We present two instances, L-GAE and L-VGAE, of the variational graph auto-encoding family (VGAE) based on separating feature propagation operations from graph convolution layers typically found in graph learning methods to a single linear matrix computation made prior to input in standard auto-encoder architectures. This decoupling enables the independent and fixed design of the auto-encoder without requiring additional GCN layers for every desired increase in the size of a node's local receptive field. Fixing the auto-encoder enables a fairer assessment on the size of a nodes receptive field in building representations. Furthermore a by-product of fixing the auto-encoder design often results in substantially smaller networks than their VGAE counterparts especially as we increase the number of feature propagations. A comparative downstream evaluation on link prediction tasks show comparable state of the art performance to similar VGAE arrangements despite considerable simplification. We also show the simple application of our methodology to more challenging representation learning scenarios such as spatio-temporal graph representation learning.
Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and $\epsilon$-neighborhood methods are among the most common methods used for neighborhood selection, due to their computational simplicity. However, the choice of parameters associated with these methods, such as k and $\epsilon$, is still ad hoc. We make two main contributions in this paper. First, we present an alternative view of neighborhood selection, where we show that neighborhood construction is equivalent to a sparse signal approximation problem. Second, we propose an algorithm, non-negative kernel regression~(NNK), for obtaining neighborhoods that lead to better sparse representation. NNK draws similarities to the orthogonal matching pursuit approach to signal representation and possesses desirable geometric and theoretical properties. Experiments demonstrate (i) the robustness of the NNK algorithm for neighborhood and graph construction, (ii) its ability to adapt the number of neighbors to the data properties, and (iii) its superior performance in local neighborhood and graph-based machine learning tasks.
Graph Convolutional Networks (GCNs) have shown very powerful for graph data representation and learning tasks. Existing GCNs usually conduct feature aggregation on a fixed neighborhood graph in which each node computes its representation by aggregating the feature representations of all its neighbors which is biased by its own representation. However, this fixed aggregation strategy is not guaranteed to be optimal for GCN based graph learning and also can be affected by some graph structure noises, such as incorrect or undesired edge connections. To address these issues, we propose a novel Graph mask Convolutional Network (GmCN) in which nodes can adaptively select the optimal neighbors in their feature aggregation to better serve GCN learning. GmCN can be theoretically interpreted by a regularization framework, based on which we derive a simple update algorithm to determine the optimal mask adaptively in GmCN training process. Experiments on several datasets validate the effectiveness of GmCN.
Financial crime is a large and growing problem, in some way touching almost every financial institution. Financial institutions are the front line in the war against financial crime and accordingly, must devote substantial human and technology resources to this effort. Current processes to detect financial misconduct have limitations in their ability to effectively differentiate between malicious behavior and ordinary financial activity. These limitations tend to result in gross over-reporting of suspicious activity that necessitate time-intensive and costly manual review. Advances in technology used in this domain, including machine learning based approaches, can improve upon the effectiveness of financial institutions' existing processes, however, a key challenge that most financial institutions continue to face is that they address financial crimes in isolation without any insight from other firms. Where financial institutions address financial crimes through the lens of their own firm, perpetrators may devise sophisticated strategies that may span across institutions and geographies. Financial institutions continue to work relentlessly to advance their capabilities, forming partnerships across institutions to share insights, patterns and capabilities. These public-private partnerships are subject to stringent regulatory and data privacy requirements, thereby making it difficult to rely on traditional technology solutions. In this paper, we propose a methodology to share key information across institutions by using a federated graph learning platform that enables us to build more accurate machine learning models by leveraging federated learning and also graph learning approaches. We demonstrated that our federated model outperforms local model by 20% with the UK FCA TechSprint data set. This new platform opens up a door to efficiently detecting global money laundering activity.
We present a relational graph learning approach for robotic crowd navigation using model-based deep reinforcement learning that plans actions by looking into the future. Our approach reasons about the relations between all agents based on their latent features and uses a Graph Convolutional Network to encode higher-order interactions in each agent's state representation, which is subsequently leveraged for state prediction and value estimation. The ability to predict human motion allows us to perform multi-step lookahead planning, taking into account the temporal evolution of human crowds. We evaluate our approach against a state-of-the-art baseline for crowd navigation and ablations of our model to demonstrate that navigation with our approach is more efficient, results in fewer collisions, and avoids failure cases involving oscillatory and freezing behaviors.
Semi-supervised learning (SSL) is effectively used for numerous classification problems, thanks to its ability to make use of abundant unlabeled data. The main assumption of various SSL algorithms is that the nearby points on the data manifold are likely to share a label. Graph-based SSL constructs a graph from point-cloud data as an approximation to the underlying manifold, followed by label inference. It is no surprise that the quality of the constructed graph in capturing the essential structure of the data is critical to the accuracy of the subsequent inference step [6]. How should one construct a graph from the input point-cloud data for graph-based SSL? In this work we introduce a new, parallel graph learning framework (called PG-learn) for the graph construction step of SSL. Our solution has two main ingredients: (1) a gradient-based optimization of the edge weights (more specifically, different kernel bandwidths in each dimension) based on a validation loss function, and (2) a parallel hyperparameter search algorithm with an adaptive resource allocation scheme. In essence, (1) allows us to search around a (random) initial hyperparameter configuration for a better one with lower validation loss. Since the search space of hyperparameters is huge for high-dimensional problems, (2) empowers our gradient-based search to go through as many different initial configurations as possible, where runs for relatively unpromising starting configurations are terminated early to allocate the time for others. As such, PG-learn is a carefully-designed hybrid of random and adaptive search. Through experiments on multi-class classification problems, we show that PG-learn significantly outperforms a variety of existing graph construction schemes in accuracy (per fixed time budget for hyperparameter tuning), and scales more effectively to high dimensional problems.
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In this paper, we first show that for a set of important graph families it is possible to convert the structural constraints of structure into eigenvalue constraints of the graph Laplacian matrix. Then we introduce a unified graph learning framework, lying at the integration of the spectral properties of the Laplacian matrix with Gaussian graphical modeling that is capable of learning structures of a large class of graph families. The proposed algorithms are provably convergent and practically amenable for large-scale semi-supervised and unsupervised graph-based learning tasks. Extensive numerical experiments with both synthetic and real data sets demonstrate the effectiveness of the proposed methods. An R package containing code for all the experimental results is available at https://cran.r-project.org/package=spectralGraphTopology.
Learning powerful data embeddings has become a center piece in machine learning, especially in natural language processing and computer vision domains. The crux of these embeddings is that they are pretrained on huge corpus of data in a unsupervised fashion, sometimes aided with transfer learning. However currently in the graph learning domain, embeddings learned through existing graph neural networks (GNNs) are task dependent and thus cannot be shared across different datasets. In this paper, we present a first powerful and theoretically guaranteed graph neural network that is designed to learn task-independent graph embeddings, thereafter referred to as deep universal graph embedding (DUGNN). Our DUGNN model incorporates a novel graph neural network (as a universal graph encoder) and leverages rich Graph Kernels (as a multi-task graph decoder) for both unsupervised learning and (task-specific) adaptive supervised learning. By learning task-independent graph embeddings across diverse datasets, DUGNN also reaps the benefits of transfer learning. Through extensive experiments and ablation studies, we show that the proposed DUGNN model consistently outperforms both the existing state-of-art GNN models and Graph Kernels by an increased accuracy of 3% - 8% on graph classification benchmark datasets.
A panoply of multi-view clustering algorithms has been developed to deal with prevalent multi-view data. Among them, spectral clustering-based methods have drawn much attention and demonstrated promising results recently. Despite progress, there are still two fundamental questions that stay unanswered to date. First, how to fuse different views into one graph. More often than not, the similarities between samples may be manifested differently by different views. Many existing algorithms either simply take the average of multiple views or just learn a common graph. These simple approaches fail to consider the flexible local manifold structures of all views. Hence, the rich heterogeneous information is not fully exploited. Second, how to learn the explicit cluster structure. Most existing methods don't pay attention to the quality of the graphs and perform graph learning and spectral clustering separately. Those unreliable graphs might lead to suboptimal clustering results. To fill these gaps, in this paper, we propose a novel multi-view spectral clustering model which performs graph fusion and spectral clustering simultaneously. The fusion graph approximates the original graph of each individual view but maintains an explicit cluster structure. Experiments on four widely used data sets confirm the superiority of the proposed method.
Graph Convolutional Neural Networks (GCNNs) extend classical CNNs to graph data domain, such as brain networks, social networks and 3D point clouds. It is critical to identify an appropriate graph for the subsequent graph convolution. Existing methods manually construct or learn one fixed graph for all the layers of a GCNN. In order to adapt to the underlying structure of node features in different layers, we propose dynamic learning of graphs and node features jointly in GCNNs. In particular, we cast the graph optimization problem as distance metric learning to capture pairwise similarities of features in each layer. We deploy the Mahalanobis distance metric and further decompose the metric matrix into a low-dimensional matrix, which converts graph learning to the optimization of a low-dimensional matrix for efficient implementation. Extensive experiments on point clouds and citation network datasets demonstrate the superiority of the proposed method in terms of both accuracies and robustness.
To explore underlying complementary information from multiple views, in this paper, we propose a novel Latent Multi-view Semi-Supervised Classification (LMSSC) method. Unlike most existing multi-view semi-supervised classification methods that learn the graph using original features, our method seeks an underlying latent representation and performs graph learning and label propagation based on the learned latent representation. With the complementarity of multiple views, the latent representation could depict the data more comprehensively than every single view individually, accordingly making the graph more accurate and robust as well. Finally, LMSSC integrates latent representation learning, graph construction, and label propagation into a unified framework, which makes each subtask optimized. Experimental results on real-world benchmark datasets validate the effectiveness of our proposed method.
Advancing research in the emerging field of deep graph learning requires new tools to support tensor computation over graphs. In this paper, we present the design principles and implementation of Deep Graph Library (DGL). DGL distills the computational patterns of GNNs into a few generalized sparse tensor operations suitable for extensive parallelization. By advocating graph as the central programming abstraction, DGL can perform optimizations transparently. By cautiously adopting a framework-neutral design, DGL allows users to easily port and leverage the existing components across multiple deep learning frameworks. Our evaluation shows that DGL significantly outperforms other popular GNN-oriented frameworks in both speed and memory consumption over a variety of benchmarks and has little overhead for small scale workloads.
Inspired by the immense success of deep learning, graph neural networks (GNNs) are widely used to learn powerful node representations and have demonstrated promising performance on different graph learning tasks. However, most real-world graphs often come with high-dimensional and sparse node features, rendering the learned node representations from existing GNN architectures less expressive. In this paper, we propose \textit{Feature Interaction-aware Graph Neural Networks (FI-GNNs)}, a plug-and-play GNN framework for learning node representations encoded with informative feature interactions. Specifically, the proposed framework is able to highlight informative feature interactions in a personalized manner and further learn highly expressive node representations on feature-sparse graphs. Extensive experiments on various datasets demonstrate the superior capability of FI-GNNs for graph learning tasks.
With the great success of graph embedding model on both academic and industry area, the robustness of graph embedding against adversarial attack inevitably becomes a central problem in graph learning domain. Regardless of the fruitful progress, most of the current works perform the attack in a white-box fashion: they need to access the model predictions and labels to construct their adversarial loss. However, the inaccessibility of model predictions in real systems makes the white-box attack impractical to real graph learning system. This paper promotes current frameworks in a more general and flexible sense -- we demand to attack various kinds of graph embedding model with black-box driven. To this end, we begin by investigating the theoretical connections between graph signal processing and graph embedding models in a principled way and formulate the graph embedding model as a general graph signal process with corresponding graph filter. As such, a generalized adversarial attacker: GF-Attack is constructed by the graph filter and feature matrix. Instead of accessing any knowledge of the target classifiers used in graph embedding, GF-Attack performs the attack only on the graph filter in a black-box attack fashion. To validate the generalization of GF-Attack, we construct the attacker on four popular graph embedding models. Extensive experimental results validate the effectiveness of our attacker on several benchmark datasets. Particularly by using our attack, even small graph perturbations like one-edge flip is able to consistently make a strong attack in performance to different graph embedding models.
Identifying an appropriate underlying graph kernel that reflects pairwise similarities is critical in many recent graph spectral signal restoration schemes, including image denoising, dequantization, and contrast enhancement. Existing graph learning algorithms compute the most likely entries of a properly defined graph Laplacian matrix $\mathbf{L}$, but require a large number of signal observations $\mathbf{z}$'s for a stable estimate. In this work, we assume instead the availability of a relevant feature vector $\mathbf{f}_i$ per node $i$, from which we compute an optimal feature graph via optimization of a feature metric. Specifically, we alternately optimize the diagonal and off-diagonal entries of a Mahalanobis distance matrix $\mathbf{M}$ by minimizing the graph Laplacian regularizer (GLR) $\mathbf{z}^{\top} \mathbf{L} \mathbf{z}$, where edge weight is $w_{i,j} = \exp\{-(\mathbf{f}_i - \mathbf{f}_j)^{\top} \mathbf{M} (\mathbf{f}_i - \mathbf{f}_j) \}$, given a single observation $\mathbf{z}$. We optimize diagonal entries via proximal gradient (PG), where we constrain $\mathbf{M}$ to be positive definite (PD) via linear inequalities derived from the Gershgorin circle theorem. To optimize off-diagonal entries, we design a block descent algorithm that iteratively optimizes one row and column of $\mathbf{M}$. To keep $\mathbf{M}$ PD, we constrain the Schur complement of sub-matrix $\mathbf{M}_{2,2}$ of $\mathbf{M}$ to be PD when optimizing via PG. Our algorithm mitigates full eigen-decomposition of $\mathbf{M}$, thus ensuring fast computation speed even when feature vector $\mathbf{f}_i$ has high dimension. To validate its usefulness, we apply our feature graph learning algorithm to the problem of 3D point cloud denoising, resulting in state-of-the-art performance compared to competing schemes in extensive experiments.
Organ segmentation in CT volumes is an important pre-processing step in many computer assisted intervention and diagnosis methods. In recent years, convolutional neural networks have dominated the state of the art in this task. However, since this problem presents a challenging environment due to high variability in the organ's shape and similarity between tissues, the generation of false negative and false positive regions in the output segmentation is a common issue. Recent works have shown that the uncertainty analysis of the model can provide us with useful information about potential errors in the segmentation. In this context, we proposed a segmentation refinement method based on uncertainty analysis and graph convolutional networks. We employ the uncertainty levels of the convolutional network in a particular input volume to formulate a semi-supervised graph learning problem that is solved by training a graph convolutional network. To test our method we refine the initial output of a 2D U-Net. We validate our framework with the NIH pancreas dataset and the spleen dataset of the medical segmentation decathlon. We show that our method outperforms the state-of-the art CRF refinement method by improving the dice score by 1% for the pancreas and 2% for spleen, with respect to the original U-Net's prediction. Finally, we discuss the results and current limitations of the model for future work in this research direction. For reproducibility purposes, we make our code publicly available.
Recently, graph neural networks (GNNs) have proved to be suitable in tasks on unstructured data. Particularly in tasks as community detection, node classification, and link prediction. However, most GNN models still operate with static relationships. We propose the Graph Learning Network (GLN), a simple yet effective process to learn node embeddings and structure prediction functions. Our model uses graph convolutions to propose expected node features, and predict the best structure based on them. We repeat these steps recursively to enhance the prediction and the embeddings.
Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressive power of graph neural networks (GNN). It was shown that the popular message passing GNN cannot distinguish between graphs that are indistinguishable by the 1-WL test (Morris et al. 2018; Xu et al. 2019). Unfortunately, many simple instances of graphs are indistinguishable by the 1-WL test. In search for more expressive graph learning models we build upon the recent k-order invariant and equivariant graph neural networks (Maron et al. 2019a,b) and present two results: First, we show that such k-order networks can distinguish between non-isomorphic graphs as good as the k-WL tests, which are provably stronger than the 1-WL test for k>2. This makes these models strictly stronger than message passing models. Unfortunately, the higher expressiveness of these models comes with a computational cost of processing high order tensors. Second, setting our goal at building a provably stronger, simple and scalable model we show that a reduced 2-order network containing just scaled identity operator, augmented with a single quadratic operation (matrix multiplication) has a provable 3-WL expressive power. Differently put, we suggest a simple model that interleaves applications of standard Multilayer-Perceptron (MLP) applied to the feature dimension and matrix multiplication. We validate this model by presenting state of the art results on popular graph classification and regression tasks. To the best of our knowledge, this is the first practical invariant/equivariant model with guaranteed 3-WL expressiveness, strictly stronger than message passing models.
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the incorporation of nonlinearity. However, most existing kernel-based graph learning mechanisms is not similarity-preserving, hence leads to sub-optimal performance. To overcome this drawback, we propose a more discriminative graph learning method which can preserve the pairwise similarities between samples in an adaptive manner for the first time. Specifically, we require the learned graph be close to a kernel matrix, which serves as a measure of similarity in raw data. Moreover, the structure is adaptively tuned so that the number of connected components of the graph is exactly equal to the number of clusters. Finally, our method unifies clustering and graph learning which can directly obtain cluster indicators from the graph itself without performing further clustering step. The effectiveness of this approach is examined on both single and multiple kernel learning scenarios in several datasets.
Image saliency detection is an active research topic in the community of computer vision and multimedia. Fusing complementary RGB and thermal infrared data has been proven to be effective for image saliency detection. In this paper, we propose an effective approach for RGB-T image saliency detection. Our approach relies on a novel collaborative graph learning algorithm. In particular, we take superpixels as graph nodes, and collaboratively use hierarchical deep features to jointly learn graph affinity and node saliency in a unified optimization framework. Moreover, we contribute a more challenging dataset for the purpose of RGB-T image saliency detection, which contains 1000 spatially aligned RGB-T image pairs and their ground truth annotations. Extensive experiments on the public dataset and the newly created dataset suggest that the proposed approach performs favorably against the state-of-the-art RGB-T saliency detection methods.