Efficiently Mining High Utility Co-location Patterns from Spatial Data Sets with Instance-Specific Utilities

The goal of spatial co-location pattern mining is to find subsets of spatial features whose instances are often neighbors in a geographical space. In many practical cases, instances of spatial features contain not only spatial location information but also attribute information. Although there have been several studies that use type-1 fuzzy membership functions to mine spatial fuzzy co-location patterns, there is great uncertainty associated with such membership functions. To address this problem, we propose a spatial fuzzy co-location pattern mining method based on interval type-2 fuzzy sets. First, we collect the interval evaluation values of the interval data of attribute information from experts to form granular data. Next, the original type-1 fuzzy membership function is extended to a granular type-2 fuzzy membership function based on elliptic curves. We use a gradual method to adjust the parameters of the fuzzy membership function so that its footprint of uncertainty satisfies both the connectivity and the given confidence. Based on this granular type-2 fuzzy membership function, we fuzzify the attribute information of instances and define the concepts of fuzzy features and fuzzy co-location patterns. A fuzzy co-location pattern mining algorithm based on spatial cliques is then proposed, termed the FCPM-Clique algorithm. In order to improve the efficiency of the algorithm, we propose two pruning strategies. In addition, we extend two classical spatial pattern mining algorithms, the Join-based algorithm and the Joinless algorithm, to mine fuzzy co-location patterns based on interval type-2 fuzzy sets. Many experiments on synthetic and real-world datasets are conducted, the performance of the three algorithms is compared, and the effectiveness and efficiency of our proposed FCPM-Clique algorithm is demonstrated.

Spatial co-location pattern mining aims to uncover associations among spatial features, enabling users to discover correlation knowledge from spatial datasets. However, as spatial datasets grow, traditional frameworks for mining co-location patterns produce an overwhelming number of redundant results, which complicates further analysis. This paper focuses on extracting worthy co-location patterns, which are concise summaries of prevalent co-location patterns. We introduce two similarity measures—feature-based similarity and distribution-based similarity—to evaluate redundancy between co-location patterns from both feature and instance perspectives. Using these measures, we propose a novel approach called the Worthy Co-location Patterns Mining algorithm (WCPM) to condense prevalent co-location patterns. Initially, we employ a clique-based method to discover prevalent co-location patterns and categorize them into Maximal Co-location Patterns (MCPs) and Non-Maximal Co-location Patterns (NMCPs). Subsequently, we cluster the MCPs to extract the feature-similar MCPs, and based on distribution similarity, identify the worthy MCPs from the clustering results. Finally, we design a top-down algorithm to mine Worthy Non-Maximal Co-location Patterns (WNMCPs). Experiments on both synthetic and real datasets demonstrate that WCPM outperforms similar state-of-the-art approaches in terms of compression power and running time.

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.

With the rapid growth and extensive applications of the spatial dataset, itpsilas getting more important to solve how to find spatial knowledge automatically from spatial datasets. Spatial co-location patterns represent the subsets of features whose instances are frequently located together in geographic space. Itpsilas difficult to discovery co-location patterns because of the huge amount of data brought by the instances of spatial features. A large fraction of the computation time is devoted to generating the table instances of co-location patterns. The essence of co-location patterns discovery and three kinds of co-location patterns mining algorithms proposed in recent years are analyzed, and a new join-less approach for co-location patterns mining, which based on a data structure - CPI-tree (Co-location Pattern Instance Tree), is proposed. The CPI-tree materializes spatial neighbor relationships. All co-location table instances can be generated quickly with a CPI-tree. This paper proves the correctness and completeness of the new approach. Finally, an experimental evaluation using synthetic datasets and a real world dataset shows that the algorithm is computationally more efficient than the join-less algorithm.

Spatial data mining is the process of finding interesting patterns that may implicitly exist in spatial database. The process of finding the subsets of features that are frequently found together in a same location is called co-location pattern discovery. Earlier methods to find co-location patterns focuses on converting neighbourhood relations to item sets. Once item sets are obtained then can apply any method for finding patterns. The criteria to know the strength of co-location patterns is participation ratio and participation index. In this paper, Delaunay triangulation approach is proposed for mining co-location patterns. Delaunay triangulation represents the closest neighbourhood structure of the features exactly which is a major concern in finding the co-location patterns. The results show that this approach achieves good performance when compared to earlier methodologies.

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

Spatial high utility co-location patterns mining takes pattern utility participation index as interest measure, but it still lacks standard method for calculating pattern utility participation index. This paper presents some reasonable definitions of spatial high utility colocation patterns based on the datasets of instance with utility value, such as Feature Actual Participation Weight, Feature Utility Participation Index and Pattern Utility Participation Index and many more. A basic algorithm BWHMA(high utility co-location patterns mining based on feature actual participation weight) is proposed. For improving the efficiency of algorithm BWHMA, one pruning algorithm FUPRA(based on feature utility participation rate) and one optimization algorithm FRPWA(based on feature actual participation weight) are put forward. Finally, a large number of comparative experiments have been done on both synthetic and real datasets. The experiments show that the proposed algorithms are feasible, correct and valid.

Temporal and spatial variability of stream waters in Wales, the Welsh borders and part of the West Midlands, UK — 1. Major ion concentrations

Spatial Co-location pattern mining and Spatio-temporal Co-occurrence pattern mining are important directions of spatial data mining. However, the existing relevant mining algorithms are computational expensive and the algorithms can't effectively deal with uncertain data which are wide spread in many areas. The fast co-occurrence data mining algorithms for the uncertain data are proposed by using the filter-refine method and efficient pruning strategy. The correctness, completeness and complexity of the proposed algorithms are analyzed, and the experimental data shows that the algorithms are effective and reasonable.

The discovery of co-location patterns among spatial events is an important task in spatial data mining. We introduce a new kind of spatial co-location patterns, named condensed spatial co-location patterns, that can be considered as a lossy compressed representation of all the co-location patterns. Each condensed pattern is the representative, and a superset, of a group of spatial co-location patterns in the full set of patterns such that the difference between the interestingness measure of the representative and the measures of the patterns belonging to the associated group are negligible. Our preliminary experiments show that condensed spatial co-location patterns are less sensitive to parameter changes and more robust in presence of missing data than closed spatial co-location patterns.

The spatial co-location pattern represents a set of spatial features, whose instances are frequently associated in the space. However, due to the exponential time complexity of the traditional algorithm, the operation efficiency of the algorithm is not high, especially in the face of massive data mining, it is unable to complete the mining task normally. Therefore, an efficient co-location pattern approximation algorithm is proposed. The new algorithm first clusters according to the feature instances, takes each center as the new instance coordinates, and associates the number of instances of each family. On this basis, the mining area is divided into branches, and the distance threshold is taken for the row spacing, so as to achieve the purpose of fast pruning. On the premise of ensuring high accuracy, the algorithm effectively solves the efficiency problem of traditional algorithms, and effectively solves the spatial colocation pattern mining of massive data. A large number of experiments show that the new algorithm has the advantages of high efficiency, stability and high accuracy.

Spatial data sets can be analysed by counting the number of objects in equally sized bins. The bin counts are related to the Pólya urn process, where coloured balls (for example, white or black) are removed from the urn at random. If there are insufficient white or black balls for the prescribed number of trials, the Pólya urn process becomes untenable. In this case, we modify the Pólya urn process so that it continues to describe the removal of volume within a spatial distribution of objects. We determine when the standard formula for the variance of the standard Pólya distribution gives a good approximation to the true variance. The variance quantifies an index for assessing whether a spatial point data set is at its most randomly distributed state, called the complete spatial randomness (CSR) state. If the bin size is an order of magnitude larger than the size of the objects, then the standard formula for the CSR limit is indicative of when the CSR state has been attained. For the special case when the object size divides the bin size, the standard formula is in fact exact. doi:10.1017/S1446181112000089

Co-location patterns are well-established on spatial objects with categorical labels, which capture the phenomenon that objects with certain labels are often located in close geographic proximity. Similar to frequent itemsets, co-location patterns are defined based on a support measure which quantifies the popularity (or prevalence) of a pattern candidate (a label set). Quite a few support measures exist for defining co-location patterns and they share an idea of counting the number of instances of a given label set C as its support, where an instance of C is an object set whose objects carry all the labels in C and are located close to one another. Unfortunately, these measures suffer from various weaknesses, e.g., some fail to capture all possible instances while some others overlook the cases when multiple instances overlap. In this paper, we propose a new measure called Fraction-Score whose idea is to count instances fractionally if they overlap. Compared to existing measures, Fraction-Score not only captures all possible instances, but also handles the cases where instances overlap appropriately (so that the supports defined are more meaningful and consistent with the desirable anti-monotonicity property). To solve the co-location pattern mining problem based on Fraction-Score, we develop efficient algorithms which are significantly faster than a baseline that adapts the state-of-the-art. We conduct extensive experiments using both real and synthetic datasets, which verified the superiority of Fraction-Score and also the efficiency of our developed algorithms.

Abstract. Due to the widespread application of geographic information systems (GIS) and GPS technology and the increasingly mature infrastructure for data collection, sharing, and integration, more and more research domains have gained access to high-quality geographic data and created new ways to incorporate spatial information and analysis in various studies. There is an urgent need for effective and efficient methods to extract unknown and unexpected information, e.g., co-location patterns, from spatial datasets of high dimensionality and complexity. A co-location pattern is defined as a subset of spatial items whose instances are often located together in spatial proximity. Current co-location mining algorithms are unable to quantify the spatial proximity of a co-location pattern. We propose a co-location pattern miner aiming to discover co-location patterns in a multidimensional spatial data by measuring the cohesion of a pattern. We present a model to measure the cohesion in an attempt to improve the efficiency of existing methods. The usefulness of our method is demonstrated by applying them on the publicly available spatial data of the city of Antwerp in Belgium. The experimental results show that our method is more efficient than existing methods.

Due to the widespread application of geographic information systems (GIS) and GPS technology and the increasingly mature infrastructure for data collection, sharing, and integration, more and more research domains have gained access to high-quality geographic data and created new ways to incorporate spatial information and analysis in various studies. There is an urgent need for effective and efficient methods to extract unknown and unexpected information, e.g., co-location patterns, from spatial datasets of high dimensionality and complexity. A co-location pattern is defined as a subset of spatial items whose instances are often located together in spatial proximity. Current co-location mining algorithms are unable to quantify the spatial proximity of a co-location pattern. We propose a co-location pattern miner aiming to discover co-location patterns in a multidimensional spatial data by measuring the cohesion of a pattern. We present a model to measure the cohesion in an attempt to improve the efficiency of existing methods. The usefulness of our method is demonstrated by applying them on the publicly available spatial data of the city of Antwerp in Belgium. The experimental results show that our method is more efficient than existing methods.