Time series modeling has attracted great research interests in the last decades. Among the literature, shapelet-based models aim to extract representative subsequences, and could offer explanatory insights. In order to capture the shapelet dynamics and evolutions, we propose a novel framework of bridging time series representation learning and graph modeling, with two different implementations. We first formulate the process of extracting time-aware shapelets, then briefly introduce the key idea of transforming time series data into shapelet evolution graphs, to model the shapelet evolutionary patterns. A straightforward solution is to enumerate all possible shapelet transitions among adjacent time series segments, and apply a random-walk-based graph embedding algorithm to learn the time series representations (Time2Graph). We further extend Time2Graph by adopting graph attention mechanism to refine the procedure of modeling shapelet evolutions, namely Time2Graph+. Specifically, we transform each time series data into a unique and unweighted shapelet graph, and use GAT to automatically capture the correlations between shapelets. Experimental results show the significant improvements of Time2Graph+, and extensive observational analysis demonstrate the effectiveness and interpretability brought by attentions. Furthermore, the success of online deployment of Time2Graph+ model in State Grid of China validates the whole framework in the real-world application.

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, EvoNet models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.

Time series modeling has attracted extensive research efforts; however, achieving both reliable efficiency and interpretability from a unified model still remains a challenging problem. Among the literature, shapelets offer interpretable and explanatory insights in the classification tasks, while most existing works ignore the differing representative power at different time slices, as well as (more importantly) the evolution pattern of shapelets. In this paper, we propose to extract time-aware shapelets by designing a two-level timing factor. Moreover, we define and construct the shapelet evolution graph, which captures how shapelets evolve over time and can be incorporated into the time series embeddings by graph embedding algorithms. To validate whether the representations obtained in this way can be applied effectively in various scenarios, we conduct experiments based on three public time series datasets, and two real-world datasets from different domains. Experimental results clearly show the improvements achieved by our approach compared with 16 state-of-the-art baselines.

Electricity theft, the behavior that involves users conducting illegal operations on electrical meters to avoid individual electricity bills, is a common phenomenon in the developing countries. Considering its harmfulness to both power grids and the public, several mechanized methods have been developed to automatically recognize electricity-theft behaviors. However, these methods, which mainly assess users’ electricity usage records, can be insufficient due to the diversity of theft tactics and the irregularity of user behaviors.

Network embedding aims to learn the low-dimensional representations of vertexes in a network, while structure and inherent properties of the network is preserved. Existing network embedding works primarily focus on preserving the microscopic structure, such as the first- and second-order proximity of vertexes, while the macroscopic scale-free property is largely ignored. Scale-free property depicts the fact that vertex degrees follow a heavy-tailed distribution (i.e., only a few vertexes have high degrees) and is a critical property of real-world networks, such as social networks. In this paper, we study the problem of learning representations for scale-free networks. We first theoretically analyze the difficulty of embedding and reconstructing a scale-free network in the Euclidean space, by converting our problem to the sphere packing problem. Then, we propose the "degree penalty" principle for designing scale-free property preserving network embedding algorithm: punishing the proximity between high-degree vertexes. We introduce two implementations of our principle by utilizing the spectral techniques and a skip-gram model respectively. Extensive experiments on six datasets show that our algorithms are able to not only reconstruct heavy-tailed distributed degree distribution, but also outperform state-of-the-art embedding models in various network mining tasks, such as vertex classification and link prediction.