We study many-class few-shot (MCFS) problem in both supervised learning and meta-learning settings. Compared to the well-studied many-class many-shot and few-class few-shot problems, the MCFS problem commonly occurs in practical applications but has been rarely studied in previous literature. It brings new challenges of distinguishing between many classes given only a few training samples per class. In this paper, we leverage the class hierarchy as a prior knowledge to train a coarse-to-fine classifier that can produce accurate predictions for MCFS problem in both settings. The propose model, "memory-augmented hierarchical-classification network (MahiNet)", performs coarse-to-fine classification where each coarse class can cover multiple fine classes. Since it is challenging to directly distinguish a variety of fine classes given few-shot data per class, MahiNet starts from learning a classifier over coarse-classes with more training data whose labels are much cheaper to obtain. The coarse classifier reduces the searching range over the fine classes and thus alleviates the challenges from "many classes". On architecture, MahiNet firstly deploys a convolutional neural network (CNN) to extract features. It then integrates a memory-augmented attention module and a multi-layer perceptron (MLP) together to produce the probabilities over coarse and fine classes. While the MLP extends the linear classifier, the attention module extends the KNN classifier, both together targeting the "few-shot" problem. We design several training strategies of MahiNet for supervised learning and meta-learning. In addition, we propose two novel benchmark datasets "mcfsImageNet" and "mcfsOmniglot" specially designed for MCFS problem. In experiments, we show that MahiNet outperforms several state-of-the-art models on MCFS problems in both supervised learning and meta-learning.

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.

Meta-learning extracts the common knowledge acquired from learning different tasks and uses it for unseen tasks. It demonstrates a clear advantage on tasks that have insufficient training data, e.g., few-shot learning. In most meta-learning methods, tasks are implicitly related via the shared model or optimizer. In this paper, we show that a meta-learner that explicitly relates tasks on a graph describing the relations of their output dimensions (e.g., classes) can significantly improve the performance of few-shot learning. This type of graph is usually free or cheap to obtain but has rarely been explored in previous works. We study the prototype based few-shot classification, in which a prototype is generated for each class, such that the nearest neighbor search between the prototypes produces an accurate classification. We introduce "Gated Propagation Network (GPN)", which learns to propagate messages between prototypes of different classes on the graph, so that learning the prototype of each class benefits from the data of other related classes. In GPN, an attention mechanism is used for the aggregation of messages from neighboring classes, and a gate is deployed to choose between the aggregated messages and the message from the class itself. GPN is trained on a sequence of tasks from many-shot to few-shot generated by subgraph sampling. During training, it is able to reuse and update previously achieved prototypes from the memory in a life-long learning cycle. In experiments, we change the training-test discrepancy and test task generation settings for thorough evaluations. GPN outperforms recent meta-learning methods on two benchmark datasets in all studied cases.

Graph clustering is a fundamental task which discovers communities or groups in networks. Recent studies have mostly focused on developing deep learning approaches to learn a compact graph embedding, upon which classic clustering methods like k-means or spectral clustering algorithms are applied. These two-step frameworks are difficult to manipulate and usually lead to suboptimal performance, mainly because the graph embedding is not goal-directed, i.e., designed for the specific clustering task. In this paper, we propose a goal-directed deep learning approach, Deep Attentional Embedded Graph Clustering (DAEGC for short). Our method focuses on attributed graphs to sufficiently explore the two sides of information in graphs. By employing an attention network to capture the importance of the neighboring nodes to a target node, our DAEGC algorithm encodes the topological structure and node content in a graph to a compact representation, on which an inner product decoder is trained to reconstruct the graph structure. Furthermore, soft labels from the graph embedding itself are generated to supervise a self-training graph clustering process, which iteratively refines the clustering results. The self-training process is jointly learned and optimized with the graph embedding in a unified framework, to mutually benefit both components. Experimental results compared with state-of-the-art algorithms demonstrate the superiority of our method.

A variety of machine learning applications expect to achieve rapid learning from a limited number of labeled data. However, the success of most current models is the result of heavy training on big data. Meta-learning addresses this problem by extracting common knowledge across different tasks that can be quickly adapted to new tasks. However, they do not fully explore weakly-supervised information, which is usually free or cheap to collect. In this paper, we show that weakly-labeled data can significantly improve the performance of meta-learning on few-shot classification. We propose prototype propagation network (PPN) trained on few-shot tasks together with data annotated by coarse-label. Given a category graph of the targeted fine-classes and some weakly-labeled coarse-classes, PPN learns an attention mechanism which propagates the prototype of one class to another on the graph, so that the K-nearest neighbor (KNN) classifier defined on the propagated prototypes results in high accuracy across different few-shot tasks. The training tasks are generated by subgraph sampling, and the training objective is obtained by accumulating the level-wise classification loss on the subgraph. The resulting graph of prototypes can be continually re-used and updated for new tasks and classes. We also introduce two practical test/inference settings which differ according to whether the test task can leverage any weakly-supervised information as in training. On two benchmarks, PPN significantly outperforms most recent few-shot learning methods in different settings, even when they are also allowed to train on weakly-labeled data.

Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the underlying relation between entities is pre-determined. However, the explicit graph structure (relation) does not necessarily reflect the true dependency and genuine relation may be missing due to the incomplete connections in the data. Furthermore, existing methods are ineffective to capture the temporal trends as the RNNs or CNNs employed in these methods cannot capture long-range temporal sequences. To overcome these limitations, we propose in this paper a novel graph neural network architecture, Graph WaveNet, for spatial-temporal graph modeling. By developing a novel adaptive dependency matrix and learn it through node embedding, our model can precisely capture the hidden spatial dependency in the data. With a stacked dilated 1D convolution component whose receptive field grows exponentially as the number of layers increases, Graph WaveNet is able to handle very long sequences. These two components are integrated seamlessly in a unified framework and the whole framework is learned in an end-to-end manner. Experimental results on two public traffic network datasets, METR-LA and PEMS-BAY, demonstrate the superior performance of our algorithm.

Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the reconstruction errors for graph data. They have mostly overlooked the embedding distribution of the latent codes, which unfortunately may lead to inferior representation in many cases. In this paper, we present a novel adversarially regularized framework for graph embedding. By employing the graph convolutional network as an encoder, our framework embeds the topological information and node content into a vector representation, from which a graph decoder is further built to reconstruct the input graph. The adversarial training principle is applied to enforce our latent codes to match a prior Gaussian or Uniform distribution. Based on this framework, we derive two variants of adversarial models, the adversarially regularized graph autoencoder (ARGA) and its variational version, adversarially regularized variational graph autoencoder (ARVGA), to learn the graph embedding effectively. We also exploit other potential variations of ARGA and ARVGA to get a deeper understanding on our designs. Experimental results compared among twelve algorithms for link prediction and twenty algorithms for graph clustering validate our solutions.

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art graph neural networks into different categories. With a focus on graph convolutional networks, we review alternative architectures that have recently been developed; these learning paradigms include graph attention networks, graph autoencoders, graph generative networks, and graph spatial-temporal networks. We further discuss the applications of graph neural networks across various domains and summarize the open source codes and benchmarks of the existing algorithms on different learning tasks. Finally, we propose potential research directions in this fast-growing field.

In this paper, we propose a self-attention mechanism, dubbed "fast directional self-attention (Fast-DiSA)", which is a fast and light extension of "directional self-attention (DiSA)". The proposed Fast-DiSA performs as expressively as the original DiSA but only uses much less computation time and memory, in which 1) both token2token and source2token dependencies are modeled by a joint compatibility function designed for a hybrid of both dot-product and multi-dim ways; 2) both multi-head and multi-dim attention combined with bi-directional temporal information captured by multiple positional masks are in consideration without heavy time and memory consumption appearing in the DiSA. The experiment results show that the proposed Fast-DiSA can achieve state-of-the-art performance as fast and memory-friendly as CNNs. The code for Fast-DiSA is released at \url{https://github.com/taoshen58/DiSAN/tree/master/Fast-DiSA}.

Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction errors of graph data, but they have mostly ignored the data distribution of the latent codes from the graphs, which often results in inferior embedding in real-world graph data. In this paper, we propose a novel adversarial graph embedding framework for graph data. The framework encodes the topological structure and node content in a graph to a compact representation, on which a decoder is trained to reconstruct the graph structure. Furthermore, the latent representation is enforced to match a prior distribution via an adversarial training scheme. To learn a robust embedding, two variants of adversarial approaches, adversarially regularized graph autoencoder (ARGA) and adversarially regularized variational graph autoencoder (ARVGA), are developed. Experimental studies on real-world graphs validate our design and demonstrate that our algorithms outperform baselines by a wide margin in link prediction, graph clustering, and graph visualization tasks.