Graph convolutional neural networks (GCNN) have been widely used in graph learning and related applications. It has been identified that the filters in the state-of-the-art spectral graph convolutional networks (SGCNs) are essentially low-pass filters that enforce smoothness across the graph and use the functions of graph Laplacian as a tool that injects graph structure into the learning algorithm. There had been research findings that connect the smoothness functional in graphs, graph Laplacian, and regularization operators. We review the existing SGCNs in this context and propose a framework where the state-of-the-art filter designs can be deduced as special cases. We designed new filters that are associated with well-defined low-pass behavior and tested their performance on semisupervised node classification tasks. Their performance was found to be superior to that of the other state-of-the-art techniques. We further investigate the representation capability of low-pass features and make useful observations. In this context, we discuss a few points to further optimize the network, new strategies for designing SGCNs, their challenges, and some latest related developments. Based on our framework, we also deduce the connection between support vector kernels and SGCN filters.

We describe the design of a reproducing kernel suitable for attributed graphs, in which the similarity between two graphs is defined based on the neighborhood information of the graph nodes with the aid of a product graph formulation. Attributed graphs are those which contain a piece of vector information and a discrete label over the nodes and edges. We represent the proposed kernel as the weighted sum of two other kernels of which one is an R-convolution kernel that processes the attribute information of the graph and the other is an optimal assignment kernel that processes label information. They are formulated in such a way that the edges processed as part of the kernel computation have the same neighborhood properties and hence the kernel proposed makes a well-defined correspondence between regions processed in graphs. These concepts are also extended to the case of the shortest paths. We identified the state-of-the-art kernels that can be mapped to such a neighborhood preserving framework. We found that the kernel value of the argument graphs in each iteration of the Weisfeiler-Lehman color refinement algorithm can be obtained recursively from the product graph formulated in our method. By incorporating the proposed kernel on support vector machines we analyzed the real-world data sets and it showed superior performance in comparison with that of the other state-of-the-art graph kernels.

Several methods for discovering interpretable directions in the latent space of pre-trained GANs have been proposed. Latent semantics discovered by unsupervised methods are less disentangled than supervised methods since they do not use pre-trained attribute classifiers. We propose Scale Ranking Estimator (SRE), which is trained using self-supervision. SRE enhances the disentanglement in directions obtained by existing unsupervised disentanglement techniques. These directions are updated to preserve the ordering of variation within each direction in latent space. Qualitative and quantitative evaluation of the discovered directions demonstrates that our proposed method significantly improves disentanglement in various datasets. We also show that the learned SRE can be used to perform Attribute-based image retrieval task without any training.

We propose Disentanglement based Active Learning (DAL), a new active learning technique based on self-supervision which leverages the concept of disentanglement. Instead of requesting labels from human oracle, our method automatically labels majority of the datapoints, thus drastically reducing the human labeling budget in Generative Adversarial Net (GAN) based active learning approaches. The proposed method uses Information Maximizing Generative Adversarial Nets (InfoGAN) to learn disentangled class category representations. Disagreement between active learner predictions and InfoGAN labels decides if the datapoints need to be human labeled. We also introduce a label correction mechanism which aims to filter out label noise that occurs due to automatic labeling. Results on three benchmark datasets for image classification task demonstrate that our method achieves better performance compared to existing GAN based active learning approaches.