Related papers: Attributed-graphs kernel implementation using loca…

The majority of popular graph kernels is based on the concept of Haussler's $\mathcal{R}$-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering…

Graph convolutional network (GCN) is now an effective tool to deal with non-Euclidean data, such as social networks in social behavior analysis, molecular structure analysis in the field of chemistry, and skeleton-based action recognition.…

Autonomous individuals establish a structural complex system through pairwise connections and interactions. Notably, the evolution reflects the dynamic nature of each complex system since it recodes a series of temporal changes from the…

Fidelity-based quantum kernels provide a direct interface between quantum feature maps and classical kernel methods, but they can exhibit exponential concentration: with increasing system size or circuit expressivity, the Gram matrix…

In this work, we propose a family of novel quantum kernels, namely the Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), for un-attributed graphs. Different from most existing classical graph kernels, the proposed HAQJSK kernels…

This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…

Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…

Decoded Quantum Interferometry (DQI) promises superpolynomial speedups for structured optimization; however, its practical realization is often hindered by significant sensitivity to hardware noise and spectral dispersion. To bridge this…

Digital-analog quantum computing (DAQC) combines digital gates with analog operations, offering an alternative paradigm for universal quantum computation. This approach leverages the higher fidelities of analog operations and the…

We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid…

The Atomic Cluster Expansion provides local, complete basis functions that enable efficient parametrization of many-atom interactions. We extend the Atomic Cluster Expansion to incorporate graph basis functions. This naturally leads to…

Graphs are complex objects that do not lend themselves easily to typical learning tasks. Recently, a range of approaches based on graph kernels or graph neural networks have been developed for graph classification and for representation…

Quantum error mitigation (QEM) provides a practical route for estimating reliable observables on noisy intermediate-scale quantum (NISQ) devices. Traditional QEM strategies, including zero-noise extrapolation (ZNE) and Clifford data…

Feature learning on point clouds has shown great promise, with the introduction of effective and generalizable deep learning frameworks such as pointnet++. Thus far, however, point features have been abstracted in an independent and…

Over the most recent years, quantized graph neural network (QGNN) attracts lots of research and industry attention due to its high robustness and low computation and memory overhead. Unfortunately, the performance gains of QGNN have never…

Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a…

Spectral graph theory is a branch of mathematics that studies the relationships between the eigenvectors and eigenvalues of Laplacian and adjacency matrices and their associated graphs. The Variational Quantum Eigensolver (VQE) algorithm…

Acquiring labels are often costly, whereas unlabeled data are usually easy to obtain in modern machine learning applications. Semi-supervised learning provides a principled machine learning framework to address such situations, and has been…