Variable-length time series classification: Benchmarking, analysis and effective spectral pooling strategy

Real-world time series classification (TSC) is challenging as time series collected in real-world conditions usually exhibit variations in their lengths, which makes standard deep learning (DL) models being difficult to directly process them (i.e., multiple variable-length time series (VTS)). Despite the existence of many pre-processing and pooling-based methods for achieving length normalization for VTS, there lacks a comprehensive and fair comparison across these methods through a uniform benchmark (e.g., standard backbones, datasets and evaluation strategies). To address this gap, we conduct the first comprehensive benchmark for variable-length time series classification tasks, evaluating the effectiveness of 22 previously widely-used length normalization methods across 14 publicly available VTS datasets and 8 backbones. Since these existing methods lead to varying degrees of information loss and distortion of the input VTS, we also propose a novel spectral pooling (SP) for variable-length time series classification (VTS classification) tasks, which is a plugin layer that can be inserted at any location within various DL models. Our SP allows DL models to process VTS or their variable-length representations in an end-to-end manner within mini-batches, without distortion or significant information loss. Experimental results demonstrate that the end-to-end length normalization methods generally outperformed pre-processing-based methods for VTS classification, where our SP achieved state-of-the-art performance across eight backbones over all existing 22 methods. Our code is publicly available at https://github.com/CVI-SZU/VTS_benchmark.