This book provides a comprehensive introduction to the foundations and frontiers of the rapidly expanding field of graph neural networks.
Correlation clustering is perhaps the most natural formulation of clustering. Given $n$ objects and a pairwise similarity measure, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same cluster and dissimilar objects are put in different clusters. Despite its theoretical appeal, the practical relevance of correlation clustering still remains largely unexplored, mainly due to the fact that correlation clustering requires the $\Theta(n^2)$ pairwise similarities as input. In this paper we initiate the investigation into \emph{local} algorithms for correlation clustering. In \emph{local correlation clustering} we are given the identifier of a single object and we want to return the cluster to which it belongs in some globally consistent near-optimal clustering, using a small number of similarity queries. Local algorithms for correlation clustering open the door to \emph{sublinear-time} algorithms, which are particularly useful when the similarity between items is costly to compute, as it is often the case in many practical application domains. They also imply $(i)$ distributed and streaming clustering algorithms, $(ii)$ constant-time estimators and testers for cluster edit distance, and $(iii)$ property-preserving parallel reconstruction algorithms for clusterability. Specifically, we devise a local clustering algorithm attaining a $(3, \varepsilon)$-approximation in time $O(1/\varepsilon^2)$ independently of the dataset size. An explicit approximate clustering for all objects can be produced in time $O(n/\varepsilon)$ (which is provably optimal). We also provide a fully additive $(1,\varepsilon)$-approximation with local query complexity $poly(1/\varepsilon)$ and time complexity $2^{poly(1/\varepsilon)}$. The latter yields the fastest polynomial-time approximation scheme for correlation clustering known to date.
People nowadays are inundated with vast amounts of text data (e.g., news articles, corporate reports, scientific papers, etc.). Turning massive text data into actionable knowledge is an essential research issue in data science. Based on our vision, it is highly beneficial to first structure raw text using taxonomies and then analyze structured text data in a more fine-grained and user-guided way. In this tutorial, we provide a comprehensive overview of recent research in this direction. We first show a series of methods to identify concept phrases from text corpora and then present methods to organize identified concepts into taxonomies. After that, we introduce techniques to automatically enrich an existing taxonomy and discuss how to explore taxonomies for different downstream applications. Finally, we demonstrate on real-world datasets from multiple domains how different taxonomies can be constructed based on different user tasks and how they can empower knowledge discovery from text data.
