Graph-structured data arise in many scenarios. A fundamental problem is to quantify the similarities of graphs for tasks such as classification. Graph kernels are positive-semidefinite functions that decompose graphs into substructures and compare them. One problem in the effective implementation of this idea is that the substructures are not independent, which leads to high-dimensional feature space. In addition, graph kernels cannot capture the high-order complex interactions between vertices. To mitigate these two problems, we propose a framework called DeepMap to learn deep representations for graph feature maps. The learnt deep representation for a graph is a dense and low-dimensional vector that captures complex high-order interactions in a vertex neighborhood. DeepMap extends Convolutional Neural Networks (CNNs) to arbitrary graphs by aligning vertices across graphs and building the receptive field for each vertex. We empirically validate DeepMap on various graph classification benchmarks and demonstrate that it achieves state-of-the-art performance.

This is our second article of the series about mutual information. In the previous articles, we have seen how to maximizes the mutual information between two variables via the MINE estimator and some practical applications of maximizing mutual information. In this article, we focus on representation learning with mutual information maximization. Specifically, we will discuss an adversarial architecture for representation learning and two other objectives of mutual information maximization that has been experimentally shown to outperform MINE estimator for downstream tasks. This article is organized into four parts.

Unsupervised deep learning is one of the most powerful representation learning techniques. Restricted Boltzman machine, sparse coding, regularized auto-encoders, and convolutional neural networks are pioneering building blocks of deep learning. In this paper, we propose a new building block -- distributed random models. The proposed method is a special full implementation of the product of experts: (i) each expert owns multiple hidden units and different experts have different numbers of hidden units; (ii) the model of each expert is a k-center clustering, whose k-centers are only uniformly sampled examples, and whose output (i.e. the hidden units) is a sparse code that only the similarity values from a few nearest neighbors are reserved. The relationship between the pioneering building blocks, several notable research branches and the proposed method is analyzed. Experimental results show that the proposed deep model can learn better representations than deep belief networks and meanwhile can train a much larger network with much less time than deep belief networks.