67 research outputs found
Fast depth-based subgraph kernels for unattributed graphs
In this paper, we investigate two fast subgraph kernels based on a depth-based representation of graph-structure. Both methods gauge depth information through a family of K-layer expansion subgraphs rooted at a vertex [1]. The first method commences by computing a centroid-based complexity trace for each graph, using a depth-based representation rooted at the centroid vertex that has minimum shortest path length variance to the remaining vertices [2]. This subgraph kernel is computed by measuring the Jensen-Shannon divergence between centroid-based complexity entropy traces. The second method, on the other hand, computes a depth-based representation around each vertex in turn. The corresponding subgraph kernel is computed using isomorphisms tests to compare the depth-based representation rooted at each vertex in turn. For graphs with n vertices, the time complexities for the two new kernels are O(n 2) and O(n 3), in contrast to O(n 6) for the classic Gärtner graph kernel [3]. Key to achieving this efficiency is that we compute the required Shannon entropy of the random walk for our kernels with O(n 2) operations. This computational strategy enables our subgraph kernels to easily scale up to graphs of reasonably large sizes and thus overcome the size limits arising in state-of-the-art graph kernels. Experiments on standard bioinformatics and computer vision graph datasets demonstrate the effectiveness and efficiency of our new subgraph kernels
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
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
HAQJSK: Hierarchical-Aligned Quantum Jensen-Shannon Kernels for Graph Classification
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 can incorporate hierarchical aligned structure information
between graphs and transform graphs of random sizes into fixed-sized aligned
graph structures, i.e., the Hierarchical Transitive Aligned Adjacency Matrix of
vertices and the Hierarchical Transitive Aligned Density Matrix of the
Continuous-Time Quantum Walk (CTQW). For a pair of graphs to hand, the
resulting HAQJSK kernels are defined by measuring the Quantum Jensen-Shannon
Divergence (QJSD) between their transitive aligned graph structures. We show
that the proposed HAQJSK kernels not only reflect richer intrinsic global graph
characteristics in terms of the CTQW, but also address the drawback of
neglecting structural correspondence information arising in most existing
R-convolution kernels. Furthermore, unlike the previous Quantum Jensen-Shannon
Kernels associated with the QJSD and the CTQW, the proposed HAQJSK kernels can
simultaneously guarantee the properties of permutation invariant and positive
definiteness, explaining the theoretical advantages of the HAQJSK kernels.
Experiments indicate the effectiveness of the proposed kernels
Labeled Subgraph Entropy Kernel
In recent years, kernel methods are widespread in tasks of similarity
measuring. Specifically, graph kernels are widely used in fields of
bioinformatics, chemistry and financial data analysis. However, existing
methods, especially entropy based graph kernels are subject to large
computational complexity and the negligence of node-level information. In this
paper, we propose a novel labeled subgraph entropy graph kernel, which performs
well in structural similarity assessment. We design a dynamic programming
subgraph enumeration algorithm, which effectively reduces the time complexity.
Specially, we propose labeled subgraph, which enriches substructure topology
with semantic information. Analogizing the cluster expansion process of gas
cluster in statistical mechanics, we re-derive the partition function and
calculate the global graph entropy to characterize the network. In order to
test our method, we apply several real-world datasets and assess the effects in
different tasks. To capture more experiment details, we quantitatively and
qualitatively analyze the contribution of different topology structures.
Experimental results successfully demonstrate the effectiveness of our method
which outperforms several state-of-the-art methods.Comment: 9 pages,5 figure
An aligned subtree kernel for weighted graphs
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 aligned 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
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