Prevalent Co-location Research Articles

Representative co-location pattern post-mining based on maximal row instances representation model

The mining result set of spatial prevalent co-location patterns(SPCPs) is often large and redundant, especially when the prevalence threshold is set to low or long SPCPs are present. Meanwhile, the distribution of SPCPs in continuous space and complex spatial relationships with each other of spatial data make the compression and reorganization of SPCPs a challenging problem. To solve this problem, in this paper, a representative co-location pattern mining framework based on the maximal row instance(MRI) representation model is proposed. First, the MRI representation model is proposed to effectively preserve the pattern distribution information of prevalent co-location patterns. To establish the MRI representation model, the basic algorithm and geometric algorithm are proposed in this paper. Two materialization methods based on the MRI representation model, 0-1 vector and key–value vector, are presented. Secondly, the similarity measure of SPCPs under the context of the MRI representation model is proposed, which calculates the similarity between any two co-location patterns without adding additional information such as domain background. Furthermore, the mining framework based on the k nearest neighbors density peak clustering algorithm is presented to extract representative co-location patterns. Finally, the efficiency and scalability of the proposed method are verified on the synthetic data and real data. Compared with the existing methods, the representative co-location patterns of the proposed method have well compression performances.

A Clique-Querying Mining Framework for Discovering High Utility Co-Location Patterns without Generating Candidates

Groups of spatial features whose instances frequently appear together in nearby areas are regarded as prevalent co-location patterns (PCPs). Traditional PCP mining ignores the significance of instances and features. However, in reality, these instances and features have different significance, the traditional PCPs may not sufficiently expose knowledge from spatial data. This study focuses on discovering high utility co-location patterns (HUCPs) in which each instance is assigned a utility to reflect its significance. To filter HUCPs, an adaptive utility participation index (UPI) is designed. Unfortunately, the UPI does not hold the downward closure property. The performance of mining HUCPs is very inefficient since unnecessary candidates cannot be early pruned. Thus, an efficient clique-querying mining framework is devised without generating candidates. This framework first divides neighboring instances into cliques, then compacts these cliques into a hash table structure. Next, the adaptive UPI of any patterns can be quickly calculated based on their participating instances that are obtained by executing a querying scheme on the hash table. Finally, HUCPs are filtered efficiently. The effectiveness and efficiency of the proposed method are proved in both theory and experiments to make a promise that the patterns mined are more meaningful and the mining performance is significantly improved compared to the previous methods.

Spatial co-location pattern mining over extended objects based on cell-relation operations

Spatial co-location pattern mining (SCPM) is intended to discover subsets of spatial features whose instances are frequently located together in geographic areas. Traditional SCPM methods are designed for point spatial instances. However, in reality, instances are mostly in the form of extended objects, e.g., lines, polygons. In addition, current SCPM methods with extended objects are less well researched and have two disadvantages: (1) Existing researches cannot effectively capture neighborhood relationships between extended objects and their mining results cannot properly reflect the distribution dependence of features; (2) These methods are not efficient enough with large datasets. This paper proposes a novel framework called cell-relation operations framework to overcome these issues. To eliminate the first shortcoming, the framework uses the area overlapping of buffers between objects to gain the neighbor relationships between extended objects and introduces participation index under buffer size k to identify prevalent co-location patterns. To address the second problem, our framework employs cell-relation operations rather than instance relation computing as the basic computing unit for co-location mining, which substantially speeds up the computation. The framework obtains spatial co-locations by counting the feature transactions of the cells and calculates the feature overlap ratio of the cells to generate co-locations. We implement experiments with real datasets to demonstrate that our framework’s mining results are more reasonable and the proposed framework’s runtime outperforms the baselines by 2 to 4 orders of magnitude.

Meta-PCP: A concise representation of prevalent co-location patterns discovered from spatial data

A prevalent co-location pattern (PCP), which is a group of spatial features whose spatial instances frequently appear together in nearby geographical areas, can expose valuable information and knowledge that can be applied to many fields. In traditional PCP mining, to filter interesting PCPs, a minimum prevalence threshold is employed. This threshold should be set to a small value to obtain as much information and knowledge as possible from spatial data sets. However, at this time, not only too many redundant patterns are found, but also mining efficiency is extremely low and memory space consumption is very high. To solve this self-contradiction, this paper proposes a new concept that is called meta-prevalent co-location pattern (meta-PCP). Meta-PCPs can eliminate redundant information and concisely represent the mining result. Although meta-PCPs are a lossy representation of all PCPs, they can be controlled by users according to their application scenarios. Moreover, a query-based mining algorithm is designed to improve mining performance when the prevalence threshold is set to very low. This algorithm discovers meta-PCPs without generating candidates (to improve efficiency) and does not collect and remain co-location instances of each pattern (to reduce memory consumption). The comprehensive experimental results on both synthetic and real data sets show that the proposed method is effective and efficient.

A maximal ordered ego-clique based approach for prevalent co-location pattern mining

Spatial data often exhibit a tendency highly similar to spatial objects located close to each other. Thus, prevalent co-location pattern (PCP) mining has been studied extensively to discover this tendency. The organization of neighboring relationships on spatial data, called neighborhood materialization (NM), is critical to the PCP problem. However, the previous NM methods suffer from poor efficiency and a large set of results. To this end, a new NM model based on maximal cliques with ego-centric points is proposed in this study, called the maximal ordered ego-clique (MOEC). Here, the correctness of the materialized neighboring relationships of spatial data is proven, and the complexity is further analyzed. In addition, a generalized algorithm GMOEC is designed to effectively transform the neighboring relationships of a spatial data set into MOECs. The geometry of the spatial data set is fully exploited to develop several optimization strategies to enhance efficiency. Furthermore, a novel generalized PCP mining method, GPCP, is proposed to avoid multiple scans of the materialized neighborhood. The GPCP method discovers all PCPs based on the materialized neighborhood using the vertical data format. Finally, extensive experiments on both synthetic and real data sets demonstrate that the proposed solution is highly effective and efficient.

Spatial Negative Co-Location Pattern Directional Mining Algorithm with Join-Based Prevalence

It is usually difficult for prevalent negative co-location patterns to be mined and calculated. This paper proposes a join-based prevalent negative co-location mining algorithm, which can quickly and effectively mine all the prevalent negative co-location patterns in spatial data. Firstly, this paper verifies the monotonic nondecreasing property of the negative co-location participation index (PI) value as the size increases. Secondly, using this property, it is deduced that any prevalent negative co-location pattern with size n can be generated by connecting prevalent co-location with size 2 and with an n − 1 size candidate negative co-location pattern or an n − 1 size prevalent positive co-location pattern. Finally, the experiment results demonstrate that while other conditions are fixed, the proposed algorithm has an excellent efficiency level. The algorithm can eliminate the 90% useless negative co-location pattern maximumly and eliminate the useless 40% negative co-location pattern averagely.

Meta-Pcp: A Concise Representation of Prevalent Co-Location Patterns Discovered from Spatial Data

Meta-Pcp: A Concise Representation of Prevalent Co-Location Patterns Discovered from Spatial Data

MCHT: A maximal clique and hash table-based maximal prevalent co-location pattern mining algorithm

Co-location patterns refer to subsets of Boolean spatial features with instances of these features frequently appear in nearby geographic space. Maximal co-location patterns are a compact representation of these patterns that lead users more easily to absorb results and make meaningful inferences. The current algorithms for maximal co-location pattern mining are based on a generate-test candidate model. The main execution time of this model is occupied by collecting co-location instances of candidates, which makes discovering maximal co-location patterns is still very challenging when data is big and/or dense. To take up the challenge, a novel maximal co-location pattern mining framework based on maximal cliques and hash tables (MCHT) is developed in this study. First, all maximal cliques that can compactly represent neighbor relationships between instances of a spatial data set are enumerated. The advantages of bit string operations are fully utilized to speed up the process of enumerating maximal cliques. Next, a participating instance hash table structure is constructed based on these maximal cliques. Then information about the co-location instances of maximal patterns can be queried and collected efficiently from the hash table. After that, by calculating participation indexes of these patterns to measure their prevalence, maximal prevalent co-location patterns can be filtered efficiently. Finally, a series of experiments is conducted on both synthetic and real-facility data sets to demonstrate that the proposed algorithm can efficiently reduce both the computational time and the memory consumption compared with the existing algorithms.

Spatial co-location pattern mining based on the improved density peak clustering and the fuzzy neighbor relationship

<abstract> <p>Spatial co-location pattern mining discovers the subsets of spatial features frequently observed together in nearby geographic space. To reduce time and space consumption in checking the clique relationship of row instances of the traditional co-location pattern mining methods, the existing work adopted density peak clustering to materialize the neighbor relationship between instances instead of judging the neighbor relationship by a specific distance threshold. This approach had two drawbacks: first, there was no consideration in the fuzziness of the distance between the center and other instances when calculating the local density; second, forcing an instance to be divided into each cluster resulted in a lack of accuracy in fuzzy participation index calculations. To solve the above problems, three improvement strategies are proposed for the density peak clustering in the co-location pattern mining in this paper. Then a new prevalence measurement of co-location pattern is put forward. Next, we design the spatial co-location pattern mining algorithm based on the improved density peak clustering and the fuzzy neighbor relationship. Many experiments are executed on the synthetic and real datasets. The experimental results show that, compared to the existing method, the proposed algorithm is more effective, and can significantly save the time and space complexity in the phase of generating prevalent co-location patterns.</p> </abstract>

An Improved Approximation Algorithm for Co-location Mining in Uncertain Data Sets using Probabilistic Approach

complete data. Many of the real world data is Uncertain, for example, Demographic data, Sensor networksdata, GIS data etc.,. Handling such data is a challenge for knowledge discovery particularly in colocation mining.One straightforward method is to find the Probabilistic Prevalent colocations (PPCs). This method tries to find allcolocations that are to be generated from a random world. For this we first apply an approximation error to find allthe PPCs which reduce the computations. Next find all the possible worlds and split them into two different worldsand compute the prevalence probability. These worlds are used to compare with a minimum probability threshold todecide whether it is Probabilistic Prevalent colocation (PPCs) or not. The experimental results on the selected dataset show the significant improvement in computational time in comparison to some of the existing methods used incolocation mining.

A MapReduce approach for spatial co-location pattern mining via ordered-clique-growth

Spatial co-location pattern is a subset of spatial features whose instances are frequently located together in geography. Mining co-location patterns are particularly valuable for discovering spatial dependencies. Traditional co-location pattern mining algorithms are computationally expensive with rapidly increasing of data volume. In this paper, we explore a novel iterative framework based on parallel ordered-clique-growth for co-location pattern mining. The ordered clique extension can re-use previously processed information and be executed in parallel, and hence speed up the identification of co-location instances. Based on the iterative framework, a MapReduce algorithm is designed to search for prevalent co-location patterns in a level-wise manner, namely PCPM_OC. To narrow the search space of ordered cliques, two pruning techniques are suggested for filtering invalid clique instances as much as possible. The completeness and correctness of PCPM_OC are proven and we also discuss its complexity in this paper. Moreover, we compare PCPM_OC with two advanced MapReduce based co-location pattern mining algorithms on multiple perspectives. At last, substantial experiments are conducted on synthetic and real-world spatial datasets to study the performance of PCPM_OC. Experimental results demonstrate that PCPM_OC has a significant improvement in efficiency and shows better scalability on massive spatial data.

A clique-based approach for co-location pattern mining

Co-location pattern mining refers to the task of discovering the group of features (geographic object types) whose instances (geographic objects) are frequently located close together in a geometric space. Current approaches on this topic adopt a prevalence threshold (a measure of a user's interest in a pattern) to generate prevalent co-location patterns. However, in practice, it is not easy to specify a suitable prevalence threshold. Thus, users have to repeatedly execute the program to find a suitable prevalence threshold. Besides, the efficiency of these approaches is limited because of the expensive cost of identifying row-instances of co-location patterns. In this paper, we propose a novel clique-based approach for discovering complete and correct prevalent co-location patterns. The proposed approach avoids identifying row-instances of co-location patterns thus making it much easier to find a proper prevalence threshold. First, two efficient schemas are designed to generate complete and correct cliques. Next, these cliques are transformed into a hash structure which is independent of the prevalence threshold. Finally, the prevalence of each co-location pattern is efficiently calculated using the hash structure. The experiments on both real and synthetic datasets show the efficiency and effectiveness of our proposed approaches.

Mining maximal sub-prevalent co-location patterns

Spatial prevalent co-location pattern mining is to discover interesting and potentially useful patterns from spatial data, and it plays an important role in identifying spatially correlated features in many domains, such as Earth science and Public transportation. Existing approaches in this field only take into account the clique instances where feature instances form a clique. However, they may neglect some important spatial correlations among features in practice. In this paper, we introduce star participation instances to measure the prevalence of co-location patterns such that spatially correlated instances which cannot form cliques will also be properly considered. Then we propose a new concept called sub-prevalent co-location patterns (SPCP) based on the star participation instances. Furthermore, two efficient algorithms -- the prefix-tree-based algorithm (PTBA) and the partition-based algorithm (PBA) -- are proposed to mine all the maximal sub-prevalent co-location patterns (MSPCP) in a spatial data set. PTBA uses a typical candidate generate-and-test way starting from candidates with the longest pattern-size, while PBA adopts a step-by-step manner starting from 3-size core patterns. We demonstrate the significance of our proposed new concepts as well as the efficiency of our algorithms through extensive experiments.

Mining strong symbiotic patterns hidden in spatial prevalent co-location patterns

Spatial co-location patterns represent the subsets of spatial features which are frequently located together in a geographic space. Spatial co-location pattern mining has been a research hot in recent years. However, maybe the features in a prevalent co-location pattern further have more interesting relationships such as symbiotic relationships, competitive relationships or causal relationships. This paper mines symbiotic relationships implied in prevalent co-location patterns from dynamic spatial databases. Firstly, after analyzing the existed definition of symbiotic patterns, a criterion of judging strong symbiotic patterns is proposed. Secondly, a novel algorithm to mine strong symbiotic patterns from prevalent co-location patterns is presented, named basic algorithm. Third, for improving the efficiency of the basic algorithm, an improved algorithm which integrates two expensive operations of the basic algorithm into together, and a pruning strategy with two pruning lemmas are presented. The experiments evaluate the effectiveness and efficiency of the proposed algorithms with “real + synthetic” data sets and the results show that strong symbiotic patterns are more concise and actionable compared to traditional prevalent co-location patterns.

Effective lossless condensed representation and discovery of spatial co-location patterns

A spatial co-location pattern is a set of spatial features frequently co-occuring in nearby geographic spaces. Similar to closed frequent itemset mining, closed co-location pattern (CCP) mining was proposed for losslessly condensing large collections of prevalent co-location patterns. However, the state-of-the-art condensation methods in mining CCP are inspired by closed frequent itemset mining and do not consider the intrinsic characteristics of spatial co-locations, e.g., the participation index and ratio in spatial feature interactions, thus causing serious containment issues in CCP mining. In this paper, we propose a novel lossless condensed representation of prevalent co-location patterns, Super Participation Index-closed (SPI-closed) co-location. An efficient SPI-closed Miner is also proposed to effectively capture the nature of spatial co-location patterns, alongside the development of three additional pruning strategies to make the SPI-closed Miner efficient. This method captures richer feature interactions in spatial co-locations and solves the containment issues in existing CCP methods. A performance evaluation conducted on both synthetic and real-life data sets shows that SPI-closed Miner reduces the number of CCPs by up to 50%, and runs much faster than the baseline CCP mining algorithm described in the literature.

Redundancy Reduction for Prevalent Co-Location Patterns

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. 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 δ-covered , where $\delta \,(0\leq \delta \leq 1)$ 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.

An Improved Approximation Algorithm for Co-location Mining in Uncertain Data Sets using Probabilistic Approach

In this paper we investigate colocation mining problem in the context of uncertain data. Uncertain data is a partially complete data. Many of the real world data is Uncertain, for example, Demographic data, Sensor networks data, GIS data etc.,. Handling such data is a challenge for knowledge discovery particularly in colocation mining. One straightforward method is to find the Probabilistic Prevalent colocations (PPCs). This method tries to find all colocations that are to be generated from a random world. For this we first apply an approximation error to find all the PPCs which reduce the computations. Next find all the possible worlds and split them into two different worlds and compute the prevalence probability. These worlds are used to compare with a minimum probability threshold to decide whether it is Probabilistic Prevalent colocation (PPCs) or not. The experimental results on the selected data set show the significant improvement in computational time in comparison to some of the existing methods used in colocation mining.

Top-k 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.

Finding Probabilistic Prevalent Colocations in Spatially Uncertain Data Sets

A spatial colocation pattern is a group of spatial features whose instances are frequently located together in geographic space. Discovering colocations has many useful applications. For example, colocated plant species discovered from plant distribution data sets can contribute to the analysis of plant geography, phytosociology studies, and plant protection recommendations. In this paper, we study the colocation mining problem in the context of uncertain data, as the data generated from a wide range of data sources are inherently uncertain. One straightforward method to mine the prevalent colocations in a spatially uncertain data set is to simply compute the expected participation index of a candidate and decide if it exceeds a minimum prevalence threshold. Although this definition has been widely adopted, it misses important information about the confidence which can be associated with the participation index of a colocation. We propose another definition, probabilistic prevalent colocations, trying to find all the colocations that are likely to be prevalent in a randomly generated possible world. Finding probabilistic prevalent colocations (PPCs) turn out to be difficult. First, we propose pruning strategies for candidates to reduce the amount of computation of the probabilistic participation index values. Next, we design an improved dynamic programming algorithm for identifying candidates. This algorithm is suitable for parallel computation, and approximate computation. Finally, the effectiveness and efficiency of the methods proposed as well as the pruning strategies and the optimization techniques are verified by extensive experiments with “real + synthetic” spatially uncertain data sets.

A multiple window-based co-location pattern mining approach for various types of spatial data

Co-location pattern analysis represents the subsets of spatial events whose instances are found in close geographic proximity. Given a collection of Boolean spatial features, the co-location pattern discovery process finds the subsets of features frequently located together. Key challenges in co-location pattern analysis are modelling of neighbourhood in spatial domain, minimum prevalent threshold to generate collocation patterns and analysing extended spatial objects. We discuss the above key challenges using event centric approach and N-most prevalent co-location patterns approach. We propose a window-based model to find the neighbourhood for point spatial datasets and the multiple window model for extended spatial data objects. We also use N-most prevalent co-location patterns approach to filter the number of co-location pattern generation. We propose a more generic and efficient window-based model algorithm to find colocation patterns. Towards the end, we have done a comparative study of the existing approaches with our proposed approach.