The accurate diagnosis of Alzheimer’s disease (AD) and prognosis of mild cognitive impairment (MCI) conversion are crucial for early intervention. However, existing multimodal methods face several challenges, from the heterogeneity of input data, to underexplored modality interactions, missing data due to patient dropouts, and limited data caused by the time-consuming and costly data collection process. In this paper, we propose a novel Prompted Hypergraph Neural Network (PHGNN) framework that addresses these limitations by integrating hypergraph based learning with prompt learning. Hypergraphs capture higher-order relationships between different modalities, while our prompt learning approach for hypergraphs, adapted from NLP, enables efficient training with limited data. Our model is validated through extensive experiments on the ADNI dataset as well as cross-domain validations using the OASIS-3 and NACC datasets. The results demonstrate that PHGNN outperforms SOTA methods in both AD diagnosis and MCI conversion prediction, showing superior cross-domain generalization capabilities. At the same time, it uses only a fraction (6%) of the tunable parameters of traditional fine-tuning and maintains a low computational load compared to alternative tuning strategies.

In this paper, we present GGSD, a novel graph generative model based on 1) the spectral decomposition of the graph Laplacian matrix and 2) a diffusion process. Specifically, we propose to use a denoising model to sample eigenvectors and eigenvalues from which we can reconstruct the graph Laplacian and adjacency matrix. Using the Laplacian spectrum allows us to naturally capture the structural characteristics of the graph and work directly in the node space while avoiding the quadratic complexity bottleneck that limits the applicability of other diffusion-based methods. This, in turn, is accomplished by truncating the spectrum, which, as we show in our experiments, results in a faster yet accurate generative process, and by designing a novel transformer-based architecture linear in the number of nodes. Our permutation invariant model can also handle node features by concatenating them to the eigenvectors of each node. An extensive set of experiments on both synthetic and real-world graphs demonstrates the strengths of our model against state-of-the-art alternatives.

The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be represented as regular grids in the Euclidean space, extending the convolution operator to work on graphs proves more challenging, due to their irregular structure. In this article, we propose to use graph kernels, i.e., kernel functions that compute an inner product on graphs, to extend the standard convolution operator to the graph domain. This allows us to define an entirely structural model that does not require computing the embedding of the input graph. Our architecture allows to plug-in any type of graph kernels and has the added benefit of providing some interpretability in terms of the structural masks that are learned during the training process, similar to what happens for convolutional masks in traditional convolutional neural networks (CNNs). We perform an extensive ablation study to investigate the model hyperparameters' impact and show that our model achieves competitive performance on standard graph classification and regression datasets.

This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transitive aligned vertices between graphs and transforms arbitrary sized graphs into fixed-sized aligned vertex grid structures. In order to learn representative graph characteristics, a new quantum spatial graph convolution is proposed and employed to extract multi-scale vertex features, in terms of quantum information propagation between grid vertices of each graph. Since the quantum spatial convolution preserves the grid structures of the input vertices (i.e., the convolution layer does not alter the original spatial position of vertices), the proposed QSGCNN model allows to directly employ the traditional convolutional neural network architecture to further learn from the global graph topology, providing an end-to-end deep learning architecture that integrates the graph representation and learning in the quantum spatial graph convolution layer and the traditional convolutional layer for graph classifications. We indicate the effectiveness of the proposed QSGCNN model in relation to existing state-of-the-art methods. Experiments on benchmark graph classification datasets demonstrate the effectiveness of the proposed QSGCNN model.

This paper proposes a novel Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. The main idea is to define a new quantum-inspired spatial graph convolution associated with pre-transformed fixed-sized aligned grid structures of graphs, in terms of quantum information propagation between grid vertices of each graph. We show that the proposed QSGCNN model can significantly reduce either the information loss or the notorious tottering problem arising in existing spatially-based Graph Convolutional Network (GCN) models. Experiments on benchmark graph datasets demonstrate the effectiveness of the proposed QSGCNN model.

Abstract The Average Mixing Kernel Signature is a novel spectral signature for points on non-rigid three-dimensional shapes. It is based on a quantum exploration process of the shape surface, where the average transition probabilities between the points of the shape are summarised in the finite-time average mixing kernel. A band-filtered spectral analysis of this kernel then yields the AMKS. Crucially, we show that opting for a finite time-evolution allows the signature to account for a mixing of the Laplacian eigenspaces, similar to what is observed in the presence of noise, explaining the increased noise robustness of this signature when compared to alternative signatures. We perform an extensive experimental analysis of the AMKS under a wide range of problem scenarios, evaluating the performance of our descriptor under different sources of noise (vertex jitter and topological), shape representations (mesh and point clouds), as well as when only a partial view of the shape is available. Our experiments show that the AMKS consistently outperforms two of the most widely used spectral signatures, the Heat Kernel Signature and the Wave Kernel Signature, and suggest that the AMKS should be the signature of choice for various compute vision problems, including as input of deep convolutional architectures for shape analysis.

In this paper, we develop a novel backtrackless aligned-spatial graph convolutional network (BASGCN) model to learn effective features for graph classification. Our idea is to transform arbitrary-sized graphs into fixed-sized backtrackless aligned grid structures and define a new spatial graph convolution operation associated with the grid structures. We show that the proposed BASGCN model not only reduces the problems of information loss and imprecise information representation arising in existing spatially-based graph convolutional network (GCN) models, but also bridges the theoretical gap between traditional convolutional neural network (CNN) models and spatially-based GCN models. Furthermore, the proposed BASGCN model can both adaptively discriminate the importance between specified vertices during the convolution process and reduce the notorious tottering problem of existing spatially-based GCNs related to the Weisfeiler-Lehman algorithm, explaining the effectiveness of the proposed model. Experiments on standard graph datasets demonstrate the effectiveness of the proposed model.

We develop a novel method for measuring the similarity between complete weighted graphs, which are probed by means of the discrete-time quantum walks. Directly probing complete graphs using discrete-time quantum walks is intractable due to the cost of simulating the quantum walk. We overcome this problem by extracting a commute time minimum spanning tree from the complete weighted graph. The spanning tree is probed by a discrete-time quantum walk which is initialized using a weighted version of the Perron-Frobenius operator. This naturally encapsulates the edge weight information for the spanning tree extracted from the original graph. For each pair of complete weighted graphs to be compared, we simulate a discrete-time quantum walk on each of the corresponding commute time minimum spanning trees and, then, compute the associated density matrices for the quantum walks. The probability of the walk visiting each edge of the spanning tree is given by the diagonal elements of the density matrices. The similarity between each pair of graphs is then computed using either: 1) the inner product or 2) the negative exponential of the Jensen-Shannon divergence between the probability distributions. We show that in both cases the resulting similarity measure is positive definite and, therefore, corresponds to a kernel on the graphs. We perform a series of experiments on publicly available graph datasets from a variety of different domains, together with time-varying financial networks extracted from data for the New York Stock Exchange. Our experiments demonstrate the effectiveness of the proposed similarity measures.

In this paper, we develop a new deep hybrid graph kernel. This is based on the depth-based matching kernel [1] and the Weisfeiler-Lehman subtree kernel [2], by jointly computing a basic deep kernel that simultaneously captures the relationship between the combined kernels through deep learning networks. Specifically, for a set of graphs under investigations, we commence by computing two kernel matrices using each of the separate kernels. With the two kernel matrices to hand, for each graph we use the kernel value between the graph and each of the training graphs as the graph characterisation vector. This vector can be seen as a kernel-based similarity embedding vector of the graph [3]. We use the embedding vectors of all graphs to train a deep auto encoder network, that is optimized using Stochastic Gradient Descent together with the Deep Belief Network for pretraining. The deep representation computed through the deep learning network captures the main relationship between the depth-based matching kernel and the Weisfeiler-Lehman subtree kernel. The resulting deep hybrid graph kernel is computed by summing the original kernels together with the dot product kernel between their deep representations. We show that the deep hybrid graph kernel not only captures the joint information between the associated depth-based matching and Weisfeiler-Lehman subtree kernels, but also reflects the information content over all graphs under investigations. Experimental evaluations demonstrate the effectiveness of the proposed kernel.

In this paper, we develop a new transitive aligned Weisfeiler-Lehman subtree kernel. This kernel not only overcomes the shortcoming of ignoring correspondence information between isomorphic substructures that arises in existing R-convolution kernels, but also guarantees the transitivity between the correspondence information that is not available for existing matching kernels. Our kernel outperforms state-of-the-art graph kernels in terms of classification accuracy on standard graph datasets.

In this paper, we propose a novel entropic signature for graphs, where we probe the graphs by means of continuous-time quantum walks. More precisely, we characterise the structure of a graph through its average mixing matrix. The average mixing matrix is a doubly-stochastic matrix that encapsulates the time-averaged behaviour of a continuous-time quantum walk on the graph, i.e., the ij-th element of the average mixing matrix represents the time-averaged transition probability of a continuous-time quantum walk from the vertex vito the vertex vj. With this matrix to hand, we can associate a probability distribution with each vertex of the graph. We define a novel entropic signature by concatenating the average Shannon entropy of these probability distributions with their Jensen-Shannon divergence. We show that this new entropic measure can encaspulate the rich structural information of the graphs, thus allowing to discriminate between different structures. We explore the proposed entropic measure on several graph datasets abstracted from bioinformatics databases and we compare it with alternative entropic signatures in the literature. The experimental results demonstrate the effectiveness and efficiency of our method.

In this paper, we develop a new entropic matching kernel for weighted graphs by aligning depth-based representations. We demonstrate that this kernel can be seen as an \textbfaligned subtree kernel that incorporates explicit subtree correspondences, and thus addresses the drawback of neglecting the relative locations between substructures that arises in the R-convolution kernels. Experiments on standard datasets demonstrate that our kernel can easily outperform state-of-the-art graph kernels in terms of classification accuracy.

People manage a spectrum of identities in cyber domains. Profiling individuals and assigning them to distinct groups or classes have potential applications in targeted services, online fraud detection, extensive social sorting, and cyber-security. This paper presents the Uncertainty of Identity Toolset, a framework for the identification and profiling of users from their social media accounts and e-mail addresses. More specifically, in this paper we discuss the design and implementation of two tools of the framework. The Twitter Geographic Profiler tool builds a map of the ethno-cultural communities of a person's friends on Twitter social media service. The E-mail Address Profiler tool identifies the probable identities of individuals from their e-mail addresses and maps their geographical distribution across the UK. To this end, this paper presents a framework for profiling the digital traces of individuals.