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_19: An increasing number of applications require processing of signals defined on weighted graphs. While wavelets provide a flexible tool for signal processing in the classical setting of regular domains, the existing graph wavelet constructions are less flexible - they are guided solely by the structure of the underlying graph and do not take directly into consideration the particular class of signals to be processed. This paper introduces a machine learning framework for constructing graph wavelets that can sparsely represent a given class of signals. Our construction uses the lifting scheme, and is based on the observation that the recurrent nature of the lifting scheme gives rise to a structure resembling a deep auto-encoder network. Particular properties that the resulting wavelets must satisfy determine the training objective and the structure of the involved neural networks. The training is unsupervised, and is conducted similarly to the greedy pre-training of a stack of auto-encoders. After training is completed, we obtain a linear wavelet transform that can be applied to any graph signal in time and memory linear in the size of the graph. Improved sparsity of our wavelet transform for the test signals is confirmed via experiments both on synthetic and real data.
@cite_20: Programming language processing (similar to natural language processing) is a hot research topic in the field of software engineering; it has also aroused growing interest in the artificial intelligence community. However, different from a natural language sentence, a program contains rich, explicit, and complicated structural information. Hence, traditional NLP models may be inappropriate for programs. In this paper, we propose a novel tree-based convolutional neural network (TBCNN) for programming language processing, in which a convolution kernel is designed over programs' abstract syntax trees to capture structural information. TBCNN is a generic architecture for programming language processing; our experiments show its effectiveness in two different program analysis tasks: classifying programs according to functionality, and detecting code snippets of certain patterns. TBCNN outperforms baseline methods, including several neural models for NLP.
@cite_8: 
Examples of deep learning applied to non-grid, non-Euclidean space include graph wavelets from applying deep auto-encoders to graphs and using the properties of automatically extracted features @cite_19 , analysis of molecular fingerprints of proteins saved as graphs @cite_8 , and a CNN-based model for handling tree structures in the context of programming language processing @cite_20 .