Graphs provide a powerful means for representing complex interactions between entities. Recently, deep learning approaches are emerging for representing and modeling graph-structured data, although the conventional deep learning methods (such as convolutional neural networks and recurrent neural networks) have mainly focused on grid-structured inputs (image and audio). Leveraged by the capability of representation learning, deep learning based techniques are reporting promising results for graph applications by detecting structural characteristics of graphs in an automated fashion. In this paper, we attempt to advance deep learning for graph-structured data by incorporating another component, transfer learning. By transferring the intrinsic geometric information learned in the source domain, our approach can help us to construct a model for a new but related task in the target domain without collecting new data and without training a new model from scratch. We thoroughly test our approach with large-scale real corpora and confirm the effectiveness of the proposed transfer learning framework for deep learning on graphs. According to our experiments, transfer learning is most effective when the source and target domains bear a high level of structural similarity in their graph representations.
@cite_10: Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows expressing long range interactions in terms of shorter, localized interactions. However, there exist other important examples, such as text documents or bioinformatic data, that may lack some or all of these strong statistical regularities. In this paper we consider the general question of how to construct deep architectures with small learning complexity on general non-Euclidean domains, which are typically unknown and need to be estimated from the data. In particular, we develop an extension of Spectral Networks which incorporates a Graph Estimation procedure, that we test on large-scale classification problems, matching or improving over Dropout Networks with far less parameters to estimate.
@cite_23: Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures.
@cite_3: In this paper, we propose a generalization of convolutional neural networks (CNN) to non-Euclidean domains for the analysis of deformable shapes. Our construction is based on localized frequency analysis (a generalization of the windowed Fourier transform to manifolds) that is used to extract the local behavior of some dense intrinsic descriptor, roughly acting as an analogy to patches in images. The resulting local frequency representations are then passed through a bank of filters whose coefficient are determined by a learning procedure minimizing a task-specific cost. Our approach generalizes several previous methods such as HKS, WKS, spectral CNN, and GPS embeddings. Experimental results show that the proposed approach allows learning class-specific shape descriptors significantly outperforming recent state-of-the-art methods on standard benchmarks.
Particularly relevant to our approach is the localized SCNN model @cite_3 , which is a deep learning approach that can extract the properties of deformable shapes. The generalized SCNN model @cite_23 @cite_10 , a key component of our framework, borrowed the Fourier transform concept from the signal processing field in order to apply CNNs in a grid domain to a graph-structured domain. In this model, the convolutional operation was re-defined for graphs.