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MTS-UNMixers: Multivariate Time Series Forecasting via Channel-Time Dual Unmixing

Xuanbing Zhu, Dunbin Shen, Zhongwen Rao, Huiyi Ma, Yingguang Hao, Hongyu Wang

TL;DR

A channel-time dual unmixing network for multivariate time series forecasting (named MTS-UNMixer), which decomposes the entire series into critical bases and coefficients across both the time and channel dimensions, establishing a robust sharing mechanism between historical and future series, enabling accurate representation and enhancing physical interpretability.

Abstract

Multivariate time series data provide a robust framework for future predictions by leveraging information across multiple dimensions, ensuring broad applicability in practical scenarios. However, their high dimensionality and mixing patterns pose significant challenges in establishing an interpretable and explicit mapping between historical and future series, as well as extracting long-range feature dependencies. To address these challenges, we propose a channel-time dual unmixing network for multivariate time series forecasting (named MTS-UNMixer), which decomposes the entire series into critical bases and coefficients across both the time and channel dimensions. This approach establishes a robust sharing mechanism between historical and future series, enabling accurate representation and enhancing physical interpretability. Specifically, MTS-UNMixers represent sequences over time as a mixture of multiple trends and cycles, with the time-correlated representation coefficients shared across both historical and future time periods. In contrast, sequence over channels can be decomposed into multiple tick-wise bases, which characterize the channel correlations and are shared across the whole series. To estimate the shared time-dependent coefficients, a vanilla Mamba network is employed, leveraging its alignment with directional causality. Conversely, a bidirectional Mamba network is utilized to model the shared channel-correlated bases, accommodating noncausal relationships. Experimental results show that MTS-UNMixers significantly outperform existing methods on multiple benchmark datasets. The code is available at https://github.com/ZHU-0108/MTS-UNMixers.

MTS-UNMixers: Multivariate Time Series Forecasting via Channel-Time Dual Unmixing

TL;DR

A channel-time dual unmixing network for multivariate time series forecasting (named MTS-UNMixer), which decomposes the entire series into critical bases and coefficients across both the time and channel dimensions, establishing a robust sharing mechanism between historical and future series, enabling accurate representation and enhancing physical interpretability.

Abstract

Multivariate time series data provide a robust framework for future predictions by leveraging information across multiple dimensions, ensuring broad applicability in practical scenarios. However, their high dimensionality and mixing patterns pose significant challenges in establishing an interpretable and explicit mapping between historical and future series, as well as extracting long-range feature dependencies. To address these challenges, we propose a channel-time dual unmixing network for multivariate time series forecasting (named MTS-UNMixer), which decomposes the entire series into critical bases and coefficients across both the time and channel dimensions. This approach establishes a robust sharing mechanism between historical and future series, enabling accurate representation and enhancing physical interpretability. Specifically, MTS-UNMixers represent sequences over time as a mixture of multiple trends and cycles, with the time-correlated representation coefficients shared across both historical and future time periods. In contrast, sequence over channels can be decomposed into multiple tick-wise bases, which characterize the channel correlations and are shared across the whole series. To estimate the shared time-dependent coefficients, a vanilla Mamba network is employed, leveraging its alignment with directional causality. Conversely, a bidirectional Mamba network is utilized to model the shared channel-correlated bases, accommodating noncausal relationships. Experimental results show that MTS-UNMixers significantly outperform existing methods on multiple benchmark datasets. The code is available at https://github.com/ZHU-0108/MTS-UNMixers.

Paper Structure

This paper contains 31 sections, 19 equations, 32 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Deep learning Models for Time Series Forecasting
  4. State space models
  5. Channel-Time Mixing
  6. Multivariate Time Series Forecasting
  7. Problem Formulation
  8. Mixing Model
  9. Explicit Mapping
  10. Optimization Process
  11. MTS-UNMixers Network
  12. Overall Architecture
  13. Unmixing Encoder
  14. Temporal (Channel-wise Representation) Unmixing Encoder
  15. Channel (Tick-wise Representation) Unmixing Encoder
  16. ...and 16 more sections

Figures (32)

  • Figure 1: Mixing problem (taking weather data as an example). (a) shows the original plot of the seven variables and their principal component composition in the weather dataset. The high correlation between variables suggests that they may be influenced by common external environmental factors. (b) illustrates the time series of a single channel and shows how it can be decomposed into a mixture of different features.
  • Figure 2: The framework of MTS-UNMixers comprises two main components: temporal unmixing and channel unmixing.
  • Figure 3: Structure of the Mamba Block.
  • Figure 4: Structure of the Bi-Mamba Block.
  • Figure 5: Electricity
  • ...and 27 more figures