This paper presents TS2Vec, a universal framework for learning representations of time series in an arbitrary semantic level. Unlike existing methods, TS2Vec performs contrastive learning in a hierarchical way over augmented context views, which enables a robust contextual representation for each timestamp. Furthermore, to obtain the representation of an arbitrary sub-sequence in the time series, we can apply a simple aggregation over the representations of corresponding timestamps. We conduct extensive experiments on time series classification tasks to evaluate the quality of time series representations. As a result, TS2Vec achieves significant improvement over existing SOTAs of unsupervised time series representation on 125 UCR datasets and 29 UEA datasets. The learned timestamp-level representations also achieve superior results in time series forecasting and anomaly detection tasks. A linear regression trained on top of the learned representations outperforms previous SOTAs of time series forecasting. Furthermore, we present a simple way to apply the learned representations for unsupervised anomaly detection, which establishes SOTA results in the literature. The source code is publicly available at https://github.com/yuezhihan/ts2vec.

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Graph Neural Networks (GNNs) have shown advantages in various graph-based applications. Most existing GNNs assume strong homophily of graph structure and apply permutation-invariant local aggregation of neighbors to learn a representation for each node. However, they fail to generalize to heterophilic graphs, where most neighboring nodes have different labels or features, and the relevant nodes are distant. Few recent studies attempt to address this problem by combining multiple hops of hidden representations of central nodes (i.e., multi-hop-based approaches) or sorting the neighboring nodes based on attention scores (i.e., ranking-based approaches). As a result, these approaches have some apparent limitations. On the one hand, multi-hop-based approaches do not explicitly distinguish relevant nodes from a large number of multi-hop neighborhoods, leading to a severe over-smoothing problem. On the other hand, ranking-based models do not joint-optimize node ranking with end tasks and result in sub-optimal solutions. In this work, we present Graph Pointer Neural Networks (GPNN) to tackle the challenges mentioned above. We leverage a pointer network to select the most relevant nodes from a large amount of multi-hop neighborhoods, which constructs an ordered sequence according to the relationship with the central node. 1D convolution is then applied to extract high-level features from the node sequence. The pointer-network-based ranker in GPNN is joint-optimized with other parts in an end-to-end manner. Extensive experiments are conducted on six public node classification datasets with heterophilic graphs. The results show that GPNN significantly improves the classification performance of state-of-the-art methods. In addition, analyses also reveal the privilege of the proposed GPNN in filtering out irrelevant neighbors and reducing over-smoothing.

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