Mining regional co-location pattern (RCP) in urban areas can reveal local correlations among urban facilities, which can inform urban planning and development. However, existing mining methods lack considerations of user demand for temporal accessibility and user preferences for the regional structure. Therefore, the mined results may be impractical. To address these issues, we propose a novel RCP mining method with temporal accessibility and regional structure (TARS). First, we utilized travel time as a measure of temporal accessibility between instances and proposed the concept of an accessible path to develop a method to regionalize temporal accessibility. To enhance efficiency, we developed a neighbor search algorithm and two pruning strategies to accelerate regional division. Second, we propose a measure called spatial region preference (SRP) to help select the preferred RCPs. Extensive experiments conducted on synthetic and real datasets show that our proposed RCP mining algorithm can discover more practical patterns and run faster than the selected baseline algorithms.

Spatial co-location pattern mining aims to discover sets of spatial features that prevalently occur together. However, existing methods for local co-location pattern (LCP) mining often yield prevalent regions with limited spatial coverage, resulting in the overestimation of pattern interest measures and the omission of implicit spatial associations. Furthermore, the distinction between pattern categories is often obscured, as global co-location patterns can be regarded as special cases of LCPs. To address these limitations, we propose a novel framework that can identify prevalent regions with broader coverage and achieve clear pat tern classification. We first prove that the problem of maximizing each prevalent region is NP-hard. Then we formally define the concept of maximal prevalent regions as a viable alternative and develop a heuristic dynamic spatial expansion algorithm for their efficient identification. In addition, we introduce a spatial occu pancy ratio and a three-level classification scheme (rare, common, and significant) to replace the traditional global/local dichotomy. Finally, a Delaunay-triangulation-based method is employed to quantify the coverage of non-convex regions, ensuring accurate occupancy calculations. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness and efficiency of the proposed framework.

Multivariate time series (MTS) forecasting is crucial for predicting the future states of complexly coupled variables based on historical observations. To effectively capture the intricate interdependencies within MTS, graph-based methods have emerged as powerful tools. However, existing graph construction methods often produce structures that fail to preserve key temporal and cross-variable dependencies, introducing redundant or irrelevant connections. To address these challenges, we propose a structural entropy-based approach for MTS forecasting. The approach optimizes graph structures by reducing structural redundancy, thereby improving forecasting accuracy. Initially, we represent the temporal dependences by constructing an encoding tree incrementally. Through hierarchical organization of time steps, the temporal evolution is adaptively captured. Subsequently, we give the community-aware representation by building an encoding tree over the variables in MTS, extracting homogeneous communities from the tree structure while integrating community influence to better capture inter-variable dependencies. Finally,we present a training algorithm designed to generate accurate predictions for MTS, accompanied by a unified loss function that integrates forecasting inaccuracies with variations in structural entropy. Empirical findings on real-world datasets substantiate that our approach outperforms state-of-the-art models in capturing dependencies and enhancing forecasting precision.

The task of finding associative entities in knowledge graph (KG) is to provide a ranking list of entities according to their association degrees. However, many entities are not only linked in KG but also associated in terms of user behaviors, which facilitates finding associative entities accurately. This manuscript incorporates KG with user-generated data to propose the Association Entity Graph Model (AEGM) to evaluate the association degrees. They first propose the joint weighting function to evaluate the entity associations and prove its submodularity theoretically as well as the greedy algorithm to select the candidates efficiently. They define the entity association information to score the entity association and give the hill climbing search based algorithm for AEGM construction. Following, they embed AEGM to calculate the association degrees and obtain the associative entities efficiently. Extensive experiments on three datasets show that the proposed method can achieve a better performance than some state-of-the-art competitors in accurately finding associative entities.

Abstract Discovering the correlation relationships of spatial facilities in urban functional regions is of great significance in analyzing urban planning and promoting urban development. However, existing regional co-location pattern mining methods do not fully consider the attributes of urban functional regions. Consequently, they fail to effectively capture the relationships between spatial facilities and regions, resulting in patterns lacking practical application value and interpretability. To address this issue, this paper proposes a novel regional co-location pattern (RCP) mining method based on urban functional region division. First, an ontology-based method for urban functional region division is proposed. On the basis of dividing urban functional regions, the expected mean distance is generated to adaptively calculate the neighbor relationships between instances in each region, and a parallel algorithm is designed to quickly mine RCPs in urban functional regions. Then, the correlation coefficient ( $$CC_{RP}$$ C C RP ) measures the association strength between RCP and function type to provide interpretability for RCPs. Finally, extensive experiments on real-world datasets are conducted to verify the effectiveness of urban functional region partition and to demonstrate the superiority of the proposed RCP mining method.

The spatial co-location pattern is a collection of spatial features in which instances of features prevalently appear in neighboring spatial regions. Due to the heterogeneity of spatial data distribution, the instances of some patterns appear prevalently in the global region (i.e., Global Prevalent Co-location Patterns, GPCPs), while some patterns are not prevalent globally, and their instances are clustered only in some local regions (i.e., Local Prevalent Co-location Patterns, LPCPs). Multi-level co-location pattern mining aims to mine these two types of patterns simultaneously, but existing methods cannot accurately judge the spatial distribution of patterns in a certain region, leading to unsuitable judgment of both GPCPs and LPCPs. To overcome this problem, this paper firstly proposes the relative distribution coefficient to identify the spatial distribution form of patterns, and provides a more refined way for discovering both GPCPs and LPCPs. Secondly, a novel multi-level co-location pattern mining algorithm is proposed by using the relative distribution coefficient as the interest metrics, and some pruning strategies are suggested to improve the mining efficiency. Finally, extensive experiments are conducted on both real and synthetic datasets to verify the effectiveness and efficiency of the proposed method.

Community search (CS) is an important research topic in network analysis, which aims to find a subgraph that satisfies the given conditions. A dynamic attribute heterogeneous information network (DAHIN) is a sequence of attribute heterogeneous information network (AHIN) snapshots, where each snapshot consists of multiple types of vertices as well as edges, and each vertex is associated a set of attribute keywords. CS over DAHIN faces many challenges. In this paper, we study the CS problem over DAHINs, aiming to search for cohesive subgraphs containing query vertex and simultaneously satisfying the connectivity, attribute cohesiveness and interaction stability. To this end, we propose a deep learning model with a three-level attention mechanism and the concept of interaction frequency with respect to multiple semantic relationships to measure the similarity of attributes and the stability of interactions between vertices respectively. In addition, we design three search algorithms to locate the target community by optimizing the degree of interaction stability and attribute similarity between vertices. Extensive experiments, including comparison with existing algorithms, ablation analysis, parameter sensitivity examination, and case studies, are conducted on four real-world datasets to validate the effectiveness and efficiency of the proposed model and search algorithms. The code and model of CS-DAHIN will be open source on GitHub.

Spatial co-location pattern mining (SCPM) aims to discover subsets of spatial features frequently located in nearby geographic space. Previous studies of SCPM only concern the inter-features association of a pattern, but neglect the interesting intra-feature behavior. In this paper, we propose spatial co-location pattern mining with coupling relation consideration (SCPM-CR) to capture complex relations in a co-location. Specifically, InterPCI is proposed to capture the inter-features coupling in a pattern, and IntraCAI is designed to capture the congregating behavior of intra-feature objects. Based on the anti-monotone property of InterPCI, a general framework which searches for patterns in a level-wise manner is suggested. To tackle the participating object search problem, a candidate-and-search algorithm with a heuristic backtracking search is proposed, namely CS-HBS. Extensive experiments are conducted to demonstrate the superiority of SCPM-CR, and also to validate the efficiency and scalability of CS-HBS.

Spatial co-location pattern mining (SCPM) aims to discover subsets of spatial features frequently located together in proximate areas. Previous studies of SCPM solely concern the inter-features association of a pattern, but neglect the interesting intra-feature behavior. In this paper, we propose the task of spatial co-location pattern mining with coupling relation consideration (SCPM-CR) to capture complex relations embedded in a co-location. Specifically, InterPCI measure is designed to capture the inter-features coupling by considering the comprehensive interaction of objects for the features in a pattern, and luckily it possesses the anti-monotone property. Another measure, IntraCAI, is proposed to capture the congregating behavior of intra-feature objects under the restriction of a co-location. A general framework is designed for SCPM-CR task and experiments show that a large fraction of computation time is devoted to identifying the participating objects of a candidate pattern. To tackle this calculation bottleneck, a novel candidate-and-search algorithm is suggested, CS-HBS, equipped with heuristic backtracking search. Extensive experiments are conducted on real and synthetic datasets to demonstrate the superiority of SCPM-CR compared with traditional SCPM methods, and also to validate the efficiency and scalability of CS-HBS. Experimental results show that CS-HBS outperforms the baselines by several times or even orders of magnitude.

A co-location pattern is a subset of spatial features whose instances are frequently located together in proximate areas. Mining co-location patterns can discover spatial dependencies in spatial datasets and have particular value in many applications. However, it is challengeable to discover co-location patterns from massive spatial datasets, due to the expensive computational cost. In this paper, we present a novel parallel co-location pattern mining approach. First, dividing spatial neighbor relationships into some neighbor-dependency partitions enables to perform mining task on each partition independently in parallel. Then, a column-based calculation approach is proposed to replace the time-consuming generation of table instances for calculating the prevalence of patterns. To further reduce the search space of patterns on each partition, two pruning strategies are suggested. We implement the parallel co-location pattern mining algorithm based on neighbor-dependency partition and column calculation via MapReduce, named PCPM-NDPCC. Substantial experiments are conducted on real and synthetic datasets to examine the performance of PCPM-NDPCC. Experimental results reveal that PCPM-NDPCC has a significant improvement in efficiency than baseline algorithms and shows better scalability for massive spatial data processing.

A co-location pattern refers to the subset of features which frequently appear together in spatial proximity. There are many literatures studied the approach of discovering co-location patterns. However, a lot of proposed approaches need some thresholds given by the user, and it is difficult to give the proper thresholds. Moreover, most proposed approaches treat the spatial object as a point during the mining process, but spatial objects are dynamic or appear in the form of a cluster normally, which means that their locations are polygons rather than points. This paper provides a novel framework to mine co-location patterns from spatial regional objects. At first, we redefine the interest measure of significant co-locations. In our framework, the user does not need to specify any threshold, and the redefined interest measure is monotonically non-increasing which can be used for improving the mining efficiency. Then, an algorithm based on the grid partition is proposed to reduce time complexity further. Finally, we verify the efficiency and effectiveness of the proposed approach by extensive experiments.

Spatial co-location mining is a key problem in urban planning and marketing. Current spatial co-location mining methods ignore the people who are related to the co-location patterns' instances, which results that the mining results are hard to explain and understand by the users. In this paper, we combine the theories of co-location mining and social networks analysis to mine a kind of special co-location patterns: Co-visiting patterns, which consider spatial information and social information at the same time. A co-visiting pattern is also a spatial feature set, whose instances are always visited by the similar users and located in a nearby region. We propose some new measures, including the user similarity, the weight of neighborhood relationship of two visited spatial instances, and the prevalent degree of a co-visiting pattern. In addition, we also explore the properties of the co-visiting patterns in this paper, and present an efficient algorithm. Finally, experiments and a detailed analysis are given at the end of this paper. Experimental results show that the rationality of co-visiting pattern, and the effectiveness and stability of the mining algorithm.

A co-location pattern is a group of spatial features whose instances are frequently appearing together in geography. Co-location pattern mining is particularly valuable for discovering spatial dependencies. Lots of co-location pattern mining approaches have been proposed, but they often emphasize the equal participation of every spatial feature. As a result, the interesting pattern which involves spatial features with significantly different for the number of instances cannot be captured. In this paper, we are committed to address the problem of mining co-location patterns from the spatial database with rare features. Specifically, we first propose a new interest measure, namely the weighted participation index. This interest measure is related to the distribution of the number of instances for spatial features, and it has ability to capture the prevalent co-location patterns with or without rare features. Furthermore, we prove that the weighted participation index possesses the approximate monotonicity property, which can be utilized to improve the computational efficiency, and thereby an efficient algorithm is developed. As demonstrated by extensive experiments, our approach is effective, efficient and scalable for mining co-location patterns embedded in the spatial database with rare features.