LGDE: Local Graph-based Dictionary Expansion

Expanding a dictionary of pre-selected keywords is crucial for tasks in information retrieval, such as database query and online data collection. Here we propose Local Graph-based Dictionary Expansion (LGDE), a method that uses tools from manifold learning and network science for the data-driven discovery of keywords starting from a seed dictionary. At the heart of LGDE lies the creation of a word similarity graph derived from word embeddings and the application of local community detection based on graph diffusion to discover semantic neighbourhoods of pre-defined seed keywords. The diffusion in the local graph manifold allows the exploration of the complex nonlinear geometry of word embeddings and can capture word similarities based on paths of semantic association. We validate our method on a corpus of hate speech-related posts from Reddit and Gab and show that LGDE enriches the list of keywords and achieves significantly better performance than threshold methods based on direct word similarities. We further demonstrate the potential of our method through a real-world use case from communication science, where LGDE is evaluated quantitatively on data collected and analysed by domain experts by expanding a conspiracy-related dictionary.

Persistent Homology of the Multiscale Clustering Filtration

In many applications in data clustering, it is desirable to find not just a single partition but a sequence of partitions that describes the data at different scales, or levels of coarseness, leading naturally to Sankey diagrams as descriptors of the data. The problem of multiscale clustering then becomes how to to select robust intrinsic scales, and how to analyse and compare the (not necessarily hierarchical) sequences of partitions. Here, we define a novel filtration, the Multiscale Clustering Filtration (MCF), which encodes arbitrary patterns of cluster assignments across scales. We prove that the MCF is a proper filtration, give an equivalent construction via nerves, and show that in the hierarchical case the MCF reduces to the Vietoris-Rips filtration of an ultrametric space. We also show that the zero-dimensional persistent homology of the MCF provides a measure of the level of hierarchy in the sequence of partitions, whereas the higher-dimensional persistent homology tracks the emergence and resolution of conflicts between cluster assignments across scales. We briefly illustrate numerically how the structure of the persistence diagram can serve to characterise multiscale data clusterings.