Prototype Graph Research Articles

PAGE: Prototype-Based Model-Level Explanations for Graph Neural Networks.

Aside from graph neural networks (GNNs) attracting significant attention as a powerful framework revolutionizing graph representation learning, there has been an increasing demand for explaining GNN models. Although various explanation methods for GNNs have been developed, most studies have focused on instance-level explanations, which produce explanations tailored to a given graph instance. In our study, we propose Prototype-bAsed GNN-Explainer ([Formula: see text]), a novel model-level GNN explanation method that explains what the underlying GNN model has learned for graph classification by discovering human-interpretable prototype graphs. Our method produces explanations for a given class, thus being capable of offering more concise and comprehensive explanations than those of instance-level explanations. First, [Formula: see text] selects embeddings of class-discriminative input graphs on the graph-level embedding space after clustering them. Then, [Formula: see text] discovers a common subgraph pattern by iteratively searching for high matching node tuples using node-level embeddings via a prototype scoring function, thereby yielding a prototype graph as our explanation. Using six graph classification datasets, we demonstrate that [Formula: see text] qualitatively and quantitatively outperforms the state-of-the-art model-level explanation method. We also carry out systematic experimental studies by demonstrating the relationship between [Formula: see text] and instance-level explanation methods, the robustness of [Formula: see text] to input data scarce environments, and the computational efficiency of the proposed prototype scoring function in [Formula: see text].

SPGMVC: Multiview Clustering via Partitioning the Signed Prototype Graph.

Multiview clustering (MVC) has been widely studied in machine learning and data mining for its capability of improving clustering performance by fusing the information from multiview data. In the past decade, a large number of MVC methods have made impressive progress, but most of them suffer from computational burdens, especially in large-scale tasks. Binary MVC (BMVC) is proposed to address this issue by representing the large-scale high-dimensional dataset as a group of consensus and low-dimensional binary codes. However, current BMVC-based approaches generate the clustering by executing binary k -means on the obtained binary codes, which fail to capture the embedded geometric information, leading to poor clustering performance. In addition, parameter selection is another "mission impossible" in unsupervised learning tasks including MVC. To tackle these challenges, a framework of multiview clustering via partitioning the signed prototype graph (SPGMVC) is proposed in this work. The SPGMVC framework offers several contributions. First, SPGMVC is designed as a unified framework for MVC. It combines effective technologies, such as consensus binary coding, code compression (CC), signed prototype graph (SPG) partitioning, and prototype-based cluster assignment. Second, SPGMVC partitions the signed graph (SG) based on the relationships between positive and negative edges. By capturing the underlying structure of the data, this partitioning strategy improves clustering accuracy (ACC). CC techniques are applied to reduce the graph's scale, enabling further partitioning and enhancing computational efficiency. Third, SPGMVC employs an alternate minimizing strategy to efficiently handle the optimization problem. This strategy has nearly linear time and space complexity with respect to the data volume, making it suitable for large-scale tasks. Fourth, SPGMVC proposes an automatic parameter selection strategy, eliminating the need for extensive parameter exploration. Comprehensive experiments illustrate the superiority of our model. The implementation of SPGMVC is available at: https://github.com/gepingyang/PSGMVC.

Fast correntropy-based multi-view clustering with prototype graph factorization

As a consequence of the ability to incorporate information from different perspectives, multi-view clustering has gained significant attention. Nevertheless, 1) its high computational cost, particularly when processing large-scale and high-dimensional multi-view data, restricts its applications in practice; and 2) complex noise in real-world data also challenges the robustness of existing algorithms. To tackle the above challenges, we develop a fast correntropy-based multi-view clustering algorithm with prototype graph factorization (FCMCPF). FCMCPF first adopts prototype graphs to effectively mitigate the complexity associated with graph construction, thereby reducing it from a quadratic complexity to a linear one. Then, it decomposes these prototype graphs under the correntropy criterion to robustly find the cluster indicator matrix without any post-processing. To solve the non-convex and non-linear model, we devise a fast half-quadratic-based strategy to first convert it into a convex formulation and then swiftly complete the optimization via the matrix properties of orthogonality and trace. The extensive experiments conducted on noisy and real-world datasets illustrate that FCMCPF is highly efficient and robust compared to other advanced algorithms, with comparable or even superior clustering effectiveness.

Parameter-Free and Scalable Incomplete Multiview Clustering With Prototype Graph.

Multiview clustering (MVC) seamlessly combines homogeneous information and allocates data samples into different communities, which has shown significant effectiveness for unsupervised tasks in recent years. However, some views of samples may be incomplete due to unfinished data collection or storage failure in reality, which refers to the so-called incomplete multiview clustering (IMVC). Despite many IMVC pioneer frameworks have been introduced, the majority of their approaches are limited by the cubic time complexity and quadratic space complexity which heavily prevent them from being employed in large-scale IMVC tasks. Moreover, the massively introduced hyper-parameters in existing methods are not practical in real applications. Inspired by recent unsupervised multiview prototype progress, we propose a novel parameter-free and scalable incomplete multiview clustering framework with the prototype graph termed PSIMVC-PG to solve the aforementioned issues. Different from existing full pair-wise graph studying, we construct an incomplete prototype graph to flexibly capture the relations between existing instances and discriminate prototypes. Moreover, PSIMVC-PG can directly obtain the prototype graph without pre-process of searching hyper-parameters. We conduct massive experiments on various incomplete multiview tasks, and the performances show clear advantages over existing methods. The code of PSIMVC-PG can be publicly downloaded at https://github.com/wangsiwei2010/PSIMVC-PG.

Physical performance of power grids against earthquakes: from framework to implementation

Resilience analysis of power grids requires their performance assessment during threatening hazards. However, the diverse connections among various constituent components make studying power grids' network behavior complicated. This study aims to present a practical framework with appropriate computational speed and acceptable accuracy in estimating the seismic physical performance of power grids, such that both electrical and earthquake experts can easily use it. The framework has provided a performance indicator by implementing the system's component-based analysis in the network-based graph model. This indicator has been calculated based on distinguishing the components under power service, failed components by direct physical damage, and failed components by indirect physical damage from each other (network-based). The proposed indicator has also considered the physical capacity lost/remaining in both under-service and out-of-service components (component-based). Consequently, It can distinguish among the network components beyond the binary classification of performance and failure. In other words, while maintaining the positive features of binary connectivity analysis, higher accuracy has been obtained for a preliminary estimation of the system's physical performance. The variety of seismic scenarios for the selected case study provided the possibility of examining and comparing different network performance states on three levels: physical blackout, physical outage, and no physical interruption. The practical functionality of the indicator, verified by a prototype graph, and the merits such as higher accuracy than commonly used connectivity analysis, simplicity, and rapidity make it a user-friendly method in interdisciplinary studies of electricity and earthquake engineering.

ProtGNN: Towards Self-Explaining Graph Neural Networks

Despite the recent progress in Graph Neural Networks (GNNs), it remains challenging to explain the predictions made by GNNs. Existing explanation methods mainly focus on post-hoc explanations where another explanatory model is employed to provide explanations for a trained GNN. The fact that post-hoc methods fail to reveal the original reasoning process of GNNs raises the need of building GNNs with built-in interpretability. In this work, we propose Prototype Graph Neural Network (ProtGNN), which combines prototype learning with GNNs and provides a new perspective on the explanations of GNNs. In ProtGNN, the explanations are naturally derived from the case-based reasoning process and are actually used during classification. The prediction of ProtGNN is obtained by comparing the inputs to a few learned prototypes in the latent space. Furthermore, for better interpretability and higher efficiency, a novel conditional subgraph sampling module is incorporated to indicate which part of the input graph is most similar to each prototype in ProtGNN+. Finally, we evaluate our method on a wide range of datasets and perform concrete case studies. Extensive results show that ProtGNN and ProtGNN+ can provide inherent interpretability while achieving accuracy on par with the non-interpretable counterparts.

Fast Multi-view Clustering via Prototype Graph

Multi-view clustering attracts considerable attention due to its effectiveness in unsupervised learning. However, previous multi-view spectral clustering methods include two separated steps: 1) Obtaining a spectral embedding; 2) Performing classical clustering methods. Although these methods have achieved promising performance, there is still some limitations. First, in computing spectral embedding, multi-view spectral clustering approaches exist high computational complexity since they usually need eigenvalue decomposition on laplacian matrix L. Its computational complexity is O(n³) where n is the number of samples; Second, in constructing similarity matrices, previous methods need to compute similarity between any two samples; Third, the two-stage approach only can obtain sub-optimal solution; Fourth, treating equally all views is unreasonable. To address these issues, we propose a Fast Multi-view Clustering via Prototype Graph (FMVPG) method. Specifically, the prototype graph is firstly constructed, and then simultaneously perform spectral embedding to obtain the real matrix and spectral rotation to get the indicator matrix. In addition, the Alternating Direction Method of Multipliers (ADMM) is used to solve the joint optimization problem. Further, we conduct extensive experiments to evaluate the proposed FMVPG approach. These experimental results show the comparable or even better clustering performance than the state-of-the-art approaches.

Zero-Shot Learning on Semantic Class Prototype Graph

Zero-Shot Learning (ZSL) for visual recognition is typically achieved by exploiting a semantic embedding space. In such a space, both seen and unseen class labels as well as image features can be embedded so that the similarity among them can be measured directly. In this work, we consider that the key to effective ZSL is to compute an optimal distance metric in the semantic embedding space. Existing ZSL works employ either euclidean or cosine distances. However, in a high-dimensional space where the projected class labels (prototypes) are sparse, these distances are suboptimal, resulting in a number of problems including hubness and domain shift. To overcome these problems, a novel manifold distance computed on a semantic class prototype graph is proposed which takes into account the rich intrinsic semantic structure, i.e., semantic manifold, of the class prototype distribution. To further alleviate the domain shift problem, a new regularisation term is introduced into a ranking loss based embedding model. Specifically, the ranking loss objective is regularised by unseen class prototypes to prevent the projected object features from being biased towards the seen prototypes. Extensive experiments on four benchmarks show that our method significantly outperforms the state-of-the-art.

Backing up digital preservation practice with empirical research

This article introduces the National Library of Australia’s Digital Preservation Knowledge Base which helps the Library to manage digital objects from its collections over the long term. The Knowledge Base includes information on file formats, rendering software, operating systems, hardware and, most importantly, the relationships between them. Most of the work on the Knowledge Base over the last few years has been focused on the mapping of functional relationships between file formats, their versions and software applications. The information is gathered through unique empirical research and is initially being recorded in a multiple-worksheet Excel file in a semi-structured format, though development of a prototype graph database is underway.

Graph matching and clustering using kernel attributes

In this paper, we exploit graph kernels for graph matching and clustering. Firstly, we analyze different kinds of graph kernels in order to extract from them attributes to be used as a similarity measure between nodes of non-attributed graphs. Next, such attributes are embedded in a graph-matching cost function, through a probabilistic framework, and we evaluate their performance within a graph-matching algorithm. Secondly, we propose a method for obtaining a representative prototype from a set of graphs, which relies on obtaining all the pairwise matchings between the input graphs, and uses the information provided by graph kernels in order to select the matchings that will be considered for obtaining the prototype. Nodes and edges in such a prototype graph register their frequency of occurrence, so that it can be considered a first-order generative model. The proposed method for building prototypes is efficiently integrated into a central clustering algorithm, which allows us to unsupervisedly learn the class-structure of a given set of graphs, and the prototypes representing each class, thus obtaining a central graph clustering algorithm with the same computational cost than a pairwise one. We successfully apply the proposed methods to structural recognition problems.

On formalizing EMF modeling operations with graph transformations

The development of software in accordance with the model-driven engineering paradigm places model transformations at a central position. Desirable yet contradicting properties of model transformations are user-friendliness as offered by-demonstration approaches and formal conciseness as provided by algebraic graph transformations which is indispensable for verification tasks. In this paper, we show how to unite the properties of the two different approaches. We employ the state-of-the-art by-demonstration environment Emo to prototype graph transformations by embedding the operations obtained from Emo in the formal framework of graph transformation theory.

Stereoscopic Highlighting: 2D Graph Visualization on Stereo Displays

In this paper we present a new technique and prototype graph visualization system, stereoscopic highlighting, to help answer accessibility and adjacency queries when interacting with a node-link diagram. Our technique utilizes stereoscopic depth to highlight regions of interest in a 2D graph by projecting these parts onto a plane closer to the viewpoint of the user. This technique aims to isolate and magnify specific portions of the graph that need to be explored in detail without resorting to other highlighting techniques like color or motion, which can then be reserved to encode other data attributes. This mechanism of stereoscopic highlighting also enables focus+context views by juxtaposing a detailed image of a region of interest with the overall graph, which is visualized at a further depth with correspondingly less detail. In order to validate our technique, we ran a controlled experiment with 16 subjects comparing static visual highlighting to stereoscopic highlighting on 2D and 3D graph layouts for a range of tasks. Our results show that while for most tasks the difference in performance between stereoscopic highlighting alone and static visual highlighting is not statistically significant, users performed better when both highlighting methods were used concurrently. In more complicated tasks, 3D layout with static visual highlighting outperformed 2D layouts with a single highlighting method. However, it did not outperform the 2D layout utilizing both highlighting techniques simultaneously. Based on these results, we conclude that stereoscopic highlighting is a promising technique that can significantly enhance graph visualizations for certain use cases.

Event-based personal retrieval

People who work in a research, academic or business envi ronment often have personal information collections which are large enough to need retrieval aids. A major difference between personal information retrieval and normal docu ment retrieval is that the items to be retrieved are often associated with events in the searcher's life and can be retrieved by their relationship to other events as well as by content. This paper describes some of the background to event-based retrieval and then describes a prototype graph ical event-based retrieval system.

Heuristic graph displayer for G-Base

A proto-type graph displaying system for a data base management system is described. The system uses a heuristic algorithm for drawing a graph. The system was developed to draw a schema graph for the G-Base-Data Base Management System based on a graph data model. For quick display, the algorithm used no or very limited backtracking and it attempts to minimize unnecessary arc intersections. The graph is embedded in an integer grid plane and displayed on a window. The graph drawer has several useful features for producing visually pleasant drawings such as automatic font selection, and automatic abbreviation of long node label. It can draw both directed graphs and non-directed graphs and can display arc labels. The system is implemented using the X-window system running on Sun workstations and Sony NEWS workstations. It is written in C language and is portable to any workstation which supports the X-window system. Complex graphs, such as a graph with 149 nodes and 153 arcs, have been displayed in a visually pleasing manner.