Adaptive aggregation on graphs

We generalize some of the functional (hyper-circle) a posteriori estimates from finite element settings to general graphs or Hilbert space settings. We provide several theoretical results in regard to the generalized a posteriori error estimators. We use these estimates to construct aggregation based coarse spaces for graph Laplacians. The estimator is used to assess the quality of an aggregation adaptively. Furthermore, a reshaping algorithm based is tested on several numerical examples.Comment: 17 page

Just Jump: Dynamic Neighborhood Aggregation in Graph Neural Networks

We propose a dynamic neighborhood aggregation (DNA) procedure guided by (multi-head) attention for representation learning on graphs. In contrast to current graph neural networks which follow a simple neighborhood aggregation scheme, our DNA procedure allows for a selective and node-adaptive aggregation of neighboring embeddings of potentially differing locality. In order to avoid overfitting, we propose to control the channel-wise connections between input and output by making use of grouped linear projections. In a number of transductive node-classification experiments, we demonstrate the effectiveness of our approach

Simple Truncated SVD based Model for Node Classification on Heterophilic Graphs

Graph Neural Networks (GNNs) have shown excellent performance on graphs that exhibit strong homophily with respect to the node labels i.e. connected nodes have same labels. However, they perform poorly on heterophilic graphs. Recent approaches have typically modified aggregation schemes, designed adaptive graph filters, etc. to address this limitation. In spite of this, the performance on heterophilic graphs can still be poor. We propose a simple alternative method that exploits Truncated Singular Value Decomposition (TSVD) of topological structure and node features. Our approach achieves up to ~30% improvement in performance over state-of-the-art methods on heterophilic graphs. This work is an early investigation into methods that differ from aggregation based approaches. Our experimental results suggest that it might be important to explore other alternatives to aggregation methods for heterophilic setting.Comment: Accepted at Deep Learning on Graphs: Method and Applications (DLG-KDD 2021

Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver

Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A Lean Algebraic Multigrid (LAMG) solver of the linear system Ax=b is presented, where A is a graph Laplacian. LAMG's run time and storage are linear in the number of graph edges. LAMG consists of a setup phase, in which a sequence of increasingly-coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional applications of algebraic multigrid. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity definition, and an energy correction of the coarse-level systems. This results in fast convergence and substantial overhead and memory savings. A serial LAMG implementation scaled linearly for a diverse set of 1666 real-world graphs with up to six million edges. This multilevel methodology can be fully parallelized and extended to eigenvalue problems and other graph computations.Comment: 28 page

A-Lamp: Adaptive Layout-Aware Multi-Patch Deep Convolutional Neural Network for Photo Aesthetic Assessment

Deep convolutional neural networks (CNN) have recently been shown to generate promising results for aesthetics assessment. However, the performance of these deep CNN methods is often compromised by the constraint that the neural network only takes the fixed-size input. To accommodate this requirement, input images need to be transformed via cropping, warping, or padding, which often alter image composition, reduce image resolution, or cause image distortion. Thus the aesthetics of the original images is impaired because of potential loss of fine grained details and holistic image layout. However, such fine grained details and holistic image layout is critical for evaluating an image's aesthetics. In this paper, we present an Adaptive Layout-Aware Multi-Patch Convolutional Neural Network (A-Lamp CNN) architecture for photo aesthetic assessment. This novel scheme is able to accept arbitrary sized images, and learn from both fined grained details and holistic image layout simultaneously. To enable training on these hybrid inputs, we extend the method by developing a dedicated double-subnet neural network structure, i.e. a Multi-Patch subnet and a Layout-Aware subnet. We further construct an aggregation layer to effectively combine the hybrid features from these two subnets. Extensive experiments on the large-scale aesthetics assessment benchmark (AVA) demonstrate significant performance improvement over the state-of-the-art in photo aesthetic assessment

EAGr: Supporting Continuous Ego-centric Aggregate Queries over Large Dynamic Graphs

In this work, we present EAGr, a system for supporting large numbers of continuous neighborhood-based ("ego-centric") aggregate queries over large, highly dynamic, and rapidly evolving graphs. Examples of such queries include computation of personalized, tailored trends in social networks, anomaly/event detection in financial transaction networks, local search and alerts in spatio-temporal networks, to name a few. Key challenges in supporting such continuous queries include high update rates typically seen in these situations, large numbers of queries that need to be executed simultaneously, and stringent low latency requirements. We propose a flexible, general, and extensible in-memory framework for executing different types of ego-centric aggregate queries over large dynamic graphs with low latencies. Our framework is built around the notion of an aggregation overlay graph, a pre-compiled data structure that encodes the computations to be performed when an update/query is received. The overlay graph enables sharing of partial aggregates across multiple ego-centric queries (corresponding to the nodes in the graph), and also allows partial pre-computation of the aggregates to minimize the query latencies. We present several highly scalable techniques for constructing an overlay graph given an aggregation function, and also design incremental algorithms for handling structural changes to the underlying graph. We also present an optimal, polynomial-time algorithm for making the pre-computation decisions given an overlay graph, and evaluate an approach to incrementally adapt those decisions as the workload changes. Although our approach is naturally parallelizable, we focus on a single-machine deployment and show that our techniques can easily handle graphs of size up to 320 million nodes and edges, and achieve update/query throughputs of over 500K/s using a single, powerful machine.Comment: 18 pages, 1 table, 14 figure

Adaptable Precomputation for Random Walker Image Segmentation and Registration

The random walker (RW) algorithm is used for both image segmentation and registration, and possesses several useful properties that make it popular in medical imaging, such as being globally optimizable, allowing user interaction, and providing uncertainty information. The RW algorithm defines a weighted graph over an image and uses the graph's Laplacian matrix to regularize its solutions. This regularization reduces to solving a large system of equations, which may be excessively time consuming in some applications, such as when interacting with a human user. Techniques have been developed that precompute eigenvectors of a Laplacian offline, after image acquisition but before any analysis, in order speed up the RW algorithm online, when segmentation or registration is being performed. However, precomputation requires certain algorithm parameters be fixed offline, limiting their flexibility. In this paper, we develop techniques to update the precomputed data online when RW parameters are altered. Specifically, we dynamically determine the number of eigenvectors needed for a desired accuracy based on user input, and derive update equations for the eigenvectors when the edge weights or topology of the image graph are changed. We present results demonstrating that our techniques make RW with precomputation much more robust to offline settings while only sacrificing minimal accuracy.Comment: 9 pages, 8 figure

Learning to Identify High Betweenness Centrality Nodes from Scratch: A Novel Graph Neural Network Approach

Betweenness centrality (BC) is one of the most used centrality measures for network analysis, which seeks to describe the importance of nodes in a network in terms of the fraction of shortest paths that pass through them. It is key to many valuable applications, including community detection and network dismantling. Computing BC scores on large networks is computationally challenging due to high time complexity. Many approximation algorithms have been proposed to speed up the estimation of BC, which are mainly sampling-based. However, these methods are still prone to considerable execution time on large-scale networks, and their results are often exacerbated when small changes happen to the network structures. In this paper, we focus on identifying nodes with high BC in a graph, since many application scenarios are built upon retrieving nodes with top-k BC. Different from previous heuristic methods, we turn this task into a learning problem and design an encoder-decoder based framework to resolve the problem. More specifcally, the encoder leverages the network structure to encode each node into an embedding vector, which captures the important structural information of the node. The decoder transforms the embedding vector for each node into a scalar, which captures the relative rank of this node in terms of BC. We use the pairwise ranking loss to train the model to identify the orders of nodes regarding their BC. By training on small-scale networks, the learned model is capable of assigning relative BC scores to nodes for any unseen networks, and thus identifying the highly-ranked nodes. Comprehensive experiments on both synthetic and real-world networks demonstrate that, compared to representative baselines, our model drastically speeds up the prediction without noticeable sacrifce in accuracy, and outperforms the state-of-the-art by accuracy on several large real-world networks.Comment: 10 pages, 4 figures, 8 table

Graph Attribute Aggregation Network with Progressive Margin Folding

Graph convolutional neural networks (GCNNs) have been attracting increasing research attention due to its great potential in inference over graph structures. However, insufficient effort has been devoted to the aggregation methods between different convolution graph layers. In this paper, we introduce a graph attribute aggregation network (GAAN) architecture. Different from the conventional pooling operations, a graph-transformation-based aggregation strategy, progressive margin folding, PMF, is proposed for integrating graph features. By distinguishing internal and margin elements, we provide an approach for implementing the folding iteratively. And a mechanism is also devised for preserving the local structures during progressively folding. In addition, a hypergraph-based representation is introduced for transferring the aggregated information between different layers. Our experiments applied to the public molecule datasets demonstrate that the proposed GAAN outperforms the existing GCNN models with significant effectiveness

Adaptive Interaction Modeling via Graph Operations Search

Interaction modeling is important for video action analysis. Recently, several works design specific structures to model interactions in videos. However, their structures are manually designed and non-adaptive, which require structures design efforts and more importantly could not model interactions adaptively. In this paper, we automate the process of structures design to learn adaptive structures for interaction modeling. We propose to search the network structures with differentiable architecture search mechanism, which learns to construct adaptive structures for different videos to facilitate adaptive interaction modeling. To this end, we first design the search space with several basic graph operations that explicitly capture different relations in videos. We experimentally demonstrate that our architecture search framework learns to construct adaptive interaction modeling structures, which provides more understanding about the relations between the structures and some interaction characteristics, and also releases the requirement of structures design efforts. Additionally, we show that the designed basic graph operations in the search space are able to model different interactions in videos. The experiments on two interaction datasets show that our method achieves competitive performance with state-of-the-arts