Wavelet Probabilistic Recurrent Convolutional Network for Multivariate Time Series Classification

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 (A WPG) 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 A WPG 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. Introduction Time series (TS) data, one of the most prevalent types of datasets, encompasses crucial physiological signals such as Electrocardiograms (ECGs) and Electroencephalograms (EEGs) that provide insights into cardiac and brain activities. A thorough analysis of the trends and patterns within TS data enables the development of resilient forecasting and classification frameworks, which are critical in applications such as financial forecasting, network traffic analysis, and the diagnosis of various physiological conditions [1-3]. In general, time series classification (TSC) methods can be categorised into two groups, the traditional methods and the Deep Learning (DL)-based methods [4]. Traditional methods include techniques such as Dynamic Time Warping with One-Nearest Neighbour (DTW-1NN) and ensemble-based solutions such as decision trees or support vector machines.