353 research outputs found
Shift Aggregate Extract Networks
We introduce an architecture based on deep hierarchical decompositions to
learn effective representations of large graphs. Our framework extends classic
R-decompositions used in kernel methods, enabling nested "part-of-part"
relations. Unlike recursive neural networks, which unroll a template on input
graphs directly, we unroll a neural network template over the decomposition
hierarchy, allowing us to deal with the high degree variability that typically
characterize social network graphs. Deep hierarchical decompositions are also
amenable to domain compression, a technique that reduces both space and time
complexity by exploiting symmetries. We show empirically that our approach is
competitive with current state-of-the-art graph classification methods,
particularly when dealing with social network datasets
Information overload in structured data
Information overload refers to the difficulty of making decisions caused by too much information. In this dissertation, we address information overload problem in two separate structured domains, namely, graphs and text.
Graph kernels have been proposed as an efficient and theoretically sound approach to compute graph similarity. They decompose graphs into certain sub-structures, such as subtrees, or subgraphs. However, existing graph kernels suffer from a few drawbacks. First, the dimension of the feature space associated with the kernel often grows exponentially as the complexity of sub-structures increase. One immediate consequence of this behavior is that small, non-informative, sub-structures occur more frequently and cause information overload. Second, as the number of features increase, we encounter sparsity: only a few informative sub-structures will co-occur in multiple graphs. In the first part of this dissertation, we propose to tackle the above problems by exploiting the dependency relationship among sub-structures. First, we propose a novel framework that learns the latent representations of sub-structures by leveraging recent advancements in deep learning. Second, we propose a general smoothing framework that takes structural similarity into account, inspired by state-of-the-art smoothing techniques used in natural language processing. Both the proposed frameworks are applicable to popular graph kernel families, and achieve significant performance improvements over state-of-the-art graph kernels.
In the second part of this dissertation, we tackle information overload in text. We first focus on a popular social news aggregation website, Reddit, and design a submodular recommender system that tailors a personalized frontpage for individual users. Second, we propose a novel submodular framework to summarize videos, where both transcript and comments are available. Third, we demonstrate how to apply filtering techniques to select a small subset of informative features from virtual machine logs in order to predict resource usage
Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes
Despite the recent successes of vanilla Graph Neural Networks (GNNs) on many
tasks, their foundation on pairwise interaction networks inherently limits
their capacity to discern latent higher-order interactions in complex systems.
To bridge this capability gap, we propose a novel approach exploiting the rich
mathematical theory of simplicial complexes (SCs) - a robust tool for modeling
higher-order interactions. Current SC-based GNNs are burdened by high
complexity and rigidity, and quantifying higher-order interaction strengths
remains challenging. Innovatively, we present a higher-order Flower-Petals (FP)
model, incorporating FP Laplacians into SCs. Further, we introduce a
Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians,
capable of discerning intrinsic features across varying topological scales. By
employing learnable graph filters, a parameter group within each FP Laplacian
domain, we can identify diverse patterns where the filters' weights serve as a
quantifiable measure of higher-order interaction strengths. The theoretical
underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated.
Additionally, our empirical investigations reveal that the proposed model
accomplishes state-of-the-art (SOTA) performance on a range of graph tasks and
provides a scalable and flexible solution to explore higher-order interactions
in graphs
- …