Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey

Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular and powerful method for dimensionality reduction. Despite its extensive use, there remains a need for a comprehensive analysis of NMF in the context of dimensionality reduction. To address this gap, this paper presents a comprehensive survey of NMF, focusing on its applications in both feature extraction and feature selection. We introduce a classification of dimensionality reduction, enhancing understanding of the underlying concepts. Subsequently, we delve into a thorough summary of diverse NMF approaches used for feature extraction and selection. Furthermore, we discuss the latest research trends and potential future directions of NMF in dimensionality reduction, aiming to highlight areas that need further exploration and development.

A Survey on Diffusion Models for Time Series and Spatio-Temporal Data

The study of time series data is crucial for understanding trends and anomalies over time, enabling predictive insights across various sectors. Spatio-temporal data, on the other hand, is vital for analyzing phenomena in both space and time, providing a dynamic perspective on complex system interactions. Recently, diffusion models have seen widespread application in time series and spatio-temporal data mining. Not only do they enhance the generative and inferential capabilities for sequential and temporal data, but they also extend to other downstream tasks. In this survey, we comprehensively and thoroughly review the use of diffusion models in time series and spatio-temporal data, categorizing them by model category, task type, data modality, and practical application domain. In detail, we categorize diffusion models into unconditioned and conditioned types and discuss time series data and spatio-temporal data separately. Unconditioned models, which operate unsupervised, are subdivided into probability-based and score-based models, serving predictive and generative tasks such as forecasting, anomaly detection, classification, and imputation. Conditioned models, on the other hand, utilize extra information to enhance performance and are similarly divided for both predictive and generative tasks. Our survey extensively covers their application in various fields, including healthcare, recommendation, climate, energy, audio, and transportation, providing a foundational understanding of how these models analyze and generate data. Through this structured overview, we aim to provide researchers and practitioners with a comprehensive understanding of diffusion models for time series and spatio-temporal data analysis, aiming to direct future innovations and applications by addressing traditional challenges and exploring innovative solutions within the diffusion model framework.

Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Models

The open-world test dataset is often mixed with out-of-distribution (OOD) samples, where the deployed models will struggle to make accurate predictions. Traditional detection methods need to trade off OOD detection and in-distribution (ID) classification performance since they share the same representation learning model. In this work, we propose to detect OOD molecules by adopting an auxiliary diffusion model-based framework, which compares similarities between input molecules and reconstructed graphs. Due to the generative bias towards reconstructing ID training samples, the similarity scores of OOD molecules will be much lower to facilitate detection. Although it is conceptually simple, extending this vanilla framework to practical detection applications is still limited by two significant challenges. First, the popular similarity metrics based on Euclidian distance fail to consider the complex graph structure. Second, the generative model involving iterative denoising steps is time-consuming especially when it runs on the enormous pool of drugs. To address these challenges, our research pioneers an approach of Prototypical Graph Reconstruction for Molecular OOD Detection, dubbed as PGR-MOOD and hinges on three innovations: i) An effective metric to comprehensively quantify the matching degree of input and reconstructed molecules; ii) A creative graph generator to construct prototypical graphs that are in line with ID but away from OOD; iii) An efficient and scalable OOD detector to compare the similarity between test samples and pre-constructed prototypical graphs and omit the generative process on every new molecule. Extensive experiments on ten benchmark datasets and six baselines are conducted to demonstrate our superiority.

Gradformer: Graph Transformer with Exponential Decay

Graph Transformers (GTs) have demonstrated their advantages across a wide range of tasks. However, the self-attention mechanism in GTs overlooks the graph's inductive biases, particularly biases related to structure, which are crucial for the graph tasks. Although some methods utilize positional encoding and attention bias to model inductive biases, their effectiveness is still suboptimal analytically. Therefore, this paper presents Gradformer, a method innovatively integrating GT with the intrinsic inductive bias by applying an exponential decay mask to the attention matrix. Specifically, the values in the decay mask matrix diminish exponentially, correlating with the decreasing node proximities within the graph structure. This design enables Gradformer to retain its ability to capture information from distant nodes while focusing on the graph's local details. Furthermore, Gradformer introduces a learnable constraint into the decay mask, allowing different attention heads to learn distinct decay masks. Such an design diversifies the attention heads, enabling a more effective assimilation of diverse structural information within the graph. Extensive experiments on various benchmarks demonstrate that Gradformer consistently outperforms the Graph Neural Network and GT baseline models in various graph classification and regression tasks. Additionally, Gradformer has proven to be an effective method for training deep GT models, maintaining or even enhancing accuracy compared to shallow models as the network deepens, in contrast to the significant accuracy drop observed in other GT models.Codes are available at \url{https://github.com/LiuChuang0059/Gradformer}.

FedPFT: Federated Proxy Fine-Tuning of Foundation Models

Adapting Foundation Models (FMs) for downstream tasks through Federated Learning (FL) emerges a promising strategy for protecting data privacy and valuable FMs. Existing methods fine-tune FM by allocating sub-FM to clients in FL, however, leading to suboptimal performance due to insufficient tuning and inevitable error accumulations of gradients. In this paper, we propose Federated Proxy Fine-Tuning (FedPFT), a novel method enhancing FMs adaptation in downstream tasks through FL by two key modules. First, the sub-FM construction module employs a layer-wise compression approach, facilitating comprehensive FM fine-tuning across all layers by emphasizing those crucial neurons. Second, the sub-FM alignment module conducts a two-step distillations-layer-level and neuron-level-before and during FL fine-tuning respectively, to reduce error of gradient by accurately aligning sub-FM with FM under theoretical guarantees. Experimental results on seven commonly used datasets (i.e., four text and three vision) demonstrate the superiority of FedPFT.

IME: Integrating Multi-curvature Shared and Specific Embedding for Temporal Knowledge Graph Completion

Temporal Knowledge Graphs (TKGs) incorporate a temporal dimension, allowing for a precise capture of the evolution of knowledge and reflecting the dynamic nature of the real world. Typically, TKGs contain complex geometric structures, with various geometric structures interwoven. However, existing Temporal Knowledge Graph Completion (TKGC) methods either model TKGs in a single space or neglect the heterogeneity of different curvature spaces, thus constraining their capacity to capture these intricate geometric structures. In this paper, we propose a novel Integrating Multi-curvature shared and specific Embedding (IME) model for TKGC tasks. Concretely, IME models TKGs into multi-curvature spaces, including hyperspherical, hyperbolic, and Euclidean spaces. Subsequently, IME incorporates two key properties, namely space-shared property and space-specific property. The space-shared property facilitates the learning of commonalities across different curvature spaces and alleviates the spatial gap caused by the heterogeneous nature of multi-curvature spaces, while the space-specific property captures characteristic features. Meanwhile, IME proposes an Adjustable Multi-curvature Pooling (AMP) approach to effectively retain important information. Furthermore, IME innovatively designs similarity, difference, and structure loss functions to attain the stated objective. Experimental results clearly demonstrate the superior performance of IME over existing state-of-the-art TKGC models.

Foundation Models for Time Series Analysis: A Tutorial and Survey

Time series analysis stands as a focal point within the data mining community, serving as a cornerstone for extracting valuable insights crucial to a myriad of real-world applications. Recent advancements in Foundation Models (FMs) have fundamentally reshaped the paradigm of model design for time series analysis, boosting various downstream tasks in practice. These innovative approaches often leverage pre-trained or fine-tuned FMs to harness generalized knowledge tailored specifically for time series analysis. In this survey, we aim to furnish a comprehensive and up-to-date overview of FMs for time series analysis. While prior surveys have predominantly focused on either the application or the pipeline aspects of FMs in time series analysis, they have often lacked an in-depth understanding of the underlying mechanisms that elucidate why and how FMs benefit time series analysis. To address this gap, our survey adopts a model-centric classification, delineating various pivotal elements of time-series FMs, including model architectures, pre-training techniques, adaptation methods, and data modalities. Overall, this survey serves to consolidate the latest advancements in FMs pertinent to time series analysis, accentuating their theoretical underpinnings, recent strides in development, and avenues for future research exploration.

Online GNN Evaluation Under Test-time Graph Distribution Shifts

Evaluating the performance of a well-trained GNN model on real-world graphs is a pivotal step for reliable GNN online deployment and serving. Due to a lack of test node labels and unknown potential training-test graph data distribution shifts, conventional model evaluation encounters limitations in calculating performance metrics (e.g., test error) and measuring graph data-level discrepancies, particularly when the training graph used for developing GNNs remains unobserved during test time. In this paper, we study a new research problem, online GNN evaluation, which aims to provide valuable insights into the well-trained GNNs's ability to effectively generalize to real-world unlabeled graphs under the test-time graph distribution shifts. Concretely, we develop an effective learning behavior discrepancy score, dubbed LeBeD, to estimate the test-time generalization errors of well-trained GNN models. Through a novel GNN re-training strategy with a parameter-free optimality criterion, the proposed LeBeD comprehensively integrates learning behavior discrepancies from both node prediction and structure reconstruction perspectives. This enables the effective evaluation of the well-trained GNNs' ability to capture test node semantics and structural representations, making it an expressive metric for estimating the generalization error in online GNN evaluation. Extensive experiments on real-world test graphs under diverse graph distribution shifts could verify the effectiveness of the proposed method, revealing its strong correlation with ground-truth test errors on various well-trained GNN models.

Revisiting Edge Perturbation for Graph Neural Network in Graph Data Augmentation and Attack

Edge perturbation is a basic method to modify graph structures. It can be categorized into two veins based on their effects on the performance of graph neural networks (GNNs), i.e., graph data augmentation and attack. Surprisingly, both veins of edge perturbation methods employ the same operations, yet yield opposite effects on GNNs' accuracy. A distinct boundary between these methods in using edge perturbation has never been clearly defined. Consequently, inappropriate perturbations may lead to undesirable outcomes, necessitating precise adjustments to achieve desired effects. Therefore, questions of ``why edge perturbation has a two-faced effect?'' and ``what makes edge perturbation flexible and effective?'' still remain unanswered. In this paper, we will answer these questions by proposing a unified formulation and establishing a clear boundary between two categories of edge perturbation methods. Specifically, we conduct experiments to elucidate the differences and similarities between these methods and theoretically unify the workflow of these methods by casting it to one optimization problem. Then, we devise Edge Priority Detector (EPD) to generate a novel priority metric, bridging these methods up in the workflow. Experiments show that EPD can make augmentation or attack flexibly and achieve comparable or superior performance to other counterparts with less time overhead.

Graph Learning under Distribution Shifts: A Comprehensive Survey on Domain Adaptation, Out-of-distribution, and Continual Learning

Graph learning plays a pivotal role and has gained significant attention in various application scenarios, from social network analysis to recommendation systems, for its effectiveness in modeling complex data relations represented by graph structural data. In reality, the real-world graph data typically show dynamics over time, with changing node attributes and edge structure, leading to the severe graph data distribution shift issue. This issue is compounded by the diverse and complex nature of distribution shifts, which can significantly impact the performance of graph learning methods in degraded generalization and adaptation capabilities, posing a substantial challenge to their effectiveness. In this survey, we provide a comprehensive review and summary of the latest approaches, strategies, and insights that address distribution shifts within the context of graph learning. Concretely, according to the observability of distributions in the inference stage and the availability of sufficient supervision information in the training stage, we categorize existing graph learning methods into several essential scenarios, including graph domain adaptation learning, graph out-of-distribution learning, and graph continual learning. For each scenario, a detailed taxonomy is proposed, with specific descriptions and discussions of existing progress made in distribution-shifted graph learning. Additionally, we discuss the potential applications and future directions for graph learning under distribution shifts with a systematic analysis of the current state in this field. The survey is positioned to provide general guidance for the development of effective graph learning algorithms in handling graph distribution shifts, and to stimulate future research and advancements in this area.