Wavelet Probabilistic Recurrent Convolutional Network for Multivariate Time Series Classification

TL;DR

The paper addresses multivariate time series classification under non-stationary, data-scarce, and noisy conditions. It introduces WPRCN, a framework that combines an Adaptive Wavelet Probabilistic Feature Generator (AWPG) with an Channel Attention-based Probabilistic Temporal Convolutional Network (APTCN), and demonstrates seamless integration with LSTM and C-FCN backbones. The AWPG comprises a GRU-based Encoder-Decoder (GED), an ensemble Multi- receptive-field Wavelet Probabilistic Network (MRWPN) over multiple $(m,j_0)$ configurations, and an Adaptive Network that selects the optimal index $I$; the APTCN analyzes probabilistic features via channel attention and a dilated causal TCN. Evaluated on 30 MTSC datasets, WPRCN achieves the best average accuracy and rank among seven baselines, with ablation studies confirming the probabilistic module’s critical contribution; the approach offers robust performance under data scarcity and non-stationarity and can generalize to other architectures. The work advances wavelet-based probabilistic modeling in deep nets, providing a low-complexity, adaptable tool for MTSC applications such as physiological signal analysis.

Abstract

This paper presents a Wavelet Probabilistic Recurrent Convolutional Network (WPRCN) for Multivariate Time Series Classification (MTSC), especially effective in handling non-stationary environments, data scarcity and noise perturbations. We introduce a versatile wavelet probabilistic module designed to extract and analyse the probabilistic features, which can seamlessly integrate with a variety of neural network architectures. This probabilistic module comprises an Adaptive Wavelet Probabilistic Feature Generator (AWPG) and a Channel Attention-based Probabilistic Temporal Convolutional Network (APTCN). Such formulation extends the application of wavelet probabilistic neural networks to deep neural networks for MTSC. The AWPG constructs an ensemble probabilistic model addressing different data scarcities and non-stationarity; it adaptively selects the optimal ones and generates probabilistic features for APTCN. The APTCN analyses the correlations of the features and forms a comprehensive feature space with existing MTSC models for classification. Here, we instantiate the proposed module to work in parallel with a Long Short-Term Memory (LSTM) network and a Causal Fully Convolutional Network (C-FCN), demonstrating its broad applicability in time series analysis. The WPRCN is evaluated on 30 diverse MTS datasets and outperforms all the benchmark algorithms on average accuracy and rank, exhibiting pronounced strength in handling scarce data and physiological data subject to perturbations and non-stationarities.

Figures (7)

• Figure 1: The proposed WPRCN workflow. The novel Probabilistic module can work with a variety of neural network architectures. An LSTM and a C-FCN are employed to show the broad applicability of the probabilistic module for MTSC TASKS. For the probabilistic module (AWPG and APTCN), the data is transformed into a probabilistic feature ensemble $\mathcal{P}(\mathbf{x})$ with different smoothness considering different levels of data scarcity and non-stationarity using AWPG. The APTCN receives $\mathcal{P}(\mathbf{x})$ and utilises the channel attention to learn the enhanced feature representations. Such representations are then subjected to further analysis within the APTCN pipeline for classification. The features collated from each feature extraction module are consolidated at the Fusion layer, and passed to a Softmax layer for classification.
• Figure 2: The proposed Adaptive Wavelet Probabilistic Feature Generator (AWPG), which contains (i) a GRU-based Encoder-Decoder to form a latent space, (ii) a MRWPN that models the latent space and provides multiple views against different rates of data variation, and (iii) an Adaptive Network that predicts the optimal index $I$ for the selection of a probabilistic model from the ensemble views.
• Figure 3: Visualisation of features in the AtrialFibrillation dataset. (a) and (b) represent the two feature dimensions of the data, illustrating the class-wise means with shaded regions indicating the respective deviations. (c-e) show the three distinct probabilistic features denoted as $\mathcal{P}_c(\mathbf{x})_{m,j_0}$ for each of the classes using $m$ and $j_0$.
• Figure 4: The workflow of the proposed APTCN. (a) A dilated causal convolutional network for modelling $\mathcal{P}(\mathbf{x})$, which involves a channel pruning stage and a channel attention stage; the output $\mathbf{o}$ is then passed to the TCN. For the TCN, the input at depth $i$ is given as $\hat{\mathbf{z}}^i$ and the output $\hat{\mathbf{z}}^{i+1}$ is used for the next level. The output of the TCN, denoted as $\hat{y}_T$, is used for classification. (b) The detailed visualisation of a $2$-level Dilated Causal Convolution with $\mathbb{K}=3$ and $d=1, 2$, where the grey blocks are the zero-paddings.
• Figure 5: The probabilistic features $\mathcal{P}(\mathbf{x})_{m,j_0}$ for three different classes. (a) The first channel of the source signal for dataset AtrialFibrillation, which is a three-class dataset with $L=640$, $n=2$. (b-g) The $\mathcal{P}_{c}(\mathbf{x})_{m,j_0}$ for different $m$ and $j_0$ are presented. Each row shows the same class of data with different $m$ and $j_0$, and each column shows the same $m$ and $j_0$ across different classes of data.