Multi-Modal Signal Processing On Non-Euclidean Domains

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.