Multi-Modal Signal Processing On Non-Euclidean Domains

随着世界进入大数据时代，多维数据正在以前所未有的水平产生，这些数据是如此庞大和复杂，以至于无法使用标准计算机进行处理。除了庞大的信息量之外，新的复杂数据集，如社交网络和蛋白质功能网络，存储在不规则的数据结构中，如图，无法使用经典方法进行处理。现代数据问题需要能够从海量信息中提取见解的解决方案，这应该以稳健、高效和可靠的方式完成。然而，这给传统的信号处理和机器学习技术带来了巨大的挑战，而这些技术是为处理图像和语音等规则结构上的小规模数据问题而设计的。为了应对大数据的挑战，本项目将探索和开发有效的数据分析方法，从定义在不规则结构上的高维数据中提取信息。这与人工智能和数字信号处理的EPSRC研究领域一致，在信息和通信技术的战略主题下。具体来说，该项目将使用来自张量分解（TD）和图形信号处理（GSP）新兴领域的工具。张量是向量和矩阵的多维推广，而TD旨在使用较小的核心张量有效地表示大型张量，从而绕过大数据固有的许多计算问题。另一方面，GSP旨在从定义在图之上的信号中提取见解，这是通过考虑图的底层结构来完成的。TD和GSP是最近获得了很大吸引力的两个领域，但在合并这两个学科方面做得并不多。例如，大多数TD应用程序忽略了不规则的数据域，而大多数GSP应用程序不考虑定义在图形之上的多维张量。考虑到这两个领域的相关性，重要的是开发统一的技术，通过利用底层数据结构来有效地处理高维数据。这在许多领域提供了有前途的应用，例如生物信息学和金融，其中高维数据之间的交互严重依赖于底层网络。

As the world enters the era of big data, multi-dimensional data are being generated on an unprecedented level, which are so large and complex that cannot be processed using a standard computer. In addition to the sheer volume of information, new complex sets of data, such as social networks and protein function networks, are stored in irregular data structures such as graphs, which cannot be processed using classical methods. Modern data problems require solutions that can extract insights from an overwhelming sea of information, which should be done in a robust, efficient, and reliable manner. However, this poses significant challenges for classical signal processing and machine learning techniques, which have been designed to work with small-scale data problems defined on regular structures such as image and speech.To address the challenges of big data, this project will explore and develop efficient data analytics methods to extract information from high-dimensional data defined on irregular structures. This is in line with the EPSRC research area of Artificial Intelligence and Digital Signal Processing, under the umbrella of the strategic theme of Information and Communication Technology. Specifically, the project will use tools from the emerging fields of Tensor Decomposition (TD) and Graph Signal Processing (GSP). Tensors are multi-dimensional generalization of vectors and matrices, while TD aims to represent large tensors efficiently using smaller core tensors, hence bypassing many computational problems inherent to the nature of big data. GSP on the other hand aims to extract insights from signals defined on top of graphs, which is done by considering the underlying structure of the graph. TD and GSP are two fields that have recently gained a lot of tractions, but not much has been done in terms of merging the two disciplines. For instance, most TD applications ignore the irregular data domain, while most GSP applications don't consider multi-dimensional tensors defined on top of graphs. Given the relevance of both fields, it is important to develop unified techniques that can efficiently process high dimensional data by leveraging the underlying data structure. This offers promising applications in many areas, such as bioinformatics and finance, where the interaction between high-dimensional data heavily depends on the underlaying network.