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TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classification

Huaiyuan Liu, Xianzhang Liu, Donghua Yang, Zhiyu Liang, Hongzhi Wang, Yong Cui, Jun Gu

arXiv:2304.05078v1cs.LG

TL;DR

MTSC models often neglect hidden dependencies between variables and dynamic relationships across time, while predefined graph structures are not generally available. TodyNet jointly learns temporal dynamic graphs, graph propagation, and temporal convolution, with hierarchical temporal graph pooling; the authors report that it outperforms state-of-the-art methods on MTSC tasks.

  • Problem

    Existing MTSC approaches often neglect hidden inter-variable dependencies and dynamic temporal relationships, and commonly depend on predefined graph structures.

    Source: §I · p. 2

  • Method

    TodyNet jointly learns dynamic graphs, graph propagation, and temporal convolution, with a hierarchical temporal graph pooling module.

    Source: §I · p. 2

  • Results

    TodyNet outperforms state-of-the-art methods and improves mainstream deep-learning classifiers on MTSC tasks.

    Source: §I · p. 2, §VI · p. 9

  • Takeaways & Limitations

    The authors conclude that TodyNet extracts hidden dependencies among series and temporal dynamics among time slots while achieving strong performance relative to other state-of-the-art methods.

    Source: §VI · p. 9

Abstract

from arXiv · show

Multivariate time series classification (MTSC) is an important data mining task, which can be effectively solved by popular deep learning technology. Unfortunately, the existing deep learning-based methods neglect the hidden dependencies in different dimensions and also rarely consider the unique dynamic features of time series, which lack sufficient feature extraction capability to obtain satisfactory classification accuracy. To address this problem, we propose a novel temporal dynamic graph neural network (TodyNet) that can extract hidden spatio-temporal dependencies without undefined graph structure. It enables information flow among isolated but implicit interdependent variables and captures the associations between different time slots by dynamic graph mechanism, which further improves the classification performance of the model. Meanwhile, the hierarchical representations of graphs cannot be learned due to the limitation of GNNs. Thus, we also design a temporal graph pooling layer to obtain a global graph-level representation for graph learning with learnable temporal parameters. The dynamic graph, graph information propagation, and temporal convolution are jointly learned in an end-to-end framework. The experiments on 26 UEA benchmark datasets illustrate that the proposed TodyNet outperforms existing deep learning-based methods in the MTSC tasks.

I. INTRODUCTION

TodyNet addresses gaps in MTSC models that neglect hidden inter-variable dependencies, dynamic temporal relationships, and hierarchical pooling. It jointly learns dynamic graphs, graph propagation, and temporal convolution, and the authors report that it outperforms state-of-the-art methods.

I. INTRODUCTION

  • MTSC is challenging because multivariate series have complex temporal-order correlations, high dimensionality, and abundant hidden information.The task assigns a discrete label to a multivariate time series.Source: §I · p. 1
  • Existing deep-learning MTSC models rarely capture hidden dependencies between variables, while many graph approaches rely on predefined structures or a single trajectory-wide graph.A single graph over the full trajectory can neglect dynamic processes.Source: §I · pp. 1–2
  • TodyNet jointly learns dynamic graphs, graph propagation, and temporal convolution to model hidden dependencies and temporal dynamics.The framework is presented as the first MTSC study based on temporal dynamic graphs.Source: §I · p. 2
  • Its dynamic graph mechanism captures dependencies among variables and between adjacent time slots, while temporal graph pooling avoids flat pooling and incorporates temporal features.The pooling approach is hierarchical.Source: §I · p. 2
  • TodyNet significantly improves mainstream deep-learning classifiers and outperforms state-of-the-art methods.The introduction reports this result without giving numerical comparisons.Source: §I · p. 2

II. RELATED WORK

Related work covers multivariate time-series classification methods and graph neural networks. The cited MTSC literature includes distance-, feature-, and deep-learning approaches, while graph structure is presented as a way to represent variable dependencies.

A. Multivariate Time Series Classification

  • MTSC approaches include distance-based, feature-based, and deep-learning methods, with CNN architectures such as MCDCNN, TapNet, and OS-CNN among the cited examples.The authors note that deep-learning methods may assume identical dependencies across variables, limiting representation of pairwise relationships.Source: A. Multivariate Time Series… · p. 2

II. RELATED WORK

  • GNNs aggregate information from neighboring nodes, and spatial-temporal GNNs can learn graph structure over temporal trajectories.The cited spatial-temporal GNN work is largely designed for traffic forecasting, and the authors identify a gap for MTSC without predefined graph structures.Source: A. Multivariate Time Series… · p. 2

B. Graph Neural Networks

This material introduces graph neural networks and formalizes the multivariate time-series classification task and its graph terminology. Variables serve as graph nodes, while edges represent relationships that can vary across time slots.

B. Graph Neural Networks

  • GNNs recursively aggregate and transform neighbor information to compute node embeddings; spatial-temporal GNNs extend graph learning across temporal trajectories.The framework figure depicts dynamic graphs for time slices, separate spatial and temporal processing, and temporal graph pooling.Source: B. Graph Neural Networks · pp. 2–3, Figure 1 · p. 3

A. Problem Formulation

  • The paper frames MTSC as learning a classifier from labeled multivariate time series to predict labels for unlabeled series.Each series has d variables and length l, and the training collection contains m series.Source: §III · p. 3, A. Problem Formulation · p. 3

B. Graph Notations and Definitions

  • A temporal graph represents variables as nodes and their relationships as edges, defined by similarity or learned structure.The graph notation is introduced for MTSC.Source: B. Graph Notations and Definitions · p. 3
  • A static graph uses one graph for the series, whereas a dynamic graph has multiple time-slot graphs with changing edges and fixed vertices.Edge weights and connections may change between time slots.Source: B. Graph Notations and Definitions · pp. 3–4

IV. PROPOSED MODEL

TodyNet constructs and learns a graph for each time slot, processes spatial and temporal dependencies, and applies hierarchical temporal graph pooling. The initial adjacency matrices are formed from learnable node embeddings and sparsified to retain top-weighted entries.

A. Model Architecture Overview

  • TodyNet uses graph construction, dynamic graph neural networks, temporal convolution, and hierarchical temporal graph pooling in its model architecture.The pooling module uses learnable temporal convolution parameters, followed by average pooling and a fully connected classification layer.Source: A. Model Architecture Overview · p. 4

B. Construction and Learning of Temporal Dynamic Graph

  • For each time slot, learnable node embeddings Θ and Ψ are multiplied to form an initial adjacency matrix that can be optimized during training.The construction starts from learned associations because universal time series lack a predefined graph structure.Source: B. Construction and Learning of… · p. 4
  • The adjacency matrix is sparsified by retaining only its top-k largest weights and setting the remaining entries to zero.The passage states that this sparsification reduces computation cost.Source: B. Construction and Learning of… · p. 4

C. Dynamic Graph Neural Network

The dynamic graph module links graphs across time slots and uses an improved GIN to propagate and aggregate node information. Its transformation connects corresponding nodes from the previous slot to the current one, allowing time-specific neighborhoods.

C. Dynamic Graph Neural Network

  • Dynamic Graph Transform connects corresponding nodes from the previous time slot to the current graph, linking the graph structures across time.The figure caption describes the later graph as aggregating information from the previous graph for corresponding nodes.Source: C. Dynamic Graph Neural Network · p. 4, Figure 2 · p. 4
  • The transformation can be implemented by aggregating source-node embeddings into target-node embeddings, then deleting the added vertices.This avoids doubling the number of vertices in the practical implementation.Source: C. Dynamic Graph Neural Network · pp. 4–5
  • DyGIN uses dynamic message passing, so the same vertex at different time slots can aggregate information from different sets of vertices.The method is based on an improved Graph Isomorphism Network and contrasts with static GNNs.Source: C. Dynamic Graph Neural Network · pp. 4–5

D. Temporal Graph Pooling

Temporal Graph Pooling combines graph pooling with temporal processing to form hierarchical, differentiable clusters. Convolution parameters learn node assignments and are used to reconstruct the adjacency matrix for each pooled graph.

D. Temporal Graph Pooling

  • Temporal Graph Pooling combines graph pooling with temporal processing to address information loss associated with flat pooling.The method performs hierarchical pooling rather than aggregating features into only a few flat features.Source: D. Temporal Graph Pooling · p. 5
  • A 2D convolution layer clusters nodes according to a specified pooled ratio, using nodes as channels to extract features.Its temporal-convolution kernel size is assigned to the pooling convolution kernel size to preserve the receptive-field window.Source: D. Temporal Graph Pooling · p. 5
  • The learnable assignment matrix maps input nodes to output clusters, and the pooled adjacency is reconstructed from that matrix and the input adjacency.The output adjacency represents the connection relationships and corresponding weights of the new clusters.Source: D. Temporal Graph Pooling · p. 5
  • TGP performs hierarchical, differentiable graph pooling with temporal information while optimizing cluster aggregation during training.At each layer, time convolution clusters nodes and extracts temporal features before adjacency matrices are reconstructed through convolution weights.Source: D. Temporal Graph Pooling · p. 5, Figure 3 · p. 5

E. Temporal Convolution

The temporal convolution module extracts temporal dependencies within each dimension using three convolution layers. The experimental studies evaluate TodyNet on UEA benchmarks, ablate key components, and visualize prototypes and embeddings.

E. Temporal Convolution

  • Three convolution layers with different kernels capture temporal dependencies within each dimension, with padding keeping output length equal to input length.The extracted temporal features are divided by time slot and passed to the GNN module.Source: E. Temporal Convolution · pp. 5–6

V. EXPERIMENTAL STUDIES

  • The experimental studies assess UEA benchmark performance, test key components through ablations, and visualize class prototypes and time-series embeddings.Source: §V · p. 6

A. Experimental Settings

The experiments use equal-length datasets from the UEA multivariate time-series archive and compare TodyNet with traditional and deep-learning baselines. The settings also include implementation details and a hyperparameter-stability study across 12 datasets.

A. Experimental Settings

  • From the 30-dataset UEA multivariate time series classification archive [33], the study excludes datasets with unequal lengths or missing values and uses all 26 remaining equal-length datasets.Source: A. Experimental Settings · p. 6
  • The supplied baseline descriptions identify OS-CNN and MOS-CNN convolutional networks, ShapeNet, hybrid TapNet, WEASEL+MUSE, WLSTM-FCN, and ED-1NN, based on Euclidean distance and nearest-neighbor classification.Source: A. Experimental Settings · p. 6
  • The implementation uses four dynamic graphs, top-k value 3, pooled ratio 0.2, and three temporal-convolution layers with kernel sizes 11, 3, and 3.The reported training setup uses 2,000 epochs and a learning rate of 10^-4.Source: A. Experimental Settings · pp. 6–7
  • Figure 4 presents boxplot accuracies for 12 UEA datasets, showing how results vary with the number of graphs nG, pool ratio η, and learning rate.Source: Figure 4 · p. 7

B. Hyperparameter Stability

TodyNet’s hyperparameter stability was examined on 12 selected UEA datasets, followed by comparisons with baselines across the 26-dataset benchmark. It achieved the best average accuracy and average rank among the reported comparisons.

B. Hyperparameter Stability

  • The hyperparameter sweep varied graph count, pooled ratio, and learning rate; the authors report that a suitable learning rate benefits accuracy and tune parameters for different datasets.The sweep covered graph counts 2–16, pooled ratios 0.1–0.5, and learning rates 10^-1–10^-5.Source: B. Hyperparameter Stability · p. 7
  • Across 12 selected datasets, accuracy fluctuated slightly as the number of dynamic graphs increased, while changing the pooled ratio first improved and then reduced performance.The authors attribute the pooled-ratio pattern to the pooling structure becoming flat when too many or too few nodes are reduced at a layer.Source: B. Hyperparameter Stability · p. 7

C. Classification Performance Evaluation

D. Ablation Study

The ablation study compares TodyNet with versions removing graph components or temporal graph pooling. The reported comparisons favor the complete model and identify contributions from graph information, dynamic graphs, and pooling.

D. Ablation Study

  • Graph information improves the convolution-based classifier by capturing hidden dependencies among variables and dynamic associations between time slots.Figure 6 compares TodyNet with variants that remove graph components.Source: D. Ablation Study · pp. 8–9, Figure 6 · p. 8
  • The dynamic-graph variant performs better than a static-graph variant, with information flowing between isolated but interdependent time slots.The static-graph ablation uses one graph and does not slice the time series.Source: D. Ablation Study · pp. 8–9, Figure 6 · p. 8
  • Temporal graph pooling improves performance by hierarchically aggregating graph data, and the ablation results report the proposed components as effective for MTSC.The no-pooling variant concatenates graph-neural-network outputs before the output module.Source: D. Ablation Study · pp. 8–9, Figure 6 · p. 8

E. Inspection of Class Prototype

The visualizations examine learned time-series representations on SWJ, Heartbeat, HandMovementDirection, and NATOPS. The conclusion also identifies reducing temporal graph pooling complexity as a future direction for improving efficiency.

E. Inspection of Class Prototype

  • On SWJ, embeddings from three selected samples showed significant differences across the Standing, Walking, and Single Jump categories.Figure 7 pairs each sample’s original sensor signals with its learned embedding.Source: E. Inspection of Class Prototype · p. 9, Figure 7 · p. 9
  • For Heartbeat, HandMovementDirection, and NATOPS, t-SNE visualizations show same-class samples closer together in the learned representation space.Figure 8 places datasets in rows and original data and learned embeddings in separate columns.Source: E. Inspection of Class Prototype · p. 9, Figure 8 · p. 9

VI. CONCLUSION

  • Reducing temporal graph pooling complexity is identified as a future direction for improving model efficiency.The conclusion also suggests transplanting other temporal convolution methods as a possible route to better classification performance.Source: §VI · pp. 9–10

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