Spatial co-location pattern discovery without thresholds

Spatial co-location pattern mining discovers the subsets of features whose events are frequently located together in geographic space. The current research on this topic adopts a threshold-based approach that requires users to specify in advance the thresholds of distance and prevalence. However, in practice, it is not easy to specify suitable thresholds. In this article, we propose a novel iterative mining framework that discovers spatial co-location patterns without predefined thresholds. With the absolute and relative prevalence of spatial co-locations, our method allows users to iteratively select informative edges to construct the neighborhood relationship graph until every significant co-location has enough confidence and eventually to discover all spatial co-location patterns. The experimental results on real world data sets indicate that our framework is effective for prevalent co-locations discovery.     

Mining spatial colocation patterns: a different framework

Recently, there has been considerable interest in mining spatial colocation patterns from large spatial datasets. Spatial colocation patterns represent the subsets of spatial events whose instances are often located in close geographic proximity. Most studies of spatial colocation mining require the specification of two parameter constraints to find interesting colocation patterns. One is a minimum prevalent threshold of colocations, and the other is a distance threshold to define spatial neighborhood. However, it is difficult for users to decide appropriate threshold values without prior knowledge of their task-specific spatial data. In this paper, we propose a different framework for spatial colocation pattern mining. To remove the first constraint, we propose the problem of finding N-most prevalent colocated event sets, where N is the desired number of colocated event sets with the highest interest measure values per each pattern size. We developed two alternative algorithms for mining the N-most patterns. They reduce candidate events effectively and use a filter-and-refine strategy for efficiently finding colocation instances from a spatial dataset. We prove the algorithms are correct and complete in finding the N-most prevalent colocation patterns. For the second constraint, a distance threshold for spatial neighborhood determination, we present various methods to estimate appropriate distance bounds from user input data. The result can help an user to set a distance for a conceptualization of spatial neighborhood. Our experimental results with real and synthetic datasets show that our algorithmic design is computationally effective in finding the N-most prevalent colocation patterns. The discovered patterns were different depending on the distance threshold, which shows that it is important to select appropriate neighbor distances.     

Spatial co-location pattern mining for location-based services in road networks

With the evolution of geographic information capture and the emergency of volunteered geographic information, it is getting more important to extract spatial knowledge automatically from large spatial datasets. Spatial co-location patterns represent the subsets of spatial features whose objects are often located in close geographic proximity. Such pattern is one of the most important concepts for geographic context awareness of location-based services (LBS). In the literature, most existing methods of co-location mining are used for events taking place in a homogeneous and isotropic space with distance expressed as Euclidean, while the physical movement in LBS is usually constrained by a road network. As a result, the interestingness value of co-location patterns involving network-constrained events cannot be accurately computed. In this paper, we propose a different method for co-location mining with network configurations of the geographical space considered. First, we define the network model with linear referencing and refine the neighborhood of traditional methods using network distances rather than Euclidean ones. Then, considering that the co-location mining in networks suffers from expensive spatial-join operation, we propose an efficient way to find all neighboring object pairs for generating clique instances. By comparison with the previous approaches based on Euclidean distance, this approach can be applied to accurately calculate the probability of occurrence of a spatial co-location on a network. Our experimental results from real and synthetic data sets show that the proposed approach is efficient and effective in identifying co-location patterns which actually rely on a network.     

含关键特征的显著Co-location模式挖掘研究

空间Co-location模式是一组在空间中频繁并置的空间特征的子集。空间Co-location模式挖掘通常假设空间实例之间相互独立,然而,在实际应用中,不同空间特征、不同实例之间往往相互作用或依赖。空间Co-location关键特征是指对模式具有主导作用的特征。在频繁模式中,识别含关键特征的Co-location模式并摘取模式中的关键特征,为用户提供更精简的挖掘结果,提高Co-location模式的可用性,对Co-location模式挖掘具有重要意义。本文首先定义了含有关键特征的显著频繁Co-location模式新概念,以及一系列度量指标以识别显著频繁Co-location模式中的关键特征;其次,给出了一个挖掘显著频繁Co-location模式和关键特征的算法;最后,在模拟和真实数据集上进行了大量的实验,验证了所提出算法的效果及性能。     

不均匀模糊空间对象的分层次co-location模式挖掘方法

针对现有的co-location模式挖掘算法无法有效处理不均匀分布空间对象的问题,提出一种不均匀模糊空间对象的分层次co-location模式挖掘方法。首先提出一种不均匀数据集的生成方法;然后对不均匀分布的数据集进行层次划分,使每个区域具有均匀的空间分布;再基于改进的PO_RI_PC算法对划分后的模糊对象进行空间数据挖掘。该方法基于距离变化系数构建每个子区域的邻域关系图,进而完成区域融合,实现co-location模式挖掘。实验结果表明,与传统方法相比,所提方法的执行效率更高,随实例个数和不均匀度的变化获得的co-location集个数更多,同比情况下平均提高约25%,获得了更精确的挖掘结果。     

CPM-MCHM:一种基于极大团和哈希表的空间并置模式挖掘算法

空间并置(co-location)模式挖掘是指在大量的空间数据中发现一组空间特征的子集,这些特征的实例在地理空间中频繁并置出现.传统的空间并置模式挖掘算法通常采用逐阶递增的挖掘框架,从低阶模式开始生成候选模式并计算其参与度(空间并置模式的频繁性度量指标).虽然这种挖掘框架可以得到正确和完整的结果,但是带来的时间和空间开...     

k-近邻关系下的空间高效用核模式挖掘

空间数据挖掘旨在从空间数据库中发现和提取有价值的潜在知识.空间co-location(共存)模式挖掘一直以来都是空间数据挖掘领域的重要研究方向之一,其目的 是发现一组频繁邻近出现的空间特征子集,而空间高效用co-location模式挖掘则考虑了特征的效用属性.二者在度量空间实例的邻近关系时一般都需要预先给定一个距离阈值...     

空间极大co-location模式挖掘研究

空间co-location模式代表了一组空间特征的子集,它们的实例在空间中频繁地关联。挖掘空间co-location模式的研究已经有很多,但是针对极大co-location模式挖掘的研究非常少。提出了一种新颖的空间极大co-location模式挖掘算法。首先扫描数据集得到二阶频繁模式,然后将二阶频繁模式转换为图,再通过极大团算法求解得到空间特征极大团,最后使用二阶频繁模式的表实例验证极大团得到空间极大co-location频繁模式。实验表明,该算法能够很好地挖掘空间极大co-location频繁模式。     

Top-<Emphasis Type="Italic">k</Emphasis> probabilistic prevalent co-location mining in spatially uncertain data sets

A co-location pattern is a set of spatial features whose instances frequently appear in a spatial neighborhood. This paper efficiently mines the top-k probabilistic prevalent co-locations over spatially uncertain data sets and makes the following contributions: 1) the concept of the top-k probabilistic prevalent co-locations based on a possible world model is defined; 2) a framework for discovering the top-k probabilistic prevalent co-locations is set up; 3) a matrix method is proposed to improve the computation of the prevalence probability of a top-k candidate, and two pruning rules of the matrix block are given to accelerate the search for exact solutions; 4) a polynomial matrix is developed to further speed up the top-k candidate refinement process; 5) an approximate algorithm with compensation factor is introduced so that relatively large quantity of data can be processed quickly. The efficiency of our proposed algorithms as well as the accuracy of the approximation algorithms is evaluated with an extensive set of experiments using both synthetic and real uncertain data sets.     

On discovering co-location patterns in datasets: a case study of pollutants and child cancers

We intend to identify relationships between cancer cases and pollutant emissions by proposing a novel co-location mining algorithm. In this context, we specifically attempt to understand whether there is a relationship between the location of a child diagnosed with cancer with any chemical combinations emitted from various facilities in that particular location. Co-location pattern mining intends to detect sets of spatial features frequently located in close proximity to each other. Most of the previous works in this domain are based on transaction-free apriori-like algorithms which are dependent on user-defined thresholds, and are designed for boolean data points. Due to the absence of a clear notion of transactions, it is nontrivial to use association rule mining techniques to tackle the co-location mining problem. Our proposed approach is focused on a grid based transactionization? of the geographic space, and is designed to mine datasets with extended spatial objects. It is also capable of incorporating uncertainty of the existence of features to model real world scenarios more accurately. We eliminate the necessity of using a global threshold by introducing a statistical test to validate the significance of candidate co-location patterns and rules. Experiments on both synthetic and real datasets reveal that our algorithm can detect a considerable amount of statistically significant co-location patterns. In addition, we explain the data modelling framework which is used on real datasets of pollutants (PRTR/NPRI) and childhood cancer cases.     

空间co-location模式挖掘中的模糊技术初探

空间并置（co-location）模式是指其特征的实例在地理空间中频繁并置出现的一组空间特征的集合。传统co-location模式挖掘通常由用户给定一个邻近阈值来确定实例的邻近关系，使用单一的邻近阈值来判定两个空间实例的邻近性可能会造成邻近关系的缺失，也没有考虑距离大小的不同对邻近关系的影响。同时，传统方法主要利用频繁性阈值来衡量模式的频繁性，存在着算法效率对频繁性阈值较为敏感的问题。由于频繁并置的特征间具有较高的邻近度，因此利用聚类算法可以将其聚集在一起，加之邻近以及特征间的并置都是模糊的概念，因此将模糊集理论与聚类算法相结合，研究了空间co-location模式挖掘中的模糊挖掘技术，在定义模糊邻近关系的基础上，定义了度量特征之间邻近度的函数，基于特征邻近度利用模糊聚类算法挖掘co-location模式，最后通过广泛的实验验证了提出方法的实用性、高效性及鲁棒性。     

Distributed computation of the knn graph for large high-dimensional point sets

High-dimensional problems arising from robot motion planning, biology, data mining, and geographic information systems often require the computation of k nearest neighbor (knn) graphs. The knn graph of a data set is obtained by connecting each point to its k closest points. As the research in the above-mentioned fields progressively addresses problems of unprecedented complexity, the demand for computing knn graphs based on arbitrary distance metrics and large high-dimensional data sets increases, exceeding resources available to a single machine. In this work we efficiently distribute the computation of knn graphs for clusters of processors with message passing. Extensions to our distributed framework include the computation of graphs based on other proximity queries, such as approximate knn or range queries. Our experiments show nearly linear speedup with over 100 processors and indicate that similar speedup can be obtained with several hundred processors.     

An order-clique-based approach for mining maximal co-locations

Most algorithms for mining spatial co-locations adopt an Apriori-like approach to generate size-k prevalence co-locations after size-(k − 1) prevalence co-locations. However, generating and storing the co-locations and table instances is costly. A novel order-clique-based approach for mining maximal co-locations is proposed in this paper. The efficiency of the approach is achieved by two techniques: (1) the spatial neighbor relationships and the size-2 prevalence co-locations are compressed into extended prefix-tree structures, which allows the order-clique-based approach to mine candidate maximal co-locations and co-location instances; and (2) the co-location instances do not need to be stored after computing some characteristics of the corresponding co-location, which significantly reduces the execution time and space required for mining maximal co-locations. The performance study shows that the new method is efficient for mining both long and short co-location patterns, and is faster than some other methods (in particular the join-based method and the join-less method).     

A framework of spatial co-location pattern mining for ubiquitous GIS

A spatial co-location pattern represents relationships between spatial features that are frequently located in close proximity to one another. Such a pattern is one of the most important concepts for geographic context awareness of ubiquitous Geographic Information System (GIS). We constructed a framework for co-location pattern mining using the transaction-based approach, which employs maximal cliques as a transaction-type dataset; we first define transaction-type data and verify that the definition satisfies the requirements, and we also propose an efficient way to generate all transaction-type data. The constructed framework can play a role as a theoretical methodology of co-location pattern mining, which supports geographic context awareness of ubiquitous GIS.     

极小负co-location模式及有效的挖掘算法

空间co-location(并置)模式是指实例在空间中频繁关联的一组空间特征的子集.在空间数据挖掘中,现有算法主要针对的是正模式的挖掘,而空间中还存在着具有强负相关性的模式,如负co-location模式,这类模式的挖掘在一些应用中同样具有重要的意义.现有的负co-location模式挖掘算法的时间复杂度较高,挖掘到的...     

An efficient algorithm for mining top-<Emphasis Type="Italic">k</Emphasis> on-shelf high utility itemsets

High on-shelf utility itemset (HOU) mining is an emerging data mining task which consists of discovering sets of items generating a high profit in transaction databases. The task of HOU mining is more difficult than traditional high utility itemset (HUI) mining, because it also considers the shelf time of items, and items having negative unit profits. HOU mining can be used to discover more useful and interesting patterns in real-life applications than traditional HUI mining. Several algorithms have been proposed for this task. However, a major drawback of these algorithms is that it is difficult for users to find a suitable value for the minimum utility threshold parameter. If the threshold is set too high, not enough patterns are found. And if the threshold is set too low, too many patterns will be found and the algorithm may use an excessive amount of time and memory. To address this issue, we propose to address the problem of top-k on-shelf high utility itemset mining, where the user directly specifies k, the desired number of patterns to be output instead of specifying a minimum utility threshold value. An efficient algorithm named KOSHU (fast top-K on-shelf high utility itemset miner) is proposed to mine the top-k HOUs efficiently, while considering on-shelf time periods of items, and items having positive and/or negative unit profits. KOSHU introduces three novel strategies, named efficient estimated co-occurrence maximum period rate pruning, period utility pruning and concurrence existing of a pair 2-itemset pruning to reduce the search space. KOSHU also incorporates several novel optimizations and a faster method for constructing utility-lists. An extensive performance study on real-life and synthetic datasets shows that the proposed algorithm is efficient both in terms of runtime and memory consumption and has excellent scalability.     

The <Emphasis Type="Italic">k</Emphasis>-Nearest Neighbour Join: Turbo Charging the KDD Process

The similarity join has become an important database primitive for supporting similarity searches and data mining. A similarity join combines two sets of complex objects such that the result contains all pairs of similar objects. Two types of the similarity join are well-known, the distance range join, in which the user defines a distance threshold for the join, and the closest pair query or k-distance join, which retrieves the k most similar pairs. In this paper, we propose an important, third similarity join operation called the k-nearest neighbour join, which combines each point of one point set with its k nearest neighbours in the other set. We discover that many standard algorithms of Knowledge Discovery in Databases (KDD) such as k-means and k-medoid clustering, nearest neighbour classification, data cleansing, postprocessing of sampling-based data mining, etc. can be implemented on top of the k-nn join operation to achieve performance improvements without affecting the quality of the result of these algorithms. We propose a new algorithm to compute the k-nearest neighbour join using the multipage index (MuX), a specialised index structure for the similarity join. To reduce both CPU and I/O costs, we develop optimal loading and processing strategies.     

带邻近作用的高增益率co-location模式挖掘

大多数空间co-location模式挖掘将距离阈值作为衡量不同对象实例间邻近关系的标准,进而挖掘出频繁co-location模式,并没有考虑具有邻近关系的实例间的相互影响和模式的增益率问题。在空间co-location模式挖掘过程中,引入实例间的相互作用率和对象的季均收益,定义了对象作用率、套间总收益和增益率等概念,并提出挖掘高增益率co-location模式的基础算法（NAGA）和有效的剪枝算法（NAGA_JZ）。最后通过大量的实验来验证基础算法的正确性和实用性,并对基础算法和剪枝算法的挖掘效率进行了对比,验证了剪枝算法的高效性。     

Using locally estimated geodesic distance to optimize neighborhood graph for isometric data embedding

To deal with the highly twisted and folded manifold, this paper propose a geodesic distance-based approach to build the neighborhood graph for isometric embedding. This approach assumes that the neighborhood of a point located at the highly twisted place of the manifold may not be linear so that its neighbors should be determined by geodesic distance. This approach firstly determines the neighborhood for each point using Euclidean distance and then applies the locally estimated geodesic distances to optimize the neighborhood. It increases only linear time complexity. Furthermore the optimized neighborhood can speed up the subsequent embedding process. The proposed approach is simple, general and easy to deal with a wider range of data. The conducted experiments on both synthetic and real data sets validate the approach.     

Mining Co-Location Patterns with Rare Events from Spatial Data Sets

A co-location pattern is a group of spatial features/events that are frequently co-located in the same region. For example, human cases of West Nile Virus often occur in regions with poor mosquito control and the presence of birds. For co-location pattern mining, previous studies often emphasize the equal participation of every spatial feature. As a result, interesting patterns involving events with substantially different frequency cannot be captured. In this paper, we address the problem of mining co-location patterns with rare spatial features. Specifically, we first propose a new measure called the maximal participation ratio (maxPR) and show that a co-location pattern with a relatively high maxPR value corresponds to a co-location pattern containing rare spatial events. Furthermore, we identify a weak monotonicity property of the maxPR measure. This property can help to develop an efficient algorithm to mine patterns with high maxPR values. As demonstrated by our experiments, our approach is effective in identifying co-location patterns with rare events, and is efficient and scalable for large-scale data sets.