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Edwin Hancock

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17 papers

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IJCAI Conference 2025 Conference Paper

AKBR: Learning Adaptive Kernel-based Representations for Graph Classification

Lu Bai
Feifei Qian
Lixin Cui
Ming Li
Hangyuan Du
Yue Wang
Edwin Hancock

In this paper, we propose a new model to learn Adaptive Kernel-based Representations (AKBR) for graph classification. Unlike state-of-the-art R-convolution graph kernels that are defined by merely counting any pair of isomorphic substructures between graphs and cannot provide an end-to-end learning mechanism for the classifier, the proposed AKBR approach aims to define an end-to-end representation learning model to construct an adaptive kernel matrix for graphs. To this end, we commence by leveraging a novel feature-channel attention mechanism to capture the interdependencies between different substructure invariants of original graphs. The proposed AKBR model can thus effectively identify the structural importance of different substructures, and compute the R-convolution kernel between pairwise graphs associated with the more significant substructures specified by their structural attentions. Furthermore, the proposed AKBR model employs all sample graphs as the prototype graphs, naturally providing an end-to-end learning architecture between the kernel computation as well as the classifier. Experimental results show that the proposed AKBR model outperforms existing state-of-the-art graph kernels and deep learning methods on standard graph benchmarks.

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IJCAI Conference 2025 Conference Paper

An End-to-End Simple Clustering Hierarchical Pooling Operation for Graph Learning Based on Top-K Node Selection

Zhehan Zhao
Lu Bai
Ming Li
Lixin Cui
Hangyuan Du
Yue Wang
Edwin Hancock

Graph Neural Networks (GNNs) are powerful tools for graph learning, but one of the important challenges is how to effectively extract representations for graph-level tasks. In this paper, we propose an end-to-end Simple Clustering Hierarchical Pooling (SCHPool) operation, which is based on Top-K node selection for learning expressive graph representations. Specifically, SCHPool considers each node and its local neighborhood as a cluster, and introduces a novel multi-view scoring function to evaluate node importance. Based on these scores, clusters centered around the Top-K nodes are retained. This design eliminates the need for complex clustering operations, significantly reducing computational overhead. Furthermore, during the coarsening process, SCHPool employs a lightweight yet comprehensive attention mechanism to adaptively aggregate both the node features within clusters and the edge connectivity strengths between clusters. This facilitates the construction of more informative coarsened graphs, enhancing model performance. Experimental results demonstrate the effectiveness of the proposed model.

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AAAI Conference 2025 Conference Paper

DHAKR: Learning Deep Hierarchical Attention-Based Kernelized Representations for Graph Classification

Feifei Qian
Lu Bai
Lixin Cui
Ming Li
Ziyu Lyu
Hangyuan Du
Edwin Hancock

Graph-based representations are powerful tools for analyzing structured data. In this paper, we propose a novel model to learn Deep Hierarchical Attention-based Kernelized Representations (DHAKR) for graph classification. To this end, we commence by learning an assignment matrix to hierarchically map the substructure invariants into a set of composite invariants, resulting in hierarchical kernelized representations for graphs. Moreover, we introduce the feature-channel attention mechanism to capture the interdependencies between different substructure invariants that will be converged into the composite invariants, addressing the shortcoming of discarding the importance of different substructures arising in most existing R-convolution graph kernels. We show that the proposed DHAKR model can adaptively compute the kernel-based similarity between graphs, identifying the common structural patterns over all graphs. Experiments demonstrate the effectiveness of the proposed DHAKR model.

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IJCAI Conference 2025 Conference Paper

DHTAGK: Deep Hierarchical Transitive-Aligned Graph Kernels for Graph Classification

Xinya Qin
Lu Bai
Lixin Cui
Ming Li
Ziyu Lyu
Hangyuan Du
Edwin Hancock

In this paper, we propose a family of novel Deep Hierarchical Transitive-Aligned Graph Kernels (DHTAGK) for graph classification. To this end, we commence by developing a new Hierarchical Aligned Graph Auto-Encoder (HA-GAE) to construct transitive-aligned embedding graphs that encapsulate the structural correspondence information between graphs. The DHTAGK kernels then measure either the Jensen-Shannon Divergence between the adjacency matrices or the Gaussian kernel between the node feature matrices of the embedding graphs. Unlike the classical R-convolution kernels and node-based alignment kernels, the DHTAGK kernels can capture the transitive structural correspondence information and thus ensure the positive definiteness. Furthermore, the HA-GAE enables the DHTAGK kernels to simultaneously reflect both local and global graph structures and identify common structural patterns. Experimental results show that the DHTAGK kernels outperform state-of-the-art graph kernels and deep learning methods on benchmark datasets.

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IJCAI Conference 2025 Conference Paper

Exploring the Over-smoothing Problem of Graph Neural Networks for Graph Classification: An Entropy-based Viewpoint

Feifei Qian
Lu Bai
Lixin Cui
Ming Li
Hangyuan Du
Yue Wang
Edwin Hancock

The over-smoothing has emerged as a major challenge in the development of Graph Neural Networks (GNNs). While existing state-of-the-art methods effectively mitigate the diminishing distance between nodes and improve the performance of node classification, they tend to be elusive for graph-level tasks. This paper introduces a novel entropy-based perspective to explore the over-smoothing problem, simultaneously enhancing the distinguishability of non-isomorphic graphs. We provide a theoretical analysis of the relationship between the smoothness and the entropy for graphs, highlighting how the over-smoothing in high-entropic regions negatively impact the graph classification performance. To tackle this issue, we propose a simple yet effective method to Sample and Discretize node features in high-Entropic regions (SDE), aiming to preserve the critical and complicated structural information. Moreover, we introduce a new evaluation metric to assess the over-smoothing for graph-level tasks, focusing on node distributions. Experimental results demonstrate that the proposed SDE method significantly outperforms existing state-of-the-art methods, establishing a new benchmark in the field of GNNs.

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IJCAI Conference 2025 Conference Paper

HA-SCN: Learning Hierarchical Aligned Subtree Convolutional Networks for Graph Classification

Xinya Qin
Lu Bai
Lixin Cui
Ming Li
Hangyuan Du
Yue Wang
Edwin Hancock

In this paper, we propose a Hierarchical Aligned Subtree Convolutional Network (HA-SCN) for graph classification. Our idea is to transform graphs of arbitrary sizes into fixed-sized aligned graphs and construct a normalized K-layer m-ary subtree for each node in the aligned graphs. By sliding convolutional filters over the entire subtree at each node, we define a novel subtree convolution and pooling operation that hierarchically abstracts node-level information. We demonstrate that the proposed HA-SCN model not only realizes the convolution mechanism similar to the Convolutional Neural Networks (CNNs), which have the characteristics of weight sharing and fixed-sized receptive fields, but also effectively mitigates the over-squashing problem. Meanwhile, it establishes the correspondence information between nodes, alleviating the information loss issue. Experimental results on various benchmark graph datasets show that our approach achieves state-of-the-art performance in graph classification tasks.

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NeurIPS Conference 2025 Conference Paper

MultiNet: Adaptive Multi-Viewed Subgraph Convolutional Networks for Graph Classification

Xinya Qin
Lu Bai
Lixin Cui
Ming Li
Hangyuan Du
Edwin Hancock

The problem of over-smoothing has emerged as a fundamental issue for Graph Convolutional Networks (GCNs). While existing efforts primarily focus on enhancing the discriminability of node representations for node classification, they tend to overlook the over-smoothing at the graph level, significantly influencing the performance of graph classification. In this paper, we provide an explanation of the graph-level over-smoothing phenomenon and propose a novel Adaptive Multi-Viewed Subgraph Convolutional Network (MultiNet) to address this challenge. Specifically, the MultiNet introduces a local subgraph convolution module that adaptively divides each input graph into multiple subgraph views. Then a number of subgraph-based view-specific convolution operations are applied to constrain the extent of node information propagation over the original global graph structure, not only mitigating the over-smoothing issue but also generating more discriminative local node representations. Moreover, we develop an alignment-based readout that establishes correspondences between nodes over different graphs, thereby effectively preserving the local node-level structure information and improving the discriminative ability of the resulting graph-level representations. Theoretical analysis and empirical studies show that the MultiNet mitigates the graph-level over-smoothing and achieves excellent performance for graph classification.

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NeurIPS Conference 2024 Conference Paper

HC-GAE: The Hierarchical Cluster-based Graph Auto-Encoder for Graph Representation Learning

Lu Bai
Zhuo Xu
Lixin Cui
Ming Li
Yue Wang
Edwin Hancock

Graph Auto-Encoders (GAEs) are powerful tools for graph representation learning. In this paper, we develop a novel Hierarchical Cluster-based GAE (HC-GAE), that can learn effective structural characteristics for graph data analysis. To this end, during the encoding process, we commence by utilizing the hard node assignment to decompose a sample graph into a family of separated subgraphs. We compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. On the other hand, during the decoding process, we adopt the soft node assignment to reconstruct the original graph structure by expanding the coarsened nodes. By hierarchically performing the above compressing procedure during the decoding process as well as the expanding procedure during the decoding process, the proposed HC-GAE can effectively extract bidirectionally hierarchical structural features of the original sample graph. Furthermore, we re-design the loss function that can integrate the information from either the encoder or the decoder. Since the associated graph convolution operation of the proposed HC-GAE is restricted in each individual separated subgraph and cannot propagate the node information between different subgraphs, the proposed HC-GAE can significantly reduce the over-smoothing problem arising in the classical convolution-based GAEs. The proposed HC-GAE can generate effective representations for either node classification or graph classification, and the experiments demonstrate the effectiveness on real-world datasets.

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NeurIPS Conference 2023 Conference Paper

ESSEN: Improving Evolution State Estimation for Temporal Networks using Von Neumann Entropy

Qiyao Huang
Yingyue Zhang
Zhihong Zhang
Edwin Hancock

Temporal networks are widely used as abstract graph representations for real-world dynamic systems. Indeed, recognizing the network evolution states is crucial in understanding and analyzing temporal networks. For instance, social networks will generate the clustering and formation of tightly-knit groups or communities over time, relying on the triadic closure theory. However, the existing methods often struggle to account for the time-varying nature of these network structures, hindering their performance when applied to networks with complex evolution states. To mitigate this problem, we propose a novel framework called ESSEN, an Evolution StateS awarE Network, to measure temporal network evolution using von Neumann entropy and thermodynamic temperature. The developed framework utilizes a von Neumann entropy aware attention mechanism and network evolution state contrastive learning in the graph encoding. In addition, it employs a unique decoder the so-called Mixture of Thermodynamic Experts (MoTE) for decoding. ESSEN extracts local and global network evolution information using thermodynamic features and adaptively recognizes the network evolution states. Moreover, the proposed method is evaluated on link prediction tasks under both transductive and inductive settings, with the corresponding results demonstrating its effectiveness compared to various state-of-the-art baselines.

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IJCAI Conference 2020 Conference Paper

Learning for Graph Matching and Related Combinatorial Optimization Problems

Junchi Yan
Shuang Yang
Edwin Hancock

This survey gives a selective review of recent development of machine learning (ML) for combinatorial optimization (CO), especially for graph matching. The synergy of these two well-developed areas (ML and CO) can potentially give transformative change to artificial intelligence, whose foundation relates to these two building blocks. For its representativeness and wide-applicability, this paper is more focused on the problem of weighted graph matching, especially from the learning perspective. For graph matching, we show that many learning techniques e. g. convolutional neural networks, graph neural networks, reinforcement learning can be effectively incorporated in the paradigm for extracting the node features, graph structure features, and even the matching engine. We further present outlook for the new settings for learning graph matching, and direction towards more integrated combinatorial optimization solvers with prediction models, and also the mutual embrace of traditional solver and machine learning components.

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IJCAI Conference 2019 Conference Paper

Latent Distribution Preserving Deep Subspace Clustering

Lei Zhou
Xiao Bai
Dong Wang
Xianglong Liu
Jun Zhou
Edwin Hancock

Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is smaller than the ambient dimension. Traditional subspace clustering methods often rely on the self-expressiveness property, which has proven effective for linear subspace clustering. However, they perform unsatisfactorily on real data with complex nonlinear subspaces. More recently, deep autoencoder based subspace clustering methods have achieved success owning to the more powerful representation extracted by the autoencoder network. Unfortunately, these methods only considering the reconstruction of original input data can hardly guarantee the latent representation for the data distributed in subspaces, which inevitably limits the performance in practice. In this paper, we propose a novel deep subspace clustering method based on a latent distribution-preserving autoencoder, which introduces a distribution consistency loss to guide the learning of distribution-preserving latent representation, and consequently enables strong capacity of characterizing the real-world data for subspace clustering. Experimental results on several public databases show that our method achieves significant improvement compared with the state-of-the-art subspace clustering methods.

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IJCAI Conference 2015 Conference Paper

A Graph Kernel Based on the Jensen-Shannon Representation Alignment

Lu Bai
Zhihong Zhang
Chaoyan Wang
Xiao Bai
Edwin Hancock

In this paper, we develop a novel graph kernel by aligning the Jensen-Shannon (JS) representations of vertices. We commence by describing how to compute the JS representation of a vertex by measuring the JS divergence (JSD) between the corresponding h-layer depth-based (DB) representations developed in [Bai et al. , 2014a]). By aligning JS representations of vertices, we identify the correspondence between the vertices of two graphs and this allows us to construct a matching-based graph kernel. Unlike existing R-convolution kernels [Haussler, 1999] that roughly record the isomorphism information between any pair of substructures under a type of graph decomposition, the new kernel can be seen as an aligned subgraph kernel that incorporates explicit local correspondences of substructures (i. e. , the local information graphs [Dehmer and Mowshowitz, 2011]) into the process of kernelization through the JS representation alignment. The new kernel thus addresses the drawback of neglecting the relative locations between substructures that arises in the R-convolution kernels. Experiments demonstrate that our kernel can easily outperform state-of-the-art graph kernels in terms of the classification accuracies.

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NeurIPS Conference 1998 Conference Paper

Graph Matching for Shape Retrieval

Benoit Huet
Andrew Cross
Edwin Hancock

We propose a new in-sample cross validation based method (randomized GACV) for choosing smoothing or bandwidth parameters that govern the bias-variance or fit-complexity tradeoff in 'soft' classification. Soft clas(cid: 173) sification refers to a learning procedure which estimates the probability that an example with a given attribute vector is in class 1 vs class O. The target for optimizing the the tradeoff is the Kullback-Liebler distance between the estimated probability distribution and the 'true' probabil(cid: 173) ity distribution, representing knowledge of an infinite population. The method uses a randomized estimate of the trace of a Hessian and mimics cross validation at the cost of a single relearning with perturbed outcome data.

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NeurIPS Conference 1997 Conference Paper

Graph Matching with Hierarchical Discrete Relaxation

Richard Wilson
Edwin Hancock

Our aim in this paper is to develop a Bayesian framework for match(cid: 173) ing hierarchical relational models. The goal is to make discrete la(cid: 173) bel assignments so as to optimise a global cost function that draws information concerning the consistency of match from different lev(cid: 173) els of the hierarchy. Our Bayesian development naturally distin(cid: 173) guishes between intra-level and inter-level constraints. This allows the impact of reassigning a match to be assessed not only at its own (or peer) level ofrepresentation, but also upon its parents and children in the hierarchy.

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NeurIPS Conference 1997 Conference Paper

Recovering Perspective Pose with a Dual Step EM Algorithm

Andrew Cross
Edwin Hancock

This paper describes a new approach to extracting 3D perspective structure from 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point(cid: 173) correspondence matches. Unification is realised by constructing a mixture model over the bi-partite graph representing the correspon(cid: 173) dence match and by effecting optimisation using the EM algorithm. According to our EM framework the probabilities of structural cor(cid: 173) respondence gate contributions to the expected likelihood function used to estimate maximum likelihood perspective pose parameters. This provides a means of rejecting structural outliers.

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NeurIPS Conference 1996 Conference Paper

Contour Organisation with the EM Algorithm

José Leite
Edwin Hancock

This paper describes how the early visual process of contour organ(cid: 173) isation can be realised using the EM algorithm. The underlying computational representation is based on fine spline coverings. Ac(cid: 173) cording to our EM approach the adjustment of spline parameters draws on an iterative weighted least-squares fitting process. The expectation step of our EM procedure computes the likelihood of the data using a mixture model defined over the set of spline cover(cid: 173) ings. These splines are limited in their spatial extent using Gaus(cid: 173) sian windowing functions. The maximisation of the likelihood leads to a set of linear equations in the spline parameters which solve the weighted least squares problem. We evaluate the technique on the localisation of road structures in aerial infra-red images.

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NeurIPS Conference 1996 Conference Paper

Softening Discrete Relaxation

Andrew Finch
Richard Wilson
Edwin Hancock

This paper describes a new framework for relational graph match(cid: 173) ing. The starting point is a recently reported Bayesian consistency measure which gauges structural differences using Hamming dis(cid: 173) tance. The main contributions of the work are threefold. Firstly, we demonstrate how the discrete components of the cost func(cid: 173) tion can be softened. The second contribution is to show how the softened cost function can be used to locate matches using continuous non-linear optimisation. Finally, we show how the res(cid: 173) ulting graph matching algorithm relates to the standard quadratic assignment problem.

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