像中。

The Temporal Markov Transition Field

  • 按时间分块,每块独立估计转移矩阵,避免全局平均带来的信息丢失。
  • 生成带纹理条带的图像,每条带反映特定时段的动态特征。
  • 适合时序分类、异常检测等任务,尤其擅长捕捉非平稳过程。

马尔可夫转移场(MTF)将时间序列转化为二维图像,通过全局转移矩阵刻画任意两时刻间的状态转移概率。但当过程随时间改变模式时,全局矩阵会模糊各阶段特征。本文提出时序马尔可夫转移场(TMTF),将序列划分为K个连续时间段,为每段估计局部转移矩阵,并构建对应的图像,使每一行反映其对应时段的动态。最终生成的T×T图像包含K个具有不同纹理的水平条带,分别编码各段的转移特性。论文给出了形式定义,分析了关键结构性质,通过数值实例展示与全局MTF的区别,研究了分块引入的偏差-方差权衡,并从持久性、均值回归、趋势行为等角度解释局部转移矩阵的几何意义。TMTF对振幅不敏感且保持顺序,适合作为卷积神经网络处理时间序列特征任务的输入通道。

原文摘要 · Abstract (English)

The Markov Transition Field (MTF), introduced by Wang and Oates (2015), encodes a time series as a two-dimensional image by mapping each pair of time steps to the transition probability between their quantile states, estimated from a single global transition matrix. This construction is efficient when the transition dynamics are stationary, but produces a misleading representation when the process changes regime over time: the global matrix averages across regimes and the resulting image loses all information about \emph{when} each dynamical regime was active. In this paper we introduce the \emph{Temporal Markov Transition Field} (TMTF), an extension that partitions the series into $K$ contiguous temporal chunks, estimates a separate local transition matrix for each chunk, and assembles the image so that each row reflects the dynamics local to its chunk rather than the global average. The resulting $T \times T$ image has $K$ horizontal bands of distinct texture, each encoding the transition dynamics of one temporal segment. We develop the formal definition, establish the key structural properties of the representation, work through a complete numerical example that makes the distinction from the global MTF concrete, analyse the bias--variance trade-off introduced by temporal chunking, and discuss the geometric interpretation of the local transition matrices in terms of process properties such as persistence, mean reversion, and trending behaviour. The TMTF is amplitude-agnostic and order-preserving, making it suitable as an input channel for convolutional neural networks applied to time series characterisation tasks.

时间序列图像化动态建模CNN输入

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。