Persistent homology (PH) has recently emerged as a powerful tool for extracting topological features. Integrating PH into both machine learning and deep learning models enhances their topology-awareness and interpretability. However, most PH methods on graphs rely on a limited set of filtrations (e.g., degree-or weight-based), which overlook richer features such as recurring information across the dataset, thereby restricting their expressive power. In this work, we propose a novel filtration on graphs, called Frequent Subgraph Filtration (FSF), which is derived from frequent subgraphs and produces stable and information-rich Frequency-based Persistent Homology (FPH) features. We explore the theoretical properties of FSF and provide proofs and experimental validations. Beyond persistent homology itself, we further introduce two approaches for graph classification: (i) an FPH-based machine learning model (FPH-ML), and (ii) a hybrid framework integrating FPH with graph neural networks (FPH-GNNs) to enhance topology-aware graph representation learning. Our proposed frameworks demonstrate the potential to bridge frequent subgraph mining and topological data analysis, providing a new perspective on topology-aware feature extraction and graph representation learning. Experimental results show that FPH-ML achieves competitive or superior accuracy compared to kernel-based and degree-based filtration methods. When injected into GNNs, FPH delivers relative gains of 0.4-21% (up to +8.2 pts) over their GCN/GIN backbones across benchmarks.

The analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The analytic continuation properties of the solution of an auxiliary problem in the Borel plane overcomes the absence of adequate domains which would guarantee summability of the formal solution. Moreover, several exponential decay rates of the difference of analytic solutions with respect to the perturbation parameter at the origin are observed, leading to several asymptotic levels relating the analytic and the formal solution.

Graphs have been widely used across scientific disciplines, from sociology to biology, particularly when modeling temporal evolution. Although many algorithms have been developed to discover patterns in graphs, they face three main limitations. First, most algorithms assume that each node or edge is associated with a single attribute, whereas real-world applications often involve multiple attributes to capture events more comprehensively. Second, existing methods typically require tuning several hyperparameters, which can vary significantly across different datasets. Third, most approaches focus on identifying frequent patterns, often overlooking rare but meaningful ones. To address these limitations, this paper proposes a framework for discovering anomalous sequences in attributed graphs. Instead of relying on frequency-based measures, the framework adopts an entropy-based method for pattern mining, thereby requiring at most one hyperparameter. Experimental results on real-world datasets demonstrate the effectiveness of the proposed approach in detecting anomalous sequences. Moreover, we extend the framework to applications in optics, where it is used to evaluate phase differences.

In this paper, we consider a general two-prey one-predator reaction–diffusion system with prey competition and double prey-taxis. We first present some preliminary results, including global-in-time existence and a priori estimates of classical solutions to this system with ratio-dependent and non-ratio-dependent predator functional responses. Our main concern is the global stability of spatially homogeneous coexistence steady states. For generalized prey-dependent models, we show that the global asymptotic stability of the coexistence steady state relates to two prey-taxis coefficients provided that the predator functional response, the conversion, and diffusion rates are given. Since there is little prospect of establishing a unified Lyapunov functional for the systems with a predator-dependent functional response, we propose an explicit predator-dependent model and construct the corresponding Lyapunov functional. The theoretical results can cover most three-species chemotaxis systems.

Accurate and efficient traffic flow prediction is crucial for modern urban transportation systems, directly impacting the effectiveness of intelligent traffic management and sustainable mobility solutions. Current spatio-temporal graph neural networks often fail to balance prediction accuracy and computational efficiency when modeling complex traffic patterns – a critical limitation for real-time applications requiring both precision and rapid processing. This paper presents UniTCP, a novel framework advancing urban traffic flow prediction through three key innovations: (1) The introduction of Universal Polynomial Basis (UniBasis) overcomes limitations of traditional spectral graph convolution by adaptively constructing optimal polynomial filters through data-driven learning, extending the concept of homophily ratio from node classification to multivariate time series forecasting and enabling dynamic modeling of complex spatial dependencies across heterogeneous traffic networks. (2) The innovative Temporal Convolutional Projection Module (TCPM) synergizes multi-scale convolutional branches with trend-aware pooling to comprehensively capture both transient traffic fluctuations and persistent periodic patterns, establishing a new paradigm for efficient temporal feature extraction. (3) A unified architecture integrating node-adaptive parameter learning with time-variant graph structure generation achieves optimal performance-efficiency balance through spectral domain parameterization and spatio-temporal embedding fusion. Experimental validation across four public datasets confirms the framework’s superior performance in addressing three core challenges: precise modeling of nonlinear spatio-temporal dependencies, computational resource optimization, and effective generalization across diverse traffic networks. The results demonstrate significant improvements in both prediction accuracy and operational efficiency compared to existing state-of-the-art approaches.

High frequency and utility are two crucial objectives in data mining, as they provide valuable insights for decision-making. Most frequent-utility pattern mining methods rely on threshold-based approaches, which can inadvertently overlook itemsets with low frequency but high utility, or those with low utility but high frequency. Skyline frequent-utility pattern mining addresses this limitation by capturing patterns that are optimal across both dimensions. However, existing skyline algorithms are primarily designed for static databases. In real-world scenarios, databases typically receive new transactions incrementally, necessitating an efficient algorithm to find skyline frequent-utility patterns in dynamic environments. This paper introduces the ISFUM (Incremental Skyline Frequent-Utility Mining) algorithm, which efficiently discovers skyline frequent-utility itemsets in dynamic transaction databases. By utilising global and local utility-lists, ISFUM avoids rescanning the original database during incremental updates. Additionally, we have developed novel pruning strategies to further reduce computational time by minimising unnecessary candidate validation. Experimental results demonstrate that our algorithm is both efficient and effective in handling dynamic data environments.

Graph mining has become popular for discovering valuable information as graph databases grow. Two primary challenges in graph mining within large-scale graph databases include designing effective support measures and managing computational resource costs. Specifically, it is difficult to achieve a balance between fast runtime, low memory consumption, and practical support because of issues such as isomorphism and overlap. This paper focuses on frequent pattern extraction and mining optimization in single graphs. We introduce a novel spanning hypertree framework that unifies support measures and elucidates the interrelationships among four measures: maximum independent edge set (MIES), minimum vertex cover (MVC), minimum instance (MI), and minimum-image-based (MNI). Within this framework, we preserve vertex information for pattern extension while reducing redundancy from hyperedges covering the same vertices, thereby improving search efficiency. Although MIES and MVC are NP-hard in hypergraphs, we prove that MIES is polynomial-time solvable in the spanning hypertree setting and that MVC admits a polynomial-time linear programming relaxation. We show that support measures hold the anti-monotonicity property in this framework and establish bounding theorems between hypergraphs and spanning hypertree. Experiments demonstrate that the hypertrees framework significantly outperforms the hypergraph framework in runtime and memory usage, especially for MVC.

With a user-specified minimum utility threshold (minutil), periodic high-utility pattern mining (PHUPM) aims to identify high-utility patterns that occur periodically in a transaction database. A pattern is deemed periodic if its period aligns with the periodicity constraint set by the user. However, users may not be interested in all periodic high-utility patterns (PHUPs). Moreover, setting minutil in advance is also a challenging issue. To address these issues, our research introduces an algorithm called TPU for extracting the most significant top-k periodic and high-utility patterns that may or may not include negative utility values. This TPU algorithm utilizes positive and negative utility lists (PNUL) and period-estimated utility co-occurrence structure (PEUCS) to store pertinent itemset information. Additionally, it incorporates the periodic real item utility (PIU), periodic co-occurrence utility descending (PCUD), and periodic real utility (PRU) threshold-raising strategies to elevate the thresholds rapidly. By using the proposed threshold-raising strategies, the runtime was reduced by approximately 5 https://github.com/DSI-Lab1/TPU .

Frequent subgraph mining is a fundamental task in data mining, widely applied in various domains such as biological networks, social networks, and computing networks. However, existing methods for frequent subgraph mining often rely solely on support as a single metric, considering subgraphs with higher support as more important. This approach overlooks the intrinsic value of subgraphs, such as in citation networks, where users tend to associate with structures related to their own research areas, not only the frequent ones. To address this limitation, we introduce utility pattern mining into the field of subgraph mining. This mining framework considers both the internal and external values of patterns. Additionally, traditional frequent subgraph mining is hindered by isomorphism calculations, including the computational cost of subgraph isomorphism, which is NP-complete. As a connected acyclic graph, free trees play a significant role in fields such as web mining and biology. Their relatively simple structure can significantly reduce the computational cost of subgraph isomorphism calculations. In this paper, we combine utility pattern mining with frequent free tree mining, defining the problem of frequent high utility free tree mining. We design utility upper bounds that satisfy the downward closure property and propose an algorithm, UFTM (utility free tree miner), for effectively and efficiently mining utility free trees. Furthermore, we collect and test our algorithm on four real-world datasets. The results demonstrate that UFTM can discover more valuable patterns and execute the mining task efficiently.

Because most data in the real world can be represented in graph structures, graph mining is essential in many fields. In recent decades, research on algorithms for mining frequent subgraphs in graph databases has matured. In addition to frequent patterns, periodic and closed patterns are important in real life. However, the definition of periodic patterns in the precedent study is rigorous and has certain limitations, so that many approximate periodic patterns cannot be mined. Thus, based on the study of periodic patterns in itemset databases, we define periodic frequent subgraphs (PFSs) in dynamic graphs using the three measures: average periodicity, maximum periodicity, and minimum periodicity. The task of PFS mining is to discover all the PFSs in a given database. We propose the PFS Miner (PFSM) algorithm to realize this task. In addition, we propose closed PFSs (CPFSs) and the corresponding mining algorithm named CPFS Miner (CPFSM) to make the excavated periodic frequent patterns more concise. Finally, we conduct experiments on real datasets to analyze the performance of the algorithms. The experimental results indicate that the PFSM algorithm can mine meaningful periodic frequent patterns and CPFSM can mine closed periodic frequent patterns with good efficiency and performance.

Real-world time series are influenced by numerous factors and exhibit complex non-stationary characteristics. Non-stationarity can lead to distribution shifts, where the statistical properties of time series change over time, negatively impacting model performance. Several instance normalization techniques have been proposed to address distribution shifts in time series forecasting. However, existing methods fail to account for shifts within individual instances, leading to suboptimal performance. To tackle inner-instance distribution shifts, we propose two novel point-level methods: Learning Distribution (LD) and Learning Conditional Distribution (LCD). LD eliminates internal discrepancies by fitting the internal distribution of input and output with different parameters at different time steps, while LCD utilizes neural networks to predict scaling coefficients of the output. We evaluate the performance of the two methods with various backbone models across public benchmarks and demonstrate the effectiveness of the point-level paradigm through comparative experiments.

While high utility mining aims to identify patterns that maximize profits, low utility mining (LUIM) focuses on uncovering exceptional patterns, enabling proactive interventions before issues escalate. Existing high utility itemset mining methods use upper-bound pruning to reduce the search space. However, this approach is ineffective for LUIM, as it inadvertently eliminates low utility itemsets (LUIs). In addition, LUIM struggles with distinguishing between LUIs and zero-utility candidates. These challenges in LUIM can be summarized as follows: (1) reducing the search space of LUIM, and (2) distinguishing genuine LUIs from zero-utility candidates. To address these issues, we propose LUIMiner, an algorithm designed to accurately and efficiently find the complete set of LUIs. LUIMiner incorporates two lower-bound pruning strategies—depth and width—to reduce search space and streamline the mining process. We also introduce a redesigned search tree that processes candidates from long to short, enabling effective lower-bound-based pruning. Additionally, a preprocessing phase filters out zero-utility itemsets early in the process by calculation of maximal non-mutually contained itemsets. The Bgenerator structure uses bitwise operations to accelerate computations and reduce database scans. Experimental comparisons with state-of-the-art LUG-Miner & LUIMA demonstrate the effectiveness and efficiency of our algorithm.

Mining various patterns in dynamic graphs is a crucial task across many domains, including social networks, web analysis, and epidemiology. This paper addresses the challenge of mining multiple attributes associated with vertices in evolving large graphs over time. Current approaches to mining attributed sequences in graph databases often overlook inter-element correlations or rely on user-defined measures to prune, limiting their universality. To address this, we present a generic framework for extracting graph sequences with various interestingness measures in dynamic attributed graphs by extending support and confidence concepts. The novel support with the anti-monotonic property reduces the search space. Additionally, we introduce adaptable support and confidence measures tailored to graph sequence mining. The proposed IS-Miner algorithm liberates the pruning strategy from specific interestingness measures. Experimental evaluations on both real-life and synthetic databases validate the efficiency and effectiveness of our approach, particularly in scenarios involving multiple attributes.

Graph neural networks (GNNs) have brought revolutionary advancements to the field of link prediction (LP), providing powerful tools for mining potential relationships in graphs. However, existing methods face challenges when dealing with large-scale sparse graphs and the need for a high degree of alignment between different datasets in transfer learning. Besides, although self-supervised methods have achieved remarkable success in many graph tasks, prior research has overlooked the potential of transfer learning to generalize across different graph datasets. To address these limitations, we propose a novel Graph Attention Adaptive Transfer Network (GAATNet). It combines the advantages of pre-training and fine-tuning to capture global node embedding information across datasets of different scales, ensuring efficient knowledge transfer and improved LP performance. To enhance the model's generalization ability and accelerate training, we design two key strategies: 1) Incorporate distant neighbor embeddings as biases in the self-attention module to capture global features. 2) Introduce a lightweight self-adapter module during fine-tuning to improve training efficiency. Comprehensive experiments on seven public datasets demonstrate that GAATNet achieves state-of-the-art performance in LP tasks. This study provides a general and scalable solution for LP tasks to effectively integrate GNNs with transfer learning. The source code and datasets are publicly available at https://github.com/DSI-Lab1/GAATNet

Knowledge discovery plays a pivotal role in the field of Artificial Intelligence as it involves extracting valuable and previously unknown patterns (information, insights) from vast datasets. Skyline pattern mining emerges to deal with multiple-objective knowledge discovery in a threshold-free manner. Existing Skyline pattern mining methods mainly have two limitations: they only settle the problem with the restriction in dimension two, which is not applicable in dimension three or more; they focus on frequency and utility (monetary) without considering the temporal information. In this paper, we aim to overcome those limitations by proposing the problem model for finding skyline patterns considering three dimensions: recency, frequency, and monetary. We also define degrees of constraints to formulate strict/weak skyline patterns and present algorithms to mine them. Several pruning strategies are designed to reduce the search space. The max monetary score matrix structure and corresponding sparse storage are designed to facilitate the implementation of the pruning strategies. The skyline pattern storage matrix helps to add and delete patterns in the mining process efficiently. Experimental results show that the proposed algorithms discover more patterns without losing to the baseline. The runtime difference is usually within 10s without a clear winner. The proposed method wins tens to hundreds of megabytes of memory in most cases.

Recent research demonstrates that linear models achieve forecasting performance competitive with complex architectures, yet methodologies for enhancing linear models remain underexplored. Motivated by the hypothesis that distinct time series instances may follow heterogeneous linear mappings, we propose the Classification Auxiliary Trend-Seasonal Decoupling Linear Model CATS-Linear, employing Classification Auxiliary Channel-Independence (CACI). CACI dynamically routes instances to dedicated predictors via classification, enabling supervised channel design. We further analyze the theoretical expected risks of different channel settings. Additionally, we redesign the trend-seasonal decomposition architecture by adding a decoupling – linear mapping – recoupling framework for trend components and complex-domain linear projections for seasonal components. Extensive experiments validate that CATS-Linear with fixed hyperparameters achieves state-of-the-art accuracy comparable to hyperparameter-tuned baselines while delivering SOTA accuracy against fixed-hyperparameter counterparts.

Pattern mining is a crucial area in data mining focused on discovering interesting patterns, primarily aiming to assess frequency and utility. However, existing approaches often overlook the full potential of temporal indicators. Two key aspects remain underexplored: (1) the greater value of recent past data compared to older data (temporal weight) and (2) the significance of temporal trends over simply observing data magnitudes (temporal trend). Some patterns may exhibit high utility initially; however, decline over time, resulting in low utility in later stages. Traditional methods classify these as high utility patterns (HUPs); however, when considering temporal weight and trend, they differ from true HUPs and are termed short-sighted patterns. Identifying these patterns helps avoid misleading conclusions and assists decision-makers in understanding the reasons behind declining utility, allowing for more effective strategies to address implicit losses. This study introduces the concept of short-sighted itemset mining (SSIM) and prior short-sighted itemset mining (PSSIM) by leveraging temporal indicators. We present two algorithms, SSIM and PSSIM, designed to address these problems. These algorithms employ new lists to minimize redundant database scans and implement innovative pruning strategies to filter out irrelevant candidates. Experimental results demonstrate the effectiveness and efficiency of both algorithms.

The identification of drug-gene associations is crucial for advancing drug development and personalized medicine. However, this task is challenging due to the intricate interactions between drugs and genetic factors. Recent advancements in artificial intelligence (AI), particularly with the use of graph neural networks (GNNs), have shown potential in this domain. GNNs are effective in exploring drug-gene relationships, but they have limitations such as over-smoothing and inadequate learning of internal gene relationships. In this paper, we propose an improved GNN-based framework called Drug-Gene Associations with Graph Learning (GLDGA) that incorporates graph sample and aggregation techniques, along with a diffusion learning perspective. This new approach aims to overcome existing limitations by enhancing the GLDGA's ability to generalize. It also seeks to better capture gene relationships. Our method outperforms current leading algorithms for predicting drug-gene associations, demonstrating significant progress in computational drug discovery.

Graph mining has numerous real-world applications. The goal is to extract interesting subgraphs or patterns in graph databases. Dynamic attributed graphs are more complex databases in which graphs change over time, and each vertex has multiple attributes. However, most algorithms only pay attention to finding rules that show relationships between nodes, and they typically have substantial limitations, such as finding rules with a single attribute or vertex and edges that do not change over time. To address these limitations, we propose an algorithm called CAR-Miner, which aims to mine credible attribute rules in dynamic attributed graphs. The algorithm incorporates a novel objective interestingness measure that is stable, anti-monotonic, and can eliminate cross-support core patterns. We conducted several experiments on real-life databases. The results show that our algorithm outperforms the state-of-the-art algorithm, especially as the number of attributes increases. Additionally, we find patterns that have practical significance and can be interpreted in various ways. Overall, CAR-Miner is a promising algorithm for mining patterns in dynamic attributed graphs, which can help researchers and practitioners identify valuable patterns that were previously difficult to discover.

Graph data-based mining is vital in various fields, such as business management, chemistry, and social networks. Frequency-based frameworks have limitations regarding large mining output. In many real-world scenarios, not all frequent patterns hold significant meaning. To address this issue, concise representation such as closed patterns is proposed. Unfortunately, existing methods utilize support or occurrence as frequency measurements, which have drawbacks. Support overlooks the isomorphic quantity of a single graph, while occurrence lacks the downward closure property. In this paper, we introduce an approach for mining frequent closed subgraphs. A novel measure MMNI (multiple minimum node image) is introduced to strike a balance between support and occurrence measures. Additionally, we design a novel structure to store occurrence information. We develop a pruning strategy and employ an early termination strategy to enhance efficiency. To evaluate the performance of our algorithm, we conduct experiments on seven real datasets, considering four aspects. The results demonstrate that our algorithm has high efficiency and performance compared to the state-of-the-art algorithm for closed subgraph mining. In several cases, our method requires only 50% of the time consumed by previous approaches. We also present a real-world application example in the domain of bike-sharing systems.