Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered data into lower dimensional space. This family of methods, while preserving local structures and features, often misses the global structure of the dataset. Clustering techniques are another class of methods operating on the data in the ambient space. They group together points that are similar according to a fixed similarity criteria, however unlike dimensionality reduction techniques, they do not provide information about the global organization of the data. Leveraging ideas from Topological Data Analysis, in this paper we provide an additional layer on the output of any clustering algorithm. Such data structure, ClusterGraph, provides information about the global layout of clusters, obtained from the considered clustering algorithm. Appropriate measures are provided to assess the quality and usefulness of the obtained representation. Subsequently the ClusterGraph, possibly with an appropriate structure--preserving simplification, can be visualized and used in synergy with state of the art exploratory data analysis techniques.

Disinformation is often presented in long textual articles, especially when it relates to domains such as health, often seen in relation to COVID-19. These articles are typically observed to have a number of trustworthy sentences among which core disinformation sentences are scattered. In this paper, we propose a novel unsupervised task of identifying sentences containing key disinformation within a document that is known to be untrustworthy. We design a three-phase statistical NLP solution for the task which starts with embedding sentences within a bespoke feature space designed for the task. Sentences represented using those features are then clustered, following which the key sentences are identified through proximity scoring. We also curate a new dataset with sentence level disinformation scorings to aid evaluation for this task; the dataset is being made publicly available to facilitate further research. Based on a comprehensive empirical evaluation against techniques from related tasks such as claim detection and summarization, as well as against simplified variants of our proposed approach, we illustrate that our method is able to identify core disinformation effectively.