# graph

### A comprehensive survey on graph neural networks

Last year we looked at'Relational inductive biases, deep learning, and graph networks,' where the authors made the case for deep learning with structured representations, which are naturally represented as graphs. Today's paper choice provides us with a broad sweep of the graph neural network landscape. It's a survey paper, so you'll find details on the key approaches and representative papers, as well as information on commonly used datasets and benchmark performance on them. We'll be talking about graphs as defined by a tuple where is the set of nodes (vertices), is the set of edges, and A is the adjacency matrix. An edge is a pair, and the adjacency matrix is an (for N nodes) matrix where if nodes and are not directly connected by a edge, and some weight value 0 if they are.

### Knowledge Graphs And Machine Learning -- The Future Of AI Analytics?

The unprecedented explosion in the amount of information we are generating and collecting, thanks to the arrival of the internet and the always-online society, powers all the incredible advances we see today in the field of artificial intelligence (AI) and Big Data. With this in mind, a great deal of thought and research has gone into working out the best way to store and organize information during the digital age. The relational database model was developed in the 1970s and organizes data into tables consisting of rows and columns – meaning the relationship between different data points can be determined at a glance. This worked very well in the early days of business computing, where information volumes grew slowly. For more complicated operations, however – such as establishing a relationship between data points stored in many different tables - the necessary operations quickly become complex, slow and cumbersome.

### Knowledge Graphs And Machine Learning -- The Future Of AI Analytics?

The unprecedented explosion in the amount of information we are generating and collecting, thanks to the arrival of the internet and the always-online society, powers all the incredible advances we see today in the field of artificial intelligence (AI) and Big Data. With this in mind, a great deal of thought and research has gone into working out the best way to store and organize information during the digital age. The relational database model was developed in the 1970s and organizes data into tables consisting of rows and columns – meaning the relationship between different data points can be determined at a glance. This worked very well in the early days of business computing, where information volumes grew slowly. For more complicated operations, however – such as establishing a relationship between data points stored in many different tables - the necessary operations quickly become complex, slow and cumbersome.

### What is TensorFlow? The machine learning library explained

Machine learning is a complex discipline. But implementing machine learning models is far less daunting and difficult than it used to be, thanks to machine learning frameworks--such as Google's TensorFlow--that ease the process of acquiring data, training models, serving predictions, and refining future results. Created by the Google Brain team, TensorFlow is an open source library for numerical computation and large-scale machine learning. TensorFlow bundles together a slew of machine learning and deep learning (aka neural networking) models and algorithms and makes them useful by way of a common metaphor. It uses Python to provide a convenient front-end API for building applications with the framework, while executing those applications in high-performance C .

### The Linked Open Data cloud is more abstract, flatter and less linked than you may think!

This paper presents an empirical study aiming at understanding the modeling style and the overall semantic structure of Linked Open Data. We observe how classes, properties and individuals are used in practice. We also investigate how hierarchies of concepts are structured, and how much they are linked. In addition to discussing the results, this paper contributes (i) a conceptual framework, including a set of metrics, which generalises over the observable constructs; (ii) an open source implementation that facilitates its application to other Linked Data knowledge graphs.

### Learning Directed Graphical Models from Gaussian Data

In this paper, we introduce two new directed graphical models from Gaussian data: the Gaussian graphical interaction model (GGIM) and the Gaussian graphical conditional expectation model (GGCEM). The development of these models comes from considering stationary Gaussian processes on graphs, and leveraging the equations between the resulting steady-state covariance matrix and the Laplacian matrix representing the interaction graph. Through the presentation of conceptually straightforward theory, we develop the new models and provide interpretations of the edges in each graphical model in terms of statistical measures. We show that when restricted to undirected graphs, the Laplacian matrix representing a GGIM is equivalent to the standard inverse covariance matrix that encodes conditional dependence relationships. We demonstrate that the problem of learning sparse GGIMs and GGCEMs for a given observation set can be framed as a LASSO problem. By comparison with the problem of inverse covariance estimation, we prove a bound on the difference between the covariance matrix corresponding to a sparse GGIM and the covariance matrix corresponding to the $l_1$-norm penalized maximum log-likelihood estimate. In all, the new models present a novel perspective on directed relationships between variables and significantly expand on the state of the art in Gaussian graphical modeling.

### Evaluating Ising Processing Units with Integer Programming

The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, present new opportunities for hybrid-optimization algorithms that are hardware accelerated by these devices. In this work, we propose the idea of an Ising processing unit as a computational abstraction for reasoning about these emerging devices. The challenges involved in using and benchmarking these devices are presented and commercial mixed integer programming solvers are proposed as a valuable tool for the validation of these disparate hardware platforms. The proposed validation methodology is demonstrated on a D-Wave 2X adiabatic quantum computer, one example of an Ising processing unit. The computational results demonstrate that the D-Wave hardware consistently produces high-quality solutions and suggests that as IPU technology matures it could become a valuable co-processor in hybrid-optimization algorithms.

### Ranking and synchronization from pairwise measurements via SVD

Given a measurement graph $G= (V,E)$ and an unknown signal $r \in \mathbb{R}^n$, we investigate algorithms for recovering $r$ from pairwise measurements of the form $r_i - r_j$; $\{i,j\} \in E$. This problem arises in a variety of applications, such as ranking teams in sports data and time synchronization of distributed networks. Framed in the context of ranking, the task is to recover the ranking of $n$ teams (induced by $r$) given a small subset of noisy pairwise rank offsets. We propose a simple SVD-based algorithmic pipeline for both the problem of time synchronization and ranking. We provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise perturbations with outliers, using results from matrix perturbation and random matrix theory. Our theoretical findings are complemented by a detailed set of numerical experiments on both synthetic and real data, showcasing the competitiveness of our proposed algorithms with other state-of-the-art methods.

### On the Constrained Least-cost Tour Problem

We introduce the Constrained Least-cost Tour (CLT) problem: given an undirected graph with weight and cost functions on the edges, minimise the total cost of a tour rooted at a start vertex such that the total weight lies within a given range. CLT is related to the family of Travelling Salesman Problems with Profits, but differs by defining the weight function on edges instead of vertices, and by requiring the total weight to be within a range instead of being at least some quota. We prove CLT is $\mathcal{NP}$-hard, even in the simple case when the input graph is a path. We derive an informative lower bound by relaxing the integrality of edges and propose a heuristic motivated by this relaxation. For the case that requires the tour to be a simple cycle, we develop two heuristics which exploit Suurballe's algorithm to find low-cost, weight-feasible cycles. We demonstrate our algorithms by addressing a real-world problem that affects urban populations: finding routes that minimise air pollution exposure for walking, running and cycling in the city of London.

### Subsumption-driven clause learning with DPLL+restarts

Complete SAT solvers make deductions until they find a model or produce the empty clause. In DPLL and CDCL solvers, these deductions are produced using assumptions generally called decisions. In DPLL solvers [DLL62], the knowledge accumulated since the beginning of the search is represented by the phases of decision literals. Each new conflict induced by decisions increases the amount of information being accumulated. This amount of information can be interpreted as a proportion of search space already explored that is known not to contain a model.