PyTSPL: A Python Library for Topological Signal Processing and Learning

Abstract

Graph-based machine learning has seen significant growth during the past years with great advancements and applicability. These approaches mostly focus on pairwise interactions, neglecting the patterns of higher-order interactions which are common to complex systems. In real-world applications, we often encounter these types of signals that naturally associate with nodes, edges or sets of nodes (e.g. triangles). While the node signals have been well-studied by graph-based methods, the other signals have been researched in the recently emerging field of topological signal processing and machine learning. In this thesis, we are particularly interested in edge flow, which models the signals over the edges of a network by signal processing and learning tasks, centring on simplicial complexes. Examples of such networks can be traffic flows in a road network or water flows in a hydrological network. Recent literature in topological signal processing shows simplicial complex as a powerful and principled higher-order network model for edge flows.

In this thesis, we introduce PyTSPL, a Python library that provides reliable and user-friendly building blocks for interacting with simplicial complexes. The library aims to provide a unified platform to read network data in different formats, preprocess them and store them in a data structure such that their properties can be easily retrieved. Users can visualize the simplicial complex simply and effectively, enhancing the interpretability of complex structures and data flows. Additionally, the library provides functionality to analyze the simplicial complexes using various advanced signal processing techniques. The motivation behind developing this master’s thesis is to provide practical bridges to analysing and processing network data based on recent research methods with a unified Python library. While various tools exist for specific aspects of network analysis, there is a lack of unified platforms that integrate reading, processing, visualization, and advanced analysis of network data through topological frameworks, specifically for simplicial complexes. This library is a comprehensive solution encapsulating the entire workflow in a single environment.