Time-Series Clustering Leveraging Inter-Network Heterogeneity from a Spectral Symmetry Perspective

Time-series clustering is a prominent research area with extensive practical applications. Given the complexity and diversity of modern time-series data, this study proposes a novel time-series clustering method based on inter-network heterogeneity. First, each time-series is converted into a network by using two types of time-series segmentation techniques. Second, an inter-network clustering approach based on graph spectral theory is introduced: we calculate the total variation (TV) distance between the empirical spectral distributions of each network and identify distinct clusters using a hierarchical clustering algorithm. From the perspective of symmetry, networks constructed from similar time-series tend to exhibit comparable spectral structures, which reflect the underlying structural symmetries of their dynamics. Differences in spectral distributions correspond to symmetry breaking among networks, providing an effective mechanism for distinguishing heterogeneous time-series patterns. Our method effectively preserves more distinctive features inherent in the original time-series. To evaluate the performance of the proposed method, simulation studies are conducted, including the recognition of both stationary and non-stationary sequences. The method also performs well on real-world datasets, such as stock closing prices. These results demonstrate that our approach can handle non-stationary sequences and identify the intrinsic correlations in time-series.