563 research outputs found
A Survey on Graph Kernels
Graph kernels have become an established and widely-used technique for
solving classification tasks on graphs. This survey gives a comprehensive
overview of techniques for kernel-based graph classification developed in the
past 15 years. We describe and categorize graph kernels based on properties
inherent to their design, such as the nature of their extracted graph features,
their method of computation and their applicability to problems in practice. In
an extensive experimental evaluation, we study the classification accuracy of a
large suite of graph kernels on established benchmarks as well as new datasets.
We compare the performance of popular kernels with several baseline methods and
study the effect of applying a Gaussian RBF kernel to the metric induced by a
graph kernel. In doing so, we find that simple baselines become competitive
after this transformation on some datasets. Moreover, we study the extent to
which existing graph kernels agree in their predictions (and prediction errors)
and obtain a data-driven categorization of kernels as result. Finally, based on
our experimental results, we derive a practitioner's guide to kernel-based
graph classification
Curvature Filtrations for Graph Generative Model Evaluation
Graph generative model evaluation necessitates understanding differences
between graphs on the distributional level. This entails being able to harness
salient attributes of graphs in an efficient manner. Curvature constitutes one
such property of graphs, and has recently started to prove useful in
characterising graphs. Its expressive properties, stability, and practical
utility in model evaluation remain largely unexplored, however. We combine
graph curvature descriptors with emerging methods from topological data
analysis to obtain robust, expressive descriptors for evaluating graph
generative models
Wide Graph Neural Networks: Aggregation Provably Leads to Exponentially Trainability Loss
Graph convolutional networks (GCNs) and their variants have achieved great
success in dealing with graph-structured data. However, it is well known that
deep GCNs will suffer from over-smoothing problem, where node representations
tend to be indistinguishable as we stack up more layers. Although extensive
research has confirmed this prevailing understanding, few theoretical analyses
have been conducted to study the expressivity and trainability of deep GCNs. In
this work, we demonstrate these characterizations by studying the Gaussian
Process Kernel (GPK) and Graph Neural Tangent Kernel (GNTK) of an
infinitely-wide GCN, corresponding to the analysis on expressivity and
trainability, respectively. We first prove the expressivity of infinitely-wide
GCNs decaying at an exponential rate by applying the mean-field theory on GPK.
Besides, we formulate the asymptotic behaviors of GNTK in the large depth,
which enables us to reveal the dropping trainability of wide and deep GCNs at
an exponential rate. Additionally, we extend our theoretical framework to
analyze residual connection-resemble techniques. We found that these techniques
can mildly mitigate exponential decay, but they failed to overcome it
fundamentally. Finally, all theoretical results in this work are corroborated
experimentally on a variety of graph-structured datasets.Comment: 23 pages, 4 figure
Measuring the expressivity of graph kernels through the rademacher complexity
Graph kernels are widely adopted in real-world applications that involve learning on graph data. Different graph kernels have been proposed in literature, but no theoretical comparison among them is present. In this paper we provide a formal definition for the expressiveness of a graph kernel by means of the Rademacher Complexity, and analyze the differences among some state-of-the-art graph kernels. Results on real world datasets confirm some known properties of graph kernels, showing that the Rademacher Complexity is indeed a suitable measure for this analysis
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
- …