255 research outputs found
QESK: Quantum-based Entropic Subtree Kernels for Graph Classification
In this paper, we propose a novel graph kernel, namely the Quantum-based
Entropic Subtree Kernel (QESK), for Graph Classification. To this end, we
commence by computing the Average Mixing Matrix (AMM) of the Continuous-time
Quantum Walk (CTQW) evolved on each graph structure. Moreover, we show how this
AMM matrix can be employed to compute a series of entropic subtree
representations associated with the classical Weisfeiler-Lehman (WL) algorithm.
For a pair of graphs, the QESK kernel is defined by computing the
exponentiation of the negative Euclidean distance between their entropic
subtree representations, theoretically resulting in a positive definite graph
kernel. We show that the proposed QESK kernel not only encapsulates complicated
intrinsic quantum-based structural characteristics of graph structures through
the CTQW, but also theoretically addresses the shortcoming of ignoring the
effects of unshared substructures arising in state-of-the-art R-convolution
graph kernels. Moreover, unlike the classical R-convolution kernels, the
proposed QESK can discriminate the distinctions of isomorphic subtrees in terms
of the global graph structures, theoretically explaining the effectiveness.
Experiments indicate that the proposed QESK kernel can significantly outperform
state-of-the-art graph kernels and graph deep learning methods for graph
classification problems
A Hierarchical Transitive-Aligned Graph Kernel for Un-attributed Graphs
In this paper, we develop a new graph kernel, namely the Hierarchical
Transitive-Aligned kernel, by transitively aligning the vertices between graphs
through a family of hierarchical prototype graphs. Comparing to most existing
state-of-the-art graph kernels, the proposed kernel has three theoretical
advantages. First, it incorporates the locational correspondence information
between graphs into the kernel computation, and thus overcomes the shortcoming
of ignoring structural correspondences arising in most R-convolution kernels.
Second, it guarantees the transitivity between the correspondence information
that is not available for most existing matching kernels. Third, it
incorporates the information of all graphs under comparisons into the kernel
computation process, and thus encapsulates richer characteristics. By
transductively training the C-SVM classifier, experimental evaluations
demonstrate the effectiveness of the new transitive-aligned kernel. The
proposed kernel can outperform state-of-the-art graph kernels on standard
graph-based datasets in terms of the classification accuracy
A transitive aligned Weisfeiler-Lehman subtree 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
A novel entropy-based graph signature from the average mixing matrix
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 vi to 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
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