TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: An emerging way to deal with highdimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work aims to elevate the notion of joint harmonic analysis to a full-fledged framework denoted as Time-Vertex Signal Processing, that links together the time-domain signal processing techniques with the new tools of graph signal processing. This entails three main contributions: (a) We provide a formal motivation for harmonic time-vertex analysis as an analysis tool for the state evolution of simple Partial Differential Equations on graphs. (b) We improve the accuracy of joint filtering operators by up-to two orders of magnitude. (c) Using our joint filters, we construct time-vertex dictionaries analyzing the different scales and the local time-frequency content of a signal. The utility of our tools is illustrated in numerous applications and datasets, such as dynamic mesh denoising and classification, still-video inpainting, and source localization in seismic events. Our results suggest that joint analysis of time-vertex signals can bring benefits to regression and learning.

SOLUTION: A Time-Vertex Signal Processing Framework Scalable processing and meaningful representations for time-series on graphs

PROBLEM: Finding inclusion-minimal hitting sets for a given collection of sets is a fundamental combinatorial problem with applications in domains as diverse as Boolean algebra, computational biology, and data mining. Much of the algorithmic literature focuses on the problem of recognizing the collection of minimal hitting sets; however, in many of the applications, it is more important to generate these hitting sets. We survey twenty algorithms from across a variety of domains, considering their history, classification, useful features, and computational performance on a variety of synthetic and real-world inputs. We also provide a suite of implementations of these algorithms with a ready-to-use, platform-agnostic interface based on Docker containers and the AlgoRun framework, so that interested computational scientists can easily perform similar tests with inputs from their own research areas on their own computers or through a convenient Web interface.

SOLUTION: The minimal hitting set generation problem: algorithms and computation

PROBLEM: Information sources such as relational databases, spreadsheets, XML, JSON, and Web APIs contain a tremendous amount of structured data that can be leveraged to build and augment knowledge graphs. However, they rarely provide a semantic model to describe their contents. Semantic models of data sources represent the implicit meaning of the data by specifying the concepts and the relationships within the data. Such models are the key ingredients to automatically publish the data into knowledge graphs. Manually modeling the semantics of data sources requires significant effort and expertise, and although desirable, building these models automatically is a challenging problem. Most of the related work focuses on semantic annotation of the data fields (source attributes). However, constructing a semantic model that explicitly describes the relationships between the attributes in addition to their semantic types is critical. We present a novel approach that exploits the knowledge from a domain ontology and the semantic models of previously modeled sources to automatically learn a rich semantic model for a new source. This model represents the semantics of the new source in terms of the concepts and relationships defined by the domain ontology. Given some sample data from the new source, we leverage the knowledge in the domain ontology and the known semantic models to construct a weighted graph that represents the space of plausible semantic models for the new source. Then, we compute the top k candidate semantic models and suggest to the user a ranked list of the semantic models for the new source. The approach takes into account user corrections to learn more accurate semantic models on future data sources. Our evaluation shows that our method generates expressive semantic models for data sources and services with minimal user input. These precise models make it possible to automatically integrate the data across sources and provide rich support for source discovery and service composition. They also make it possible to automatically publish semantic data into knowledge graphs.

SOLUTION:
Learning the Semantics of Structured Data Sources