Fitter: post-mining user-preferred co-location patterns interactively

This research addresses the colocation or agglomeration patterns of foreign-owned firms in the small open economy of the Netherlands. The empirical evidence shows that foreign-owned firms exhibit different regional colocation patterns than domestic firms for the following industries: mining, construction, transport and communications, services, and trade industry across the 12 Dutch provinces. In the agriculture industry, forestry and fishing industry, and the manufacturing industry the colocation patterns of the domestics and foreign-owned firms are similar. Empirical results also validate that firm size affects the agglomeration behaviour of foreign-owned firms; large foreign companies exhibit different collocation blueprints than smaller and, medium-sized enterprises. Related to industry, large foreign-owned firms target mainly the trade industry and the manufacturing industry. Results confirm that young established foreign-owned firms exhibit similar colocation patterns around older, more experienced foreign counterparts in the host economy. Furthermore, the colocation patterns of foreign-owned firms vary also according to different home countries. Firms coming from countries in proximity with the host economy reveal different colocation patterns than firms coming from more distanced countries. Our results strengthen the theoretical argumentation line that foreign-owned firms value location attributes differently depending on firm characteristics and they also exhibit a different location pattern than domestic counterparts.

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.

Spatial co-location patterns represent the subsets of features (co-location) whose events are frequently located together in geographic space. Spatio-temporal co-location (co-occurrence) pattern mining extends the mining task to the scope of both space and time. However, embedding the time factor into spatial co-location pattern mining process is a subtle problem. Previous researches either treat the time factor as an alternative dimension or simply carry out the mining process on each time segment. In this paper, we propose a weighted sliding window model (WSW-Model) which introduces the impact of time interval between the spatio-temporal events into the interest measure of the spatio-temporal co-location patterns. We figure out that the aforementioned two approaches fit into the two special cases in our proposed model. We also propose an algorithm (STCP-Miner) to mine spatio-temporal co-location patterns. The experimental evaluation with both the synthetic data sets and a real world data set shows that our algorithm is relatively effective with different parameters.

Co-location pattern mining plays an important role in spatial data mining. With the rapid growth of spatial datasets, the usefulness of co-location patterns is strongly limited by the huge amount of discovered patterns. Although several methods have been proposed to reduce the number of discovered patterns, these statistical algorithms are unable to guarantee that the extracted co-location patterns are user preferred. Therefore, it is crucial to help the decision maker discover his/her preferred co-location patterns via efficient interactive procedures. This article proposes a new interactive approach that enables the user to discover his/her preferred co-location patterns. First, we present a novel and flexible interactive framework to assist the user in discovering his/her preferred co-location patterns. Second, we propose using ontologies to measure the similarity of two co-location patterns. Furthermore, we design a pruning scheme by introducing a pattern filtering model for expressing the user's preference, to reduce the number of the final output. By applying our proposed approach over voluminous sets of co-location patterns, we show that the number of filtered co-location patterns is reduced to several dozen or less and, on average, 80% of the selected co-location patterns are user preferred.

* Corresponding author Abstract—The co-location pattern mining discovers the subsets of spatial features which are located together frequently in geography. However, the huge number of the co-location mining results limit the usability of co-location patterns. Furthermore, users hardly identify and understand the interesting knowledge directly from the single co-location pattern.In this paper, we studied the problem of extractingcombined co-location patterns from a large collectionof prevalent co-location patterns.We first gave the definitions of atomic co-location pattern, combined co-location pattern pair and cluster; secondly, we designed a series of interesting metrics to measure the interestingness of atomic co-location patterns, combined co-location pattern pairs and clusters; thirdly, an combined co-location mining algorithm and redundant elimination strategies were proposed. The experiments evaluated the method both on real data sets and syntheticdata sets. The results show that our method can effectively discover combined co-location patterns. Keywords-co-location pattern mining; combined mining; post-analysis

With immense extent of applications, one of the important tasks in data mining is the spatial pattern identification. Discovering spatial co-location patterns presents challenges as spatial objects are embedded in a continuous space. For co-location pattern mining, previous studies often emphasize on the association analysis of every spatial feature. As a result, interesting patterns involving events with different frequency cannot be captured. In this paper, we study the problem of efficiently mining co-location patterns with lattice structure called, Multi-dimensional Circlet Lattice-based Spatial Co-location Pattern Mining (MCL-SCPM), frequently located together in spatial proximity. MCL-SCPM initially identifies the candidate co-location using feature inclusive ratio which incorporates the spatial co-location patterns at minimum time interval with maximum coverage ratio. Next, MCL-SCPM discovers co-location patterns in a multi-dimensional spatial structure for different movements of an object by measuring the cohesion of a pattern. To extract maximal co-located patterns, MCL-SCPM method finally, uses Circlet Lattice-based structure to extract maximal co-located patterns. We conduct an extensive performance study to test and evaluate the effectiveness of MCL-SCPM method. Our experimental results show that MCL-SCPM method minimizes the execution time for mining co-location patterns without producing large computational overheads.

Spatial co-location patterns represent the subsets of features whose instances are frequently located together in geographic space. It is difficult to discover co-location patterns because of the huge amount of space data. A common framework for mining spatial co-location patterns employs a level-wised search method to discover co-location patterns, and generates numerous redundant patterns which need huge cost of space storage and time consumption. Longer size patterns may have more interesting information for users, which causes the requirement for mining longer size patterns preferentially. In this paper, a novel algorithm is proposed to discover compact co-location patterns called top-k-size maximal co-location patterns by introducing a new data structure — MCP-tree, where k is a desired number of distinct sizes of mined co-location patterns. Our algorithm doesn't need to generate all candidate co-locations and it only checks partial candidates to mine top-k-size maximal co-location patterns, so it needs less space and costs less time. The experiment result shows that the proposed algorithm is efficient.

With the rapid growth and extensive applications of the spatial dataset, it's 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. It's difficult to discovery co-location patterns be- cause of the huge amount of data brought by the instances of spatial features. A large fraction of the computation time is devoted to identifying the table instances of co-location patterns. The essence of co-location patterns discovery and four 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----iCPI-tree (Improved Co-location Pattern Instance Tree), is proposed. The iCPI-tree is an improved version of the CPI-tree which materializes spatial neighbor relationships in order to acceler- ate the process of identifying co-location instances. This paper proves the correctness and completeness of the new ap- proach. Finally, an experimental evaluations using synthetic and real world datasets show that the algorithm is computa- tionally more efficient.

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.

ABSTRACTRegional co-location patterns represent subsets of feature types that are frequently located together in sub-regions in a study area. These sub-regions are unknown a priori, and instances of these co-location patterns are usually unevenly distributed across a study area. Regional co-location patterns remain challenging to discover. This study developed a multi-level method to identify regional co-location patterns in two steps. First, global co-location patterns were detected, and other non-prevalent co-location patterns were identified as candidates for regional co-location patterns. Second, an adaptive spatial clustering method was applied to detect the sub-regions where regional co-location patterns are prevalent. To improve computational efficiency, an overlap method was developed to deduce the sub-regions of (k + 1)-size co-location patterns from the sub-regions of k-size co-location patterns. Experiments based on both synthetic and ecological data sets showed that the proposed method is effective in the detection of regional 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.

Spatial co-location pattern mining is an important task in spatial data mining. However, traditional mining frameworks often produce too many prevalent patterns of which only a small proportion may be truly interesting to end users. To satisfy user preferences, this work proposes an interactive probabilistic post-mining method to discover user-preferred co-location patterns from the early-round of mined results by iteratively involving user's feedback and probabilistically refining preferred patterns. We first introduce a framework of interactively post-mining preferred co-location patterns, which enables a user to effectively discover the co-location patterns tailored to his/her specific preference. A probabilistic model is further introduced to measure the user feedback-based subjective preferences on resultant co-location patterns. This measure is used to not only select sample co-location patterns in the iterative user feedback process but also rank the results. The experimental results on real and synthetic data sets demonstrate the effectiveness of our approach.

A spatial co-location pattern is a subset of a spatial feature set whose instances prevalently appear in nearby locations in space. The objective of spatial co-location pattern mining is to detect co-location patterns that are non-obvious, informative, or predictive. Due to the heterogeneity in the distribution of spatial instances, spatial co-location patterns are classified into global co-location patterns (GCPs) and local co-location patterns (LCPs). The technique that discovers both simultaneously is termed multi-level co-location pattern mining (MLCPM). However, existing MLCPM methods have room for improvement in efficiently identifying GCPs and perform poorly in discovering prevalent sub-areas of LCPs. To address these issues, we propose a novel MLCPM framework called ML-CCHDB. This framework enhances GCP mining efficiency by optimizing the column calculation method tailored for MLCPM. Furthermore, it utilizes the HDBSCAN clustering method to identify potential prevalent sub-areas of LCPs and develops an adaptive approach for generating input parameters to enhance detection efficiency and quality. Experimental results on both synthetic and real datasets demonstrate that the column calculation optimizations in ML-CCHDB effectively enhance efficiency. Moreover, HDBSCAN strikes a balance between efficiency and quality in prevalent sub-area mining. These results fully validate the proposed framework's effectiveness and efficiency.

A spatial colocation pattern is a group of spatial features whose instances frequently appear together in close proximity to each other. The proximity of instances is generally measured by the distance between them. If the distance is smaller than a distance threshold that is specified by users, they have a neighbor relationship. However, it is difficult for users to give a suitable distance threshold and mining results also vary widely with different distance thresholds. In addition, using distance thresholds are hard to accurately obtain neighborhoods of instances in heterogeneous distribution density data sets. In this study, we propose a new method for determining the neighbor relationship of instances in space without the distance threshold based on Delaunay triangulation (DT). We design three filtering strategies, such as a feature invalid edge, a global positive edge, and a local positive edge, to constrain the original DT to accurately extract the neighborhoods of instances in space. Then, a miner called DT‐based colocation (DTC) pattern mining is developed. Different from the traditional algorithms which adopt the time‐consuming generate‐test candidate model, DTC directly collects the table instances of colocation patterns from the constrained DT by building neighboring polygons and filters prevalent patterns. We compare the results mined by DTC with by the traditional algorithms at macrolevel and microlevel on both real and synthetic data sets to prove that the DTC algorithm improves the effectiveness and fineness of mining results.

Spatial co-location patterns represent the subsets of spatial features whose instances are frequently located together in geographic space. Common frameworks for mining co-location patterns generate numerous redundant co-location patterns. Thus, several methods were proposed to overcome this drawback. However, most of these methods do not guarantee that the extracted co-location patterns are interesting for the user because they are generally based on statistical information. Thus, it is crucial to help the decision-maker choose interesting co-location patterns with an efficient interactive procedure. This paper proposed an interactive approach to prune and filter discovered co-location patterns. First, ontologies were used to improve the integration of user knowledge. Second, an interactive process was designed to collaborate with the user to find the interesting co-location patterns efficiently. The experimental results on a real data set demonstrated the effectiveness of our approach.