Graph Classification via Reference Distribution Learning: Theory and Practice

Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs). Graph kernels often suffer from computational costs and manual feature engineering, while GNNs commonly utilize global pooling operations, risking the loss of structural or semantic information. This work introduces Graph Reference Distribution Learning (GRDL), an efficient and accurate graph classification method. GRDL treats each graph's latent node embeddings given by GNN layers as a discrete distribution, enabling direct classification without global pooling, based on maximum mean discrepancy to adaptively learned reference distributions. To fully understand this new model (the existing theories do not apply) and guide its configuration (e.g., network architecture, references' sizes, number, and regularization) for practical use, we derive generalization error bounds for GRDL and verify them numerically. More importantly, our theoretical and numerical results both show that GRDL has a stronger generalization ability than GNNs with global pooling operations. Experiments on moderate-scale and large-scale graph datasets show the superiority of GRDL over the state-of-the-art, emphasizing its remarkable efficiency, being at least 10 times faster than leading competitors in both training and inference stages.

DA-Flow: Dual Attention Normalizing Flow for Skeleton-based Video Anomaly Detection

Cooperation between temporal convolutional networks (TCN) and graph convolutional networks (GCN) as a processing module has shown promising results in skeleton-based video anomaly detection (SVAD). However, to maintain a lightweight model with low computational and storage complexity, shallow GCN and TCN blocks are constrained by small receptive fields and a lack of cross-dimension interaction capture. To tackle this limitation, we propose a lightweight module called the Dual Attention Module (DAM) for capturing cross-dimension interaction relationships in spatio-temporal skeletal data. It employs the frame attention mechanism to identify the most significant frames and the skeleton attention mechanism to capture broader relationships across fixed partitions with minimal parameters and flops. Furthermore, the proposed Dual Attention Normalizing Flow (DA-Flow) integrates the DAM as a post-processing unit after GCN within the normalizing flow framework. Simulations show that the proposed model is robust against noise and negative samples. Experimental results show that DA-Flow reaches competitive or better performance than the existing state-of-the-art (SOTA) methods in terms of the micro AUC metric with the fewest number of parameters. Moreover, we found that even without training, simply using random projection without dimensionality reduction on skeleton data enables substantial anomaly detection capabilities.

Diving Deep into Regions: Exploiting Regional Information Transformer for Single Image Deraining

Transformer-based Single Image Deraining (SID) methods have achieved remarkable success, primarily attributed to their robust capability in capturing long-range interactions. However, we've noticed that current methods handle rain-affected and unaffected regions concurrently, overlooking the disparities between these areas, resulting in confusion between rain streaks and background parts, and inabilities to obtain effective interactions, ultimately resulting in suboptimal deraining outcomes. To address the above issue, we introduce the Region Transformer (Regformer), a novel SID method that underlines the importance of independently processing rain-affected and unaffected regions while considering their combined impact for high-quality image reconstruction. The crux of our method is the innovative Region Transformer Block (RTB), which integrates a Region Masked Attention (RMA) mechanism and a Mixed Gate Forward Block (MGFB). Our RTB is used for attention selection of rain-affected and unaffected regions and local modeling of mixed scales. The RMA generates attention maps tailored to these two regions and their interactions, enabling our model to capture comprehensive features essential for rain removal. To better recover high-frequency textures and capture more local details, we develop the MGFB as a compensation module to complete local mixed scale modeling. Extensive experiments demonstrate that our model reaches state-of-the-art performance, significantly improving the image deraining quality. Our code and trained models are publicly available.

Spectral Clustering for Discrete Distributions

Discrete distribution clustering (D2C) was often solved by Wasserstein barycenter methods. These methods are under a common assumption that clusters can be well represented by barycenters, which may not hold in many real applications. In this work, we propose a simple yet effective framework based on spectral clustering and distribution affinity measures (e.g., maximum mean discrepancy and Wasserstein distance) for D2C. To improve the scalability, we propose to use linear optimal transport to construct affinity matrices efficiently on large datasets. We provide theoretical guarantees for the success of the proposed methods in clustering distributions. Experiments on synthetic and real data show that our methods outperform the baselines largely in terms of both clustering accuracy and computational efficiency.

Self-Discriminative Modeling for Anomalous Graph Detection

This paper studies the problem of detecting anomalous graphs using a machine learning model trained on only normal graphs, which has many applications in molecule, biology, and social network data analysis. We present a self-discriminative modeling framework for anomalous graph detection. The key idea, mathematically and numerically illustrated, is to learn a discriminator (classifier) from the given normal graphs together with pseudo-anomalous graphs generated by a model jointly trained, where we never use any true anomalous graphs and we hope that the generated pseudo-anomalous graphs interpolate between normal ones and (real) anomalous ones. Under the framework, we provide three algorithms with different computational efficiencies and stabilities for anomalous graph detection. The three algorithms are compared with several state-of-the-art graph-level anomaly detection baselines on nine popular graph datasets (four with small size and five with moderate size) and show significant improvement in terms of AUC. The success of our algorithms stems from the integration of the discriminative classifier and the well-posed pseudo-anomalous graphs, which provide new insights for anomaly detection. Moreover, we investigate our algorithms for large-scale imbalanced graph datasets. Surprisingly, our algorithms, though fully unsupervised, are able to significantly outperform supervised learning algorithms of anomalous graph detection. The corresponding reason is also analyzed.

ESMC: Entire Space Multi-Task Model for Post-Click Conversion Rate via Parameter Constraint

Large-scale online recommender system spreads all over the Internet being in charge of two basic tasks: Click-Through Rate (CTR) and Post-Click Conversion Rate (CVR) estimations. However, traditional CVR estimators suffer from well-known Sample Selection Bias and Data Sparsity issues. Entire space models were proposed to address the two issues via tracing the decision-making path of "exposure_click_purchase". Further, some researchers observed that there are purchase-related behaviors between click and purchase, which can better draw the user's decision-making intention and improve the recommendation performance. Thus, the decision-making path has been extended to "exposure_click_in-shop action_purchase" and can be modeled with conditional probability approach. Nevertheless, we observe that the chain rule of conditional probability does not always hold. We report Probability Space Confusion (PSC) issue and give a derivation of difference between ground-truth and estimation mathematically. We propose a novel Entire Space Multi-Task Model for Post-Click Conversion Rate via Parameter Constraint (ESMC) and two alternatives: Entire Space Multi-Task Model with Siamese Network (ESMS) and Entire Space Multi-Task Model in Global Domain (ESMG) to address the PSC issue. Specifically, we handle "exposure_click_in-shop action" and "in-shop action_purchase" separately in the light of characteristics of in-shop action. The first path is still treated with conditional probability while the second one is treated with parameter constraint strategy. Experiments on both offline and online environments in a large-scale recommendation system illustrate the superiority of our proposed methods over state-of-the-art models. The real-world datasets will be released.

Restricted Generative Projection for One-Class Classification and Anomaly Detection

We present a simple framework for one-class classification and anomaly detection. The core idea is to learn a mapping to transform the unknown distribution of training (normal) data to a known target distribution. Crucially, the target distribution should be sufficiently simple, compact, and informative. The simplicity is to ensure that we can sample from the distribution easily, the compactness is to ensure that the decision boundary between normal data and abnormal data is clear and reliable, and the informativeness is to ensure that the transformed data preserve the important information of the original data. Therefore, we propose to use truncated Gaussian, uniform in hypersphere, uniform on hypersphere, or uniform between hyperspheres, as the target distribution. We then minimize the distance between the transformed data distribution and the target distribution while keeping the reconstruction error for the original data small enough. Comparative studies on multiple benchmark datasets verify the effectiveness of our methods in comparison to baselines.

Deep Graph-Level Orthogonal Hypersphere Compression for Anomaly Detection

Graph-level anomaly detection aims to identify anomalous graphs from a collection of graphs in an unsupervised manner. A common assumption of anomaly detection is that a reasonable decision boundary has a hypersphere shape, but may appear some non-conforming phenomena in high dimensions. Towards this end, we firstly propose a novel deep graph-level anomaly detection model, which learns the graph representation with maximum mutual information between substructure and global structure features while exploring a hypersphere anomaly decision boundary. The idea is to ensure the training data distribution consistent with the decision hypersphere via an orthogonal projection layer. Moreover, we further perform the bi-hypersphere compression to emphasize the discrimination of anomalous graphs from normal graphs. Note that our method is not confined to graph data and is applicable to anomaly detection of other data such as images. The numerical and visualization results on benchmark datasets demonstrate the effectiveness and superiority of our methods in comparison to many baselines and state-of-the-arts.

Deep Graph-Level Clustering Using Pseudo-Label-Guided Mutual Information Maximization Network

In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously, although there have been a lot of work on node clustering and graph classification. The problem is challenging because it is difficult to measure the similarity or distance between graphs. One feasible approach is using graph kernels to compute a similarity matrix for the graphs and then performing spectral clustering, but the effectiveness of existing graph kernels in measuring the similarity between graphs is very limited. To solve the problem, we propose a novel method called Deep Graph-Level Clustering (DGLC). DGLC utilizes a graph isomorphism network to learn graph-level representations by maximizing the mutual information between the representations of entire graphs and substructures, under the regularization of a clustering module that ensures discriminative representations via pseudo labels. DGLC achieves graph-level representation learning and graph-level clustering in an end-to-end manner. The experimental results on six benchmark datasets of graphs show that our DGLC has state-of-the-art performance in comparison to many baselines.

Decoupled Cross-Scale Cross-View Interaction for Stereo Image Enhancement in The Dark

Low-light stereo image enhancement (LLSIE) is a relatively new task to enhance the quality of visually unpleasant stereo images captured in dark condition. However, current methods achieve inferior performance on detail recovery and illumination adjustment. We find it is because: 1) the insufficient single-scale inter-view interaction makes the cross-view cues unable to be fully exploited; 2) lacking long-range dependency leads to the inability to deal with the spatial long-range effects caused by illumination degradation. To alleviate such limitations, we propose a LLSIE model termed Decoupled Cross-scale Cross-view Interaction Network (DCI-Net). Specifically, we present a decoupled interaction module (DIM) that aims for sufficient dual-view information interaction. DIM decouples the dual-view information exchange into discovering multi-scale cross-view correlations and further exploring cross-scale information flow. Besides, we present a spatial-channel information mining block (SIMB) for intra-view feature extraction, and the benefits are twofold. One is the long-range dependency capture to build spatial long-range relationship, and the other is expanded channel information refinement that enhances information flow in channel dimension. Extensive experiments on Flickr1024, KITTI 2012, KITTI 2015 and Middlebury datasets show that our method obtains better illumination adjustment and detail recovery, and achieves SOTA performance compared to other related methods. Our codes, datasets and models will be publicly available.