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.

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.

Abstract Multi-view clustering (MVC), which aims to explore the underlying structure of data by leveraging heterogeneous information of different views, has brought along a growth of attention. Multi-view clustering algorithms based on different theories have been proposed and extended in various applications. However, most existing MVC algorithms are shallow models, which learn structure information of multi-view data by mapping multi-view data to low-dimensional representation space directly, ignoring the nonlinear structure information hidden in each view, and thus, the performance of multi-view clustering is weakened to a certain extent. In this paper, we propose a deep multi-view clustering algorithm based on multiple auto-encoder, termed MVC-MAE, to cluster multi-view data. MVC-MAE adopts auto-encoder to capture the nonlinear structure information of each view in a layer-wise manner and incorporate the local invariance within each view and consistent as well as complementary information between any two views together. Besides, we integrate the representation learning and clustering into a unified framework, such that two tasks can be jointly optimized. Extensive experiments on six real-world datasets demonstrate the promising performance of our algorithm compared with 15 baseline algorithms in terms of two evaluation metrics.

Network embedding (NE) is a method that maps nodes in a network into a low-dimensional and continuous vector space while maintains inherent features of the network. Most existing algorithms for NE focus on one or two of the aspects of topological structure, node attributes or community structure information, but without integrating the three in a unified framework. In this study, we develop a deep neural network-based framework for Attributed Network Embedding with Community Preservation (ANECP), which simultaneously incorporates the topological structure, node attributes as well as community structure together to obtain the low-dimensional distributed representations of nodes in the network. The use of deep neural networks captures the underlying high non-linearity in both topology and attribute information, while the incorporation of the community structure resolves the issues of data sparsity from microscopic perspective. Consequently, the obtained node representations can preserve proximity and discriminative. We conducted experimental studies using six real-world datasets. The experimental results show that proposed ANECP has superior performance over the existing methods.

Spatial co-location patterns are groups of spatial features whose instances are frequently located together in spatial proximity. Most existing algorithms of discovering spatial co-location patterns are based on the candidate-test model, which is computationally expensive. When the user adjusts the participation index (PI) threshold, these algorithms have to be re-executed from the size 2 co-location patterns. In this paper, we propose a novel spatial instance partition method for mining co-location patterns which called overlap maximal clique partitioning algorithm (OMCP). The OMCP co-location mining algorithm divides instances of an input spatial dataset into a set of overlap maximal cliques. Table instances of all colocation patterns are collected by the overlap maximal cliques. Prevalent co-location patterns are directly calculated without generating the candidate patterns. The OMCP algorithm only needs to execute once to get the PI of all patterns, without re-executing when the PI threshold is adjusted. Our algorithm is performed on both synthetic and real-world datasets to demonstrate that the OMCP algorithm improvements in efficiency of co-location pattern mining.

Influence is a complex and subtle force that changes the behavior of involved users. Measuring influence can benefit to identify the influential users, and also benefit to provide important insights into the design of social platforms and applications. However, most existing work on social influence analysis has focused on homogeneous information networks. Few studies systematically investigate how to mine the strength of influence between nodes in heterogeneous information networks. In this paper, we present a meta path-based information entropy for modeling social influence in heterogeneous information networks (MPIE). Through setting meta paths, MPIE not only flexibly integrates heterogeneous information, but also obtains potential link information to measure the influence of nodes. Experiments on real data sets demonstrate the effectiveness of our proposed method.

Spatial co-location pattern mining is an interesting and important task in spatial data mining which discovers the subsets of spatial features frequently observed together in nearby geographic space. However, the traditional framework of mining prevalent co-location patterns produces numerous redundant co-location patterns, which makes it hard for users to understand or apply. In this paper we study the problem of reducing redundancy in a collection of prevalent co-location patterns. We first introduce the concept of semantic distance between two co-location patterns, and then define redundant co-locations by introducing the concept of δ-covered, where δ (0≤δ≤1) is a coverage measure. We develop two algorithms RRclosed and RRnull to perform the redundancy reduction for prevalent co-location patterns. Our performance studies on the synthetic and real-world data sets demonstrate that our method effectively reduces the size of the original collection of closed co-location patterns by about 50%. Furthermore, the RRnull method runs much faster than the related closed co-location pattern mining algorithm.

Spatial co-location pattern mining is an interesting and important task in spatial data mining which discovers the subsets of spatial features frequently observed together in nearby geographic space. However, the traditional framework of mining prevalent colocation patterns produces numerous redundant co-location patterns, which makes it hard for users to understand or apply. To address this issue, in this paper, we study the problem of reducing redundancy in a collection of prevalent co-location patterns by utilizing the spatial distribution information of co-location instances. We first introduce the concept of semantic distance between a co-location pattern and its super-patterns, and then define redundant co-locations by introducing the concept of d-covered, where δ (0 ≤ δ ≤ 1) is a coverage measure. We develop two algorithms RRclosed and RRnull to perform the redundancy reduction for prevalent co-location patterns. The former adopts the post-mining framework that is commonly used by existing redundancy reduction techniques, while the latter employs the mine-and-reduce framework that pushes redundancy reduction into the co-location mining process. Our performance studies on the synthetic and real-world data sets demonstrate that our method effectively reduces the size of the original collection of closed co-location patterns by about 50 percent. Furthermore, the RRnull method runs much faster than the related closed co-location pattern mining algorithm.

Conventional fuzzy cognitive maps (FCMs) can only represent monotonic or symmetric causal relationships and cannot simulate the AND/OR combinations of the antecedent nodes. The rule-based fuzzy cognitive maps (RBFCMs) usually suffer from the well-known combinatorial rule explosion problem. A hybrid fuzzy cognitive model based on weighted OWA operators and single-antecedent rules is proposed to eliminate the drawbacks of the existing FCM models. Hybrid fuzzy cognitive maps (HFCMs) represent the causal relationships with single-antecedent fuzzy rules and handle the various AND/OR relationships among the antecedent nodes with weighted OWA aggregation operators. Compared with conventional FCMs, HFCMs have more powerful cognitive capability. Compared with RBFCMs, HFCMs reduce the scale and complexity of the rule bases significantly and have better representation and inference performance. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1189–1196, 2007.