Clustering Techniques and Network Analysis for High-Dimensional Nonlinear Data with Financial Applications

This research focuses on the development and refinement of clustering techniques and network analysis methods tailored to high-dimensional, non-linear datasets, with particular emphasis on their applications in financial systems. The increasing complexity and volume of financial data, such as market transactions, supply chain linkages, asset correlations, and risk measures, pose significant challenges to traditional data analysis methods. These datasets often exhibit non-linear relationships, making it crucial to explore advanced techniques for data classification, pattern recognition, and connectivity analysis.
This project will integrate state-of-the-art machine learning algorithms such as spectral clustering, density-based methods and deep learning approaches to improve the accuracy and scalability of clustering in high-dimensional spaces. Network analysis will be applied to understand the structure and behaviour of financial systems, particularly in areas such as systemic risk, contagion effects and portfolio optimisation. The aim is to provide insights into the interconnectedness of financial instruments, markets and institutions, and to improve predictive modelling in finance.
Using both clustering and network analysis, the research will contribute to the identification of hidden patterns, the understanding of complex relationships and the prediction of emerging trends in financial markets. Much of the literature on clustering and community detection has focused on unsigned and undirected graphs, where each edge carries a non-negative scalar weight that encodes a measure of pairwise affinity. In many applications, this affinity takes negative values and encodes a measure of dissimilarity or anticorrelation, motivating the development of methods to analyze signed networks.
Also in a time series context, directed networks have recently been used to encode lead-lag relationships between pairs of time series. Extensions to the time-dependent network setup are considered, where the network of interest evolves over time, with nodes and edges joining and leaving the network, and one is interested in exploiting past temporal information to improve the prediction task. Also of interest in this setting is the detection of regime changes in the structure of the dynamically evolving network, also known as the network change point detection (NCPD) problem.
In addition, connections to the constrained clustering problem are explored, a machine learning task in which the goal is to cluster the given network given available information that certain pairs of nodes should or should not belong to the same cluster (encoded as must-link and cannot-link constraints).

Overall, this project explores several ways to discover relationships in large groups of time series by using a set of techniques that are broadly understood as inverse problems on graphs. The application domain is financial time series that exhibit strong cross-asset interaction effects, although the methods to be developed are broadly applicable to other settings involving cross-interactions in high-dimensional time series data. Potential techniques to be explored include spectral method