Stationary time-vertex signal processing

Geometric algebra based recurrent neural network for multi-dimensional time-series prediction

Recent RNN models deal with various dimensions of MTS as independent channels, which may lead to the loss of dependencies between different dimensions or the loss of associated information between each dimension and the global. To process MTS in a holistic way without losing the inter-relationship among dimensions, this paper proposes a novel Long-and Short-term Time-series network based on geometric algebra (GA), dubbed GA-LSTNet. Specifically, taking advantage of GA, multi-dimensional data at each time point of MTS is represented as GA multi-vectors to capture the inherent structures and preserve the correlation of those dimensions. In particular, traditional real-valued RNN, real-valued LSTM, and the back-propagation through time are extended to the GA domain. We evaluate the performance of the proposed GA-LSTNet model in prediction tasks on four well-known MTS datasets, and compared the prediction performance with other six methods. The experimental results indicate that our GA-LSTNet model outperforms traditional real-valued LSTNet with higher prediction accuracy, providing a more accurate solution for the existing shortcomings of MTS prediction models.

Multiway Graph Signal Processing on Tensors: Integrative analysis of irregular geometries

Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures. As acquired data is increasingly taking the form of multi-way tensors, new signal processing tools are needed to maximally utilize the multi-way structure within the data. In this paper, we review modern signal processing frameworks generalizing GSP to multi-way data, starting from graph signals coupled to familiar regular axes such as time in sensor networks, and then extending to general graphs across all tensor modes. This widely applicable paradigm motivates reformulating and improving upon classical problems and approaches to creatively address the challenges in tensor-based data. We synthesize common themes arising from current efforts to combine GSP with tensor analysis and highlight future directions in extending GSP to the multi-way paradigm.