Spatio-temporal time series forecasting has attracted great attention in various fields, including climate, power, and traffic forecasting. Recently, Spatio-temporal Graph Neural Networks (STGNNs) have shown promising performance in modeling spatial dependencies based on graph neural networks (GNNs) and temporal dependencies based on temporal learning modules. However, most STGNNs do not effectively integrate explicit and implicit relationships between nodes, nor do they adequately capture long and short-term time dependencies. To address these challenges, this paper presents a Quaternion Spatio-temporal Graph Neural Network(QSTGNN). Specifically, the quaternion spatio-temporal graph is constructed firstly, such that the information of both short and long-term time steps are preserved in quaternion feature tensor, and information of multiple explicit graphs and implicit graph are integrated in quaternion graph adjacency matrix. Then, two modules are designed: a 1D quaternion convolution module and a quaternion graph convolution module. In the 1D quaternion convolution module, complex temporal correlations among short and long-term time steps can be well exploited by 1D quaternion convolution operator based on the quaternion Hamilton product. In the quaternion graph convolution module, quaternion graph convolution is designed to characterize nonlinear dependencies among multiple spatial graphs, including explicit and implicit graphs. Extensive experiments are conducted on six datasets, and the results show that QSTGNN achieves state-of-the-art performances over the existing ten methods. Explainable analysis presents that multiple spatial correlations can accurately illustrate the traffic flow and road functional information in real traffic roads.

Spectral clustering with graph learning usually performs eigen-decomposition on the adaptive graph to obtain embedded representation for clustering. In terms of adaptive graph learning, the embedded representation is usually treated as the principal component of the graph to help improve graph structure. However, most adaptive graph learning methods only use a single graph layer. Therefore, the extraction power of embedded representation is restricted to single graph layer and insufficient to explore the intrinsic information. To break through this limitation, this article proposes a stacked network to realize spectral clustering with adaptive graph learning (SCnet-AGL). Specifically, the network allows the development of latent embedded representation underlying the multiple graph layers to reveal the intrinsic information. Meanwhile, we have designed an adaptive graph learning scheme to exploit the latent embedded representation for graph learning. With the advantage of the network, an augmented graph is obtained by incorporating the representation information for graph learning layer by layer. Finally, an efficient algorithm with feedback training scheme is proposed for network training. Experiments on real datasets demonstrate the effectiveness of the proposed network, and show that it is feasible to develop latent embedded representation to improve clustering performance.

Multi-view clustering aims at integrating information from different views to improve clustering performance. Recent methods integrate multiple view-specific partition matrices to seek a consensus one and have demonstrated promising clustering performance in various applications. However, the clustering performance of such methods heavily relies on the consensus partition matrix estimated by the arithmetic mean in euclidean space and thus is highly susceptible to noise corruption. To this end, this article proposes to learn a consensus partition matrix through the geometric mean on the manifold to achieve robust clustering. Specifically, the multiple view-specific partition matrices can be regarded as points residing in the Stiefel manifold and enable a manifold-based integration. Consequently, the view-specific partition matrices are integrated by estimating a consensus partition matrix as the center point on the Stiefel manifold. Such a partition integration boils down to the Fréchet mean problem on a manifold, which is solved by the intrinsic manifold-based optimization and proves effective in providing a more robust estimation against noise. Experimental results on seven benchmark datasets demonstrate the effectiveness and noise-robustness of our proposed method in comparison to eight competitive methods.

Users submit queries to an online database via its query interface. Query interface parsing, which is important for many applications, understands the query capabilities of a query interface. Since most query interfaces are organized hierarchically, we present a novel query interface parsing method, StatParser (Statistical Parser), to automatically extract the hierarchical query capabilities of query interfaces. StatParser automatically learns from a set of parsed query interfaces and parses new query interfaces. StatParser starts from a small grammar and enhances the grammar with a set of probabilities learned from parsed query interfaces under the maximum-entropy principle. Given a new query interface, the probability-enhanced grammar identifies the parse tree with the largest global probability to be the query capabilities of the query interface. Experimental results show that StatParser very accurately extracts the query capabilities and can effectively overcome the problems of existing query interface parsers.