We address the problem of graph classification based only on structural information. Inspired by natural language processing techniques (NLP), our model sequentially embeds information to estimate class membership probabilities. Besides, we experiment with NLP-like variational regularization techniques, making the model predict the next node in the sequence as it reads it. We experimentally show that our model achieves state-of-the-art classification results on several standard molecular datasets. Finally, we perform a qualitative analysis and give some insights on whether the node prediction helps the model better classify graphs.
Some random walk models are used to address node classification or graph classification problems. The idea is to sequentially walk on a graph, one node at a time in a random fashion, and agglomerate information. The graph is represented by a discrete-time Markov chain where each node is associated to a state of the chain, and each probability of transition is proportional to its adjacency. More recently, @cite_0 or @cite_1 transform a graph into a sequence of fixed size vectors. Each of these vectors is an embedding of one node of the graph. The sequence of embeddings is then fed to a recurrent neural network (RNN). The two main challenges in this kind of approaches are the design of the embedding function for the nodes and the order in which the embeddings are given to the recurrent neural network.
@cite_0 @cite_1
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In this paper, we formulate visual tracking as random walks on graph models with nodes representing superpixels and edges denoting relationships between superpixels. We integrate two novel graphs with the theory of Markov random walks, resulting in two Markov chains. First, an ergodic Markov chain is enforced to globally search for the candidate nodes with similar features to the template nodes. Second, an absorbing Markov chain is utilized to model the temporal coherence between consecutive frames. The final confidence map is generated by a structural model which combines both appearance similarity measurement derived by the random walks and internal spatial layout demonstrated by different target parts. The effectiveness of the proposed Markov chains as well as the structural model is evaluated both qualitatively and quantitatively. Experimental results on challenging sequences show that the proposed tracking algorithm performs favorably against state-of-the-art methods. Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level structure and can benefit from it. Spatiotemporal graphs are a popular tool for imposing such high-level intuitions in the formulation of real world problems. In this paper, we propose an approach for combining the power of high-level spatio-temporal graphs and sequence learning success of Recurrent Neural Networks (RNNs). We develop a scalable method for casting an arbitrary spatio-temporal graph as a rich RNN mixture that is feedforward, fully differentiable, and jointly trainable. The proposed method is generic and principled as it can be used for transforming any spatio-temporal graph through employing a certain set of well defined steps. The evaluations of the proposed approach on a diverse set of problems, ranging from modeling human motion to object interactions, shows improvement over the state-of-the-art with a large margin. We expect this method to empower new approaches to problem formulation through high-level spatio-temporal graphs and Recurrent Neural Networks. Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level structure and can benefit from it. Spatio-temporal graphs are a popular tool for imposing such high-level intuitions in the formulation of real world problems. In this paper, we propose an approach for combining the power of high-level spatio-temporal graphs and sequence learning success of Recurrent Neural Networks (RNNs). We develop a scalable method for casting an arbitrary spatio-temporal graph as a rich RNN mixture that is feedforward, fully differentiable, and jointly trainable. The proposed method is generic and principled as it can be used for transforming any spatio-temporal graph through employing a certain set of well defined steps. The evaluations of the proposed approach on a diverse set of problems, ranging from modeling human motion to object interactions, shows improvement over the state-of-the-art with a large margin. We expect this method to empower new approaches to problem formulation through high-level spatio-temporal graphs and Recurrent Neural Networks. We quantify the effectiveness of random walks for searching and construction of unstructured peer-to-peer (P2P) networks. We have identified two cases where the use of random walks for searching achieves better results than flooding: a) when the overlay topology is clustered, and h) when a client re-issues the same query while its horizon does not change much. For construction, we argue that an expander can he maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk can achieve statistical properties similar to independent sampling (if the second eigenvalue of the transition matrix is hounded away from 1, which translates to good expansion of the network; such connectivity is desired, and believed to hold, in every reasonable network and network model). This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead.