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Graph clustering is a fundamental problem in machine learning. Deep learning methods achieve the state-of-the-art results in recent years, but they still cannot work without predefined cluster numbers. Such limitation motivates us to pose a more challenging problem of graph clustering with unknown cluster number. We propose to address this problem from a fresh perspective of graph information theory (i.e., structural information). In the literature, structural information has not yet been introduced to deep clustering, and its classic definition falls short of discrete formulation and modeling node features. In this work, we first formulate a differentiable structural information (DSI) in the continuous realm, accompanied by several theoretical results. By minimizing DSI, we construct the optimal partitioning tree where densely connected nodes in the graph tend to have the same assignment, revealing the cluster structure. DSI is also theoretically presented as a new graph clustering objective, not requiring the predefined cluster number. Furthermore, we design a neural LSEnet in the Lorentz model of hyperbolic space, where we integrate node features to structural information via manifold-valued graph convolution. Extensive empirical results on real graphs show the superiority of our approach., Comment: Accepted by ICML24, 26 pages

Semi-supervised clustering techniques have emerged as valuable tools for leveraging prior information in the form of constraints to improve the quality of clustering outcomes. Despite the proliferation of such methods, the ability to seamlessly integrate various types of constraints remains limited. While structural entropy has proven to be a powerful clustering approach with wide-ranging applications, it has lacked a variant capable of accommodating these constraints. In this work, we present Semi-supervised clustering via Structural Entropy (SSE), a novel method that can incorporate different types of constraints from diverse sources to perform both partitioning and hierarchical clustering. Specifically, we formulate a uniform view for the commonly used pairwise and label constraints for both types of clustering. Then, we design objectives that incorporate these constraints into structural entropy and develop tailored algorithms for their optimization. We evaluate SSE on nine clustering datasets and compare it with eleven semi-supervised partitioning and hierarchical clustering methods. Experimental results demonstrate the superiority of SSE on clustering accuracy with different types of constraints. Additionally, the functionality of SSE for biological data analysis is demonstrated by cell clustering experiments conducted on four single-cell RNAseq datasets., Comment: 9 pages, 3 figures, accepted by SDM 2024

Traffic forecasting is a complex multivariate time-series regression task of paramount importance for traffic management and planning. However, existing approaches often struggle to model complex multi-range dependencies using local spatiotemporal features and road network hierarchical knowledge. To address this, we propose MultiSPANS. First, considering that an individual recording point cannot reflect critical spatiotemporal local patterns, we design multi-filter convolution modules for generating informative ST-token embeddings to facilitate attention computation. Then, based on ST-token and spatial-temporal position encoding, we employ the Transformers to capture long-range temporal and spatial dependencies. Furthermore, we introduce structural entropy theory to optimize the spatial attention mechanism. Specifically, The structural entropy minimization algorithm is used to generate optimal road network hierarchies, i.e., encoding trees. Based on this, we propose a relative structural entropy-based position encoding and a multi-head attention masking scheme based on multi-layer encoding trees. Extensive experiments demonstrate the superiority of the presented framework over several state-of-the-art methods in real-world traffic datasets, and the longer historical windows are effectively utilized. The code is available at https://github.com/SELGroup/MultiSPANS., Comment: 10 pages, 7 figures, conference. The work has been accepted by WSDM2024

Skin lesion segmentation is a fundamental task in dermoscopic image analysis. The complex features of pixels in the lesion region impede the lesion segmentation accuracy, and existing deep learning-based methods often lack interpretability to this problem. In this work, we propose a novel unsupervised Skin Lesion sEgmentation framework based on structural entropy and isolation forest outlier Detection, namely SLED. Specifically, skin lesions are segmented by minimizing the structural entropy of a superpixel graph constructed from the dermoscopic image. Then, we characterize the consistency of healthy skin features and devise a novel multi-scale segmentation mechanism by outlier detection, which enhances the segmentation accuracy by leveraging the superpixel features from multiple scales. We conduct experiments on four skin lesion benchmarks and compare SLED with nine representative unsupervised segmentation methods. Experimental results demonstrate the superiority of the proposed framework. Additionally, some case studies are analyzed to demonstrate the effectiveness of SLED., Comment: 10 pages, 8 figures, conference. Accepted by IEEE ICDM 2023

State abstraction optimizes decision-making by ignoring irrelevant environmental information in reinforcement learning with rich observations. Nevertheless, recent approaches focus on adequate representational capacities resulting in essential information loss, affecting their performances on challenging tasks. In this article, we propose a novel mathematical Structural Information principles-based State Abstraction framework, namely SISA, from the information-theoretic perspective. Specifically, an unsupervised, adaptive hierarchical state clustering method without requiring manual assistance is presented, and meanwhile, an optimal encoding tree is generated. On each non-root tree node, a new aggregation function and condition structural entropy are designed to achieve hierarchical state abstraction and compensate for sampling-induced essential information loss in state abstraction. Empirical evaluations on a visual gridworld domain and six continuous control benchmarks demonstrate that, compared with five SOTA state abstraction approaches, SISA significantly improves mean episode reward and sample efficiency up to 18.98 and 44.44%, respectively. Besides, we experimentally show that SISA is a general framework that can be flexibly integrated with different representation-learning objectives to improve their performances further.

Automatic and periodic recompiling of building databases with up-to-date high-resolution images has become a critical requirement for rapidly developing urban environments. However, the architecture of most existing approaches for change extraction attempts to learn features related to changes but ignores objectives related to buildings. This inevitably leads to the generation of significant pseudo-changes, due to factors such as seasonal changes in images and the inclination of building fa\c{c}ades. To alleviate the above-mentioned problems, we developed a contrastive learning approach by validating historical building footprints against single up-to-date remotely sensed images. This contrastive learning strategy allowed us to inject the semantics of buildings into a pipeline for the detection of changes, which is achieved by increasing the distinguishability of features of buildings from those of non-buildings. In addition, to reduce the effects of inconsistencies between historical building polygons and buildings in up-to-date images, we employed a deformable convolutional neural network to learn offsets intuitively. In summary, we formulated a multi-branch building extraction method that identifies newly constructed and removed buildings, respectively. To validate our method, we conducted comparative experiments using the public Wuhan University building change detection dataset and a more practical dataset named SI-BU that we established. Our method achieved F1 scores of 93.99% and 70.74% on the above datasets, respectively. Moreover, when the data of the public dataset were divided in the same manner as in previous related studies, our method achieved an F1 score of 94.63%, which surpasses that of the state-of-the-art method.

Graph Neural Networks (GNNs) are de facto solutions to structural data learning. However, it is susceptible to low-quality and unreliable structure, which has been a norm rather than an exception in real-world graphs. Existing graph structure learning (GSL) frameworks still lack robustness and interpretability. This paper proposes a general GSL framework, SE-GSL, through structural entropy and the graph hierarchy abstracted in the encoding tree. Particularly, we exploit the one-dimensional structural entropy to maximize embedded information content when auxiliary neighbourhood attributes are fused to enhance the original graph. A new scheme of constructing optimal encoding trees is proposed to minimize the uncertainty and noises in the graph whilst assuring proper community partition in hierarchical abstraction. We present a novel sample-based mechanism for restoring the graph structure via node structural entropy distribution. It increases the connectivity among nodes with larger uncertainty in lower-level communities. SE-GSL is compatible with various GNN models and enhances the robustness towards noisy and heterophily structures. Extensive experiments show significant improvements in the effectiveness and robustness of structure learning and node representation learning., Comment: 12 pages,5 figures, accepted by WWW2023

Structural entropy is a metric that measures the amount of information embedded in graph structure data under a strategy of hierarchical abstracting. To measure the structural entropy of a dynamic graph, we need to decode the optimal encoding tree corresponding to the best community partitioning for each snapshot. However, the current methods do not support dynamic encoding tree updating and incremental structural entropy computation. To address this issue, we propose Incre-2dSE, a novel incremental measurement framework that dynamically adjusts the community partitioning and efficiently computes the updated structural entropy for each updated graph. Specifically, Incre-2dSE includes incremental algorithms based on two dynamic adjustment strategies for two-dimensional encoding trees, i.e., the naive adjustment strategy and the node-shifting adjustment strategy, which support theoretical analysis of updated structural entropy and incrementally optimize community partitioning towards a lower structural entropy. We conduct extensive experiments on 3 artificial datasets generated by Hawkes Process and 3 real-world datasets. Experimental results confirm that our incremental algorithms effectively capture the dynamic evolution of the communities, reduce time consumption, and provide great interpretability.

In recent years, online ride-hailing platforms have become an indispensable part of urban transportation. After a passenger is matched up with a driver by the platform, both the passenger and the driver have the freedom to simply accept or cancel a ride with one click. Hence, accurately predicting whether a passenger-driver pair is a good match turns out to be crucial for ride-hailing platforms to devise instant order assignments. However, since the users of ride-hailing platforms consist of two parties, decision-making needs to simultaneously account for the dynamics from both the driver and the passenger sides. This makes it more challenging than traditional online advertising tasks. Moreover, the amount of available data is severely imbalanced across different cities, creating difficulties for training an accurate model for smaller cities with scarce data. Though a sophisticated neural network architecture can help improve the prediction accuracy under data scarcity, the overly complex design will impede the model's capacity of delivering timely predictions in a production environment. In the paper, to accurately predict the MSR of passenger-driver, we propose the Multi-View model (MV) which comprehensively learns the interactions among the dynamic features of the passenger, driver, trip order, as well as context. Regarding the data imbalance problem, we further design the Knowledge Distillation framework (KD) to supplement the model's predictive power for smaller cities using the knowledge from cities with denser data and also generate a simple model to support efficient deployment. Finally, we conduct extensive experiments on real-world datasets from several different cities, which demonstrates the superiority of our solution., Comment: This article is accepted as a regular paper in an upcoming issue of the Transactions on Knowledge and Data Engineering

In recent years, ride-hailing services have been increasingly prevalent as they provide huge convenience for passengers. As a fundamental problem, the timely prediction of passenger demands in different regions is vital for effective traffic flow control and route planning. As both spatial and temporal patterns are indispensable passenger demand prediction, relevant research has evolved from pure time series to graph-structured data for modeling historical passenger demand data, where a snapshot graph is constructed for each time slot by connecting region nodes via different relational edges (e.g., origin-destination relationship, geographical distance, etc.). Consequently, the spatiotemporal passenger demand records naturally carry dynamic patterns in the constructed graphs, where the edges also encode important information about the directions and volume (i.e., weights) of passenger demands between two connected regions. However, existing graph-based solutions fail to simultaneously consider those three crucial aspects of dynamic, directed, and weighted (DDW) graphs, leading to limited expressiveness when learning graph representations for passenger demand prediction. Therefore, we propose a novel spatiotemporal graph attention network, namely Gallat (Graph prediction with all attention) as a solution. In Gallat, by comprehensively incorporating those three intrinsic properties of DDW graphs, we build three attention layers to fully capture the spatiotemporal dependencies among different regions across all historical time slots. Moreover, the model employs a subtask to conduct pretraining so that it can obtain accurate results more quickly. We evaluate the proposed model on real-world datasets, and our experimental results demonstrate that Gallat outperforms the state-of-the-art approaches.

In this paper, we study the asymptotic behavior of Asian option prices in the worst case scenario under an uncertain volatility model. We give a procedure to approximate the Asian option prices with a small volatility interval. By imposing additional conditions on the boundary condition and cutting the obtained Black-Scholes-Barenblatt equation into two Black-Scholes-like equations, we obtain an approximation method to solve the fully nonlinear PDE., Comment: 19pages