Trend-aware time series clustering via self-attentive LSTM

Abstract

Time series clustering aims to partition time series into subsets with similar patterns, uncovering their underlying structures and dynamics. This paper proposes a novel clustering method that integrates polynomial curve fitting, an enhanced self-attention mechanism, and a long short-term memory (LSTM) network. First, the Hodrick-Prescott (HP) filter is applied to denoise the raw time series. Then, polynomial curve fitting (PCF) is employed to extract multi-order derivative features at each time point, capturing local trend information and constructing a high-dimensional feature space. An enhanced self-attention LSTM model is designed to encode both raw and trend-based features into a hidden state sequence, enabling the model to capture key patterns and long-range dependencies. Finally, a distance metric based on the hidden states is defined and incorporated into a hierarchical clustering (HC) algorithm. Experiments on several public univariate datasets with long sequences demonstrate that the proposed method outperforms conventional approaches, offering a robust solution for modeling and interpreting complex time series.