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，这些数据如此之大和复杂，无法使用标准计算机进行处理。除了信息量巨大之外，新的复杂数据集，如社会网络和蛋白质功能网络，被存储在不规则的数据结构中，如图形，这些数据无法使用经典方法进行处理。现代数据问题需要能够从铺天盖地的信息海洋中提取洞察力的解决方案，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，这些技术被设计用于处理定义在图像和语音等规则结构上的小规模数据问题。为了应对大数据的挑战，该项目将探索和开发高效的数据分析方法，以从定义在不规则结构上的高维数据中提取信息。这与EPSRC在信息和通信技术战略主题下的人工智能和数字信号处理研究领域是一致的。具体地说，该项目将使用张量分解(TD)和图形信号处理(GSP)等新兴领域的工具。张量是向量和矩阵的多维推广，而TD的目标是使用更小的核心张量有效地表示大张量，从而绕过了许多大数据固有的计算问题。另一方面，GSP的目标是从定义在图形顶部的信号中提取洞察力，这是通过考虑图形的底层结构来实现的。TD和GSP是最近备受关注的两个领域，但在合并这两个学科方面做的并不多。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的顶部的多维张量。考虑到这两个字段的相关性，开发能够通过利用底层数据结构高效地处理高维数据的统一技术非常重要。这在生物信息学和金融等许多领域提供了有前途的应用，在这些领域，高维数据之间的交互在很大程度上依赖于底层网络。

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.