SimGNN: A Neural Network Approach to Fast Graph Similarity Computation

Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity computation, such as Graph Edit Distance (GED) and Maximum Common Subgraph (MCS), is the core operation of graph similarity search and many other applications, but very costly to compute in practice. Inspired by the recent success of neural network approaches to several graph applications, such as node or graph classification, we propose a novel neural network based approach to address this classic yet challenging graph problem, aiming to alleviate the computational burden while preserving a good performance. The proposed approach, called SimGNN, combines two strategies. First, we design a learnable embedding function that maps every graph into a vector, which provides a global summary of a graph. A novel attention mechanism is proposed to emphasize the important nodes with respect to a specific similarity metric. Second, we design a pairwise node comparison method to supplement the graph-level embeddings with fine-grained node-level information. Our model achieves better generalization on unseen graphs, and in the worst case runs in quadratic time with respect to the number of nodes in two graphs. Taking GED computation as an example, experimental results on three real graph datasets demonstrate the effectiveness and efficiency of our approach. Specifically, our model achieves smaller error rate and great time reduction compared against a series of baselines, including several approximation algorithms on GED computation, and many existing graph neural network based models. To the best of our knowledge, we are among the first to adopt neural networks to explicitly model the similarity between two graphs, and provide a new direction for future research on graph similarity computation and graph similarity search.Comment: WSDM 201

SUMMARIZED: Efficient Framework for Analyzing Multidimensional Process Traces under Edit-distance Constraint

Domains such as scientific workflows and business processes exhibit data models with complex relationships between objects. This relationship is typically represented as sequences, where each data item is annotated with multi-dimensional attributes. There is a need to analyze this data for operational insights. For example, in business processes, users are interested in clustering process traces into smaller subsets to discover less complex process models. This requires expensive computation of similarity metrics between sequence-based data. Related work on dimension reduction and embedding methods do not take into account the multi-dimensional attributes of data, and do not address the interpretability of data in the embedding space (i.e., by favoring vector-based representation). In this work, we introduce Summarized, a framework for efficient analysis on sequence-based multi-dimensional data using intuitive and user-controlled summarizations. We introduce summarization schemes that provide tunable trade-offs between the quality and efficiency of analysis tasks and derive an error model for summary-based similarity under an edit-distance constraint. Evaluations using real-world datasets show the effectives of our framework

Graph edit distance : a new binary linear programming formulation

Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming formulations for computing the exact GED between two graphs are proposed. A major strength of the formulations lies in their genericity since the GED can be computed between directed or undirected fully attributed graphs (i.e. with attributes on both vertices and edges). Moreover, a relaxation of the domain constraints in the formulations provides efficient lower bound approximations of the GED. A complete experimental study comparing the proposed formulations with 4 state-of-the-art algorithms for exact and approximate graph edit distances is provided. By considering both the quality of the proposed solution and the efficiency of the algorithms as performance criteria, the results show that none of the compared methods dominates the others in the Pareto sense. As a consequence, faced to a given real-world problem, a trade-off between quality and efficiency has to be chosen w.r.t. the application constraints. In this context, this paper provides a guide that can be used to choose the appropriate method

Recognizing Cuneiform Signs Using Graph Based Methods

The cuneiform script constitutes one of the earliest systems of writing and is realized by wedge-shaped marks on clay tablets. A tremendous number of cuneiform tablets have already been discovered and are incrementally digitalized and made available to automated processing. As reading cuneiform script is still a manual task, we address the real-world application of recognizing cuneiform signs by two graph based methods with complementary runtime characteristics. We present a graph model for cuneiform signs together with a tailored distance measure based on the concept of the graph edit distance. We propose efficient heuristics for its computation and demonstrate its effectiveness in classification tasks experimentally. To this end, the distance measure is used to implement a nearest neighbor classifier leading to a high computational cost for the prediction phase with increasing training set size. In order to overcome this issue, we propose to use CNNs adapted to graphs as an alternative approach shifting the computational cost to the training phase. We demonstrate the practicability of both approaches in an extensive experimental comparison regarding runtime and prediction accuracy. Although currently available annotated real-world data is still limited, we obtain a high accuracy using CNNs, in particular, when the training set is enriched by augmented examples

Few Algorithms for ascertaining merit of a document and their applications

Existing models for ranking documents(mostly in world wide web) are prestige based. In this article, three algorithms to objectively judge the merit of a document are proposed - 1) Citation graph maxflow 2) Recursive Gloss Overlap based intrinsic merit scoring and 3) Interview algorithm. A short discussion on generic judgement and its mathematical treatment is presented in introduction to motivate these algorithms.Comment: 32 page

Properties of the Sample Mean in Graph Spaces and the Majorize-Minimize-Mean Algorithm

One of the most fundamental concepts in statistics is the concept of sample mean. Properties of the sample mean that are well-defined in Euclidean spaces become unwieldy or even unclear in graph spaces. Open problems related to the sample mean of graphs include: non-existence, non-uniqueness, statistical inconsistency, lack of convergence results of mean algorithms, non-existence of midpoints, and disparity to midpoints. We present conditions to resolve all six problems and propose a Majorize-Minimize-Mean (MMM) Algorithm. Experiments on graph datasets representing images and molecules show that the MMM-Algorithm best approximates a sample mean of graphs compared to six other mean algorithms

An interdisciplinary survey of network similarity methods

Comparative graph and network analysis play an important role in both systems biology and pattern recognition, but existing surveys on the topic have historically ignored or underserved one or the other of these fields. We present an integrative introduction to the key objectives and methods of graph and network comparison in each field, with the intent of remaining accessible to relative novices in order to mitigate the barrier to interdisciplinary idea crossover. To guide our investigation, and to quantitatively justify our assertions about what the key objectives and methods of each field are, we have constructed a citation network containing 5,793 vertices from the full reference lists of over two hundred relevant papers, which we collected by searching Google Scholar for ten different network comparison-related search terms. We investigate its basic statistics and community structure, and frame our presentation around the papers found to have high importance according to five different standard centrality measures

Unsupervised Inductive Graph-Level Representation Learning via Graph-Graph Proximity

We introduce a novel approach to graph-level representation learning, which is to embed an entire graph into a vector space where the embeddings of two graphs preserve their graph-graph proximity. Our approach, UGRAPHEMB, is a general framework that provides a novel means to performing graph-level embedding in a completely unsupervised and inductive manner. The learned neural network can be considered as a function that receives any graph as input, either seen or unseen in the training set, and transforms it into an embedding. A novel graph-level embedding generation mechanism called Multi-Scale Node Attention (MSNA), is proposed. Experiments on five real graph datasets show that UGRAPHEMB achieves competitive accuracy in the tasks of graph classification, similarity ranking, and graph visualization.Comment: IJCAI 2019 camera ready version with supplementary materia

Convolutional Set Matching for Graph Similarity

We introduce GSimCNN (Graph Similarity Computation via Convolutional Neural Networks) for predicting the similarity score between two graphs. As the core operation of graph similarity search, pairwise graph similarity computation is a challenging problem due to the NP-hard nature of computing many graph distance/similarity metrics. We demonstrate our model using the Graph Edit Distance (GED) as the example metric. Experiments on three real graph datasets demonstrate that our model achieves the state-of-the-art performance on graph similarity search.Comment: NIPS 2018 Workshop: Relational Representation Learning. Note: Substantial text overlap with arXiv:1809.0444

Separating Structure from Noise in Large Graphs Using the Regularity Lemma

How can we separate structural information from noise in large graphs? To address this fundamental question, we propose a graph summarization approach based on Szemer\'edi's Regularity Lemma, a well-known result in graph theory, which roughly states that every graph can be approximated by the union of a small number of random-like bipartite graphs called `regular pairs'. Hence, the Regularity Lemma provides us with a principled way to describe the essential structure of large graphs using a small amount of data. Our paper has several contributions: (i) We present our summarization algorithm which is able to reveal the main structural patterns in large graphs. (ii) We discuss how to use our summarization framework to efficiently retrieve from a database the top-k graphs that are most similar to a query graph. (iii) Finally, we evaluate the noise robustness of our approach in terms of the reconstruction error and the usefulness of the summaries in addressing the graph search task