Join-count Statistics Research Articles

Identifying the determinants of E-commerce offerings among grocery store locations in the United States: A spatial econometric analysis

This paper leverages store location data and analysis software from retail industry vendors to analyze the unique geographies of electronic commerce (e-commerce) offerings among major grocery chains in the United States. Join-Count statistics are calculated to identify patterns of clustering among offerings, and a spatial probit model is implemented to regress various trade area characteristics on a given grocery banner's decision to offer some form of e-commerce (pickup, delivery, or both) or no offering at a given store location. A regional case study of the Southeastern United States demonstrates how model results can shift based on scale, pointing to unique regional dynamics that deviate from broader national trends. This analysis carries implications for location planning and competitive defense strategies in the grocery industry, and also establishes avenues for future research.

Transformation of coastal wetlands in the Sundarban Delta (1999–2020)

Spanning across Bangladesh and India, the Sundarban Delta consists of over a thousand islands, the majority of which are protected. These islands are important for the rich biodiversity and unique species found here. However, these islands are also at the forefront of climate change due to the impact of rising sea levels and extreme weather events. Therefore, we analyzed the long-term transformations in the land use land cover (LULC) between 1999 and 2020. We used a variety of geostatistical methods, including optimized hot spots cold spots and join count statistics, to examine the spatial patterns of changes in LULC across the study area. The results of our analysis revealed substantial changes in the spatial patterns of mangroves and pond aquaculture. The changes revealed a distinct north–south demarcation in spatial patterns, in the form of clustering of mangroves in the uninhabited islands located in the south and pond aquaculture clustered in the northern inhabited islands. The loss of area under mangroves was concentrated in the southern edges of the islands, which were most exposed to erosion in the open ocean. Nevertheless, we observed an increase in the area under mangroves in some of the northern riverine islands (17 km2). In the case of pond aquaculture, it was mostly concentrated in inhabited islands in the north. Most of the expansions were concentrated in the Indian part of the delta (631 km2). It is noteworthy that because of effective conservation measures, there was very limited overlap between mangroves and pond aquaculture, denoting the conversion of agricultural land to pond aquaculture instead of mangroves. Thus, the results of our study revealed the importance of local level conservation policies and anthropogenic activities, such as deforestation and local level disturbance like over-extraction of water and pollution, on the changing patterns of LULC across this unique, fragile ecosystem. Future studies may incorporate a finer resolution time series of LULC changes over time and space to enable more detailed analysis.

Spatial Distributions of Diarrheal Cases in Relation to Housing Conditions in Informal Settlements: A Cross-Sectional Study in Abidjan, Côte d'Ivoire.

In addition to individual practices and access to water, sanitation, and hygiene (WASH) facilities, housing conditions may also be associated with the risk of diarrhea. Our study embraced a broad approach to health determinants by looking at housing deprivation characteristics as exposures of interest and confronting the latter's spatial distribution to that of diarrheal cases. We tested the hypothesis that the risk of diarrhea in informal settlements is not only associated with WASH services, but also with inadequate dwelling characteristics, and that their spatial distributions follow similar patterns. We designed a cross-sectional study and collected primary data through georeferenced household surveys in two informal settlements in Abidjan, Côte d'Ivoire. We used local join count statistics to assess the spatial distribution of events and multiple logistic regressions to calculate adjusted odds ratios between diarrhea and exposures. A total of 567 households were enrolled. We found that constant access to basic WASH services, non-durable building materials, cooking outdoors, and water service discontinuity were associated with higher risks of diarrhea in the general population. The spatial distribution of diarrheal cases coincided with that of dwelling deprivation characteristics. We observed significant heterogeneity within the study sites regarding the spatial distribution of diarrheal cases and deprived dwellings. Along with WASH infrastructure, communities also need dignified housing to effectively prevent diarrhea. We recommend that decision-makers acknowledge a "spectrum" of deprivation within the heterogeneous universe of informal settlements, adopting a site-specific approach based on high-resolution data to address diarrhea and improve people's well-being.

Estimating termite population size using spatial statistics for termite tunnel patterns

Subterranean termites build underground tunnels for foraging. The obtained food is transported to the nest through these tunnels, and consumed to maintain the termite colony. In this process, termites can cause damage to wooden structures. To develop effective control strategies to reduce termite damage, it is important to know the sizes of the termite populations in the tunnels. In this study, we proposed a method for estimating the termite population size using the spatial statistic indices including fractal dimension (FD), local density (LD), and join count statistic (JCS) for the tunnel patterns. However, the method needs further improvement to be applied in field conditions. For the method, we generated 8,000 tunnel pattern images (1,000 images for each N) using an agent-based model based on experimental data. Here, N (= 3, 4, ..., 10) represents the number of termites participating in tunnel construction in the simulation. Subsequently, we calculated the FD, LD and JCS values of the tunnel pattern and trained and verified the k-nearest neighbors (KNN) algorithm, using 5,600 and 2,400 images, respectively. The population size (N) was estimated based on the FD, LD and JCS using the KNN algorithm. The estimated accuracy for all N was 60% to 97% in the range of k = 1 to 300. If the model for tunnel pattern generation includes heterogeneous environmental conditions, the proposed method could be used to effectively estimate the actual number of termite populations. Finally, we briefly discuss the challenges affecting our model, and how these could be overcome.

Abstract 2032: Comprehensive spatial transcriptomic analysis of an integrated, diverse cohort reveals distinct molecular topographic patterns in triple negative breast cancer

Abstract Background: Triple negative breast cancer (TNBC) is an aggressive subtype of breast cancer that disproportionately affects African-American and black (AAB) women, who have higher rates of incidence and mortality. To understand this disparity, we must apply advanced molecular profiling to racially diverse cohorts. We propose the use of spatial transcriptomics to map whole transcriptome data to several thousand coordinates within tissue sections, for comprehensive and unbiased characterization of TNBC tumors and their microenvironment. Methods: We applied the Visium Spatial Gene Expression method (10x Genomics) to 28 fresh frozen TNBC tissue sections obtained from 14 patients (7 AAB and 7 Non-Hispanic White). Sections were stained with H&E, and regions of tumor and stroma were annotated by a pathologist. The assay yielded whole transcriptome data from over 36,000 spatially-defined features, averaging 1,380 features per section. Expression data from each sample was normalized and subject to dimensionality reduction and clustering analysis. All sections were also integrated into a single dataset, from which integrated clusters (IC) were defined. Several bioinformatics tools were used to annotate the data at the feature, cluster, and IC level. Join count statistical analysis was employed to quantify patterns of spatial aggregation or dispersion of ICs across samples. Results: Clustering analysis revealed that all samples exhibited a great deal of heterogeneity; most contained several transcriptionally distinct regions of both tumor and stroma. Application of the ESTIMATE gene sets at the feature level accurately defined tumor and non-malignant regions when compared to histopathological annotation. Gene set enrichment analysis at the cluster level allowed further classification of biological processes within each sample. Following integration of all 28 samples, 9 ICs were defined from transcriptional data. Although all ICs were present in all samples, IC5 - characterized by a strong hypoxic signature - was overrepresented in AAB samples. ICs were then mapped back to individual samples and subject to join count statistics. This revealed strong spatial autocorrelation within each IC, as well as significant spatial pairings of ICs. The fibrotic clusters IC3 and IC7 were strongly contiguous in all samples (z-score > 5), as were tumor clusters IC1 and IC4. Conversely, we found spatial exclusion between IC3 and tumor clusters IC5 and IC2. Conclusion: Our study provides novel evidence of spatially related populations across diverse TNBC samples. Our findings suggest that, while TNBC tumors are highly heterogeneous, they exhibit elements of a common spatio-transcriptional architecture. Moreover, this provides a new framework in which to evaluate transcriptional differences between racial groups within a broader spatial context. Citation Format: Rania Bassiouni, Michael Idowu, Lee D. Gibbs, Pamela J. Grizzard, Michelle G. Webb, Ashley Noriega, Valentina Robila, David W. Craig, John D. Carpten. Comprehensive spatial transcriptomic analysis of an integrated, diverse cohort reveals distinct molecular topographic patterns in triple negative breast cancer [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2032.

STICC: a multivariate spatial clustering method for repeated geographic pattern discovery with consideration of spatial contiguity

Spatial clustering has been widely used for spatial data mining and knowledge discovery. An ideal multivariate spatial clustering should consider both spatial contiguity and aspatial attributes. Existing spatial clustering approaches may face challenges for discovering repeated geographic patterns with spatial contiguity maintained. In this paper, we propose a Spatial Toeplitz Inverse Covariance-Based Clustering (STICC) method that considers both attributes and spatial relationships of geographic objects for multivariate spatial clustering. A subregion is created for each geographic object serving as the basic unit when performing clustering. A Markov random field is then constructed to characterize the attribute dependencies of subregions. Using a spatial consistency strategy, nearby objects are encouraged to belong to the same cluster. To test the performance of the proposed STICC algorithm, we apply it in two use cases. The comparison results with several baseline methods show that the STICC outperforms others significantly in terms of adjusted rand index and macro-F1 score. Join count statistics is also calculated and shows that the spatial contiguity is well preserved by STICC. Such a spatial clustering method may benefit various applications in the fields of geography, remote sensing, transportation, and urban planning, etc.

Spatial Dependence of CT Emphysema in Chronic Obstructive Pulmonary Disease Quantified by Using Join-Count Statistics.

Background Existing CT emphysema measurements quantify the extent or clustering of emphysema voxels in chronic obstructive pulmonary disease (COPD); however, these measurements do not quantify how those voxels are clustered. Purpose To develop a CT measurement to quantify the "compactness" of emphysema voxels, called the normalized join count (NJC), and to determine whether the NJC measurement differentiates COPD disease severity and correlates with lung function and visual emphysema scores. Materials and Methods In this secondary analysis of a prospective study, lung function and CT images were obtained from the Canadian Cohort Obstructive Lung Disease study visit 1 from 2009 to 2013. Participants were categorized as never-smokers, at risk, mild COPD, or moderate-severe COPD. Diffusion capacity for carbon monoxide/alveolar volume was measured. CT emphysema was scored visually by radiologists. CT measurements included the percentage low-attenuation area with attenuation less than -950 HU (%LAA-950insp), low-attenuation cluster (LAC), and lowest 15th percentile point of the CT lung density histogram. NJC was developed to measure compactness of CT emphysema voxels. An analysis of variance determined differences between groups. Multivariable ridge regression determined association between CT measurements with lung function and radiologist scores. Results A total of 1294 participants (750 men; mean age, 67 years ± 10) were analyzed (277 never-smokers, 306 at risk, 427 mild COPD, and 284 moderate-severe COPD). NJC, %LAA-950insp, and LAC measurements were higher in moderate-severe COPD than in never-smokers and at-risk participants (P < .05 for all comparisons), but only NJC was different between mild and ;moderate-severe COPD (mean, 1.98% ± 3.61 vs 1.44% ± 2.14; P < .05). In multivariable regression analysis, among all CT measurements NJC had the greatest relative contribution to diffusion capacity for carbon monoxide/alveolar volume (P = .002) and visual emphysema score (P < .001). Conclusion The relationship of normalized join count with severity of chronic obstructive pulmonary disease may indicate that the assessment of this disease is dependent on the number of low attenuating voxels or the size of clusters and the spatial arrangement of such voxels. © RSNA, 2021 Online supplemental material is available for this article. See also the editorial by Grenier in this issue.

Spatial and Temporal Analysis of Phytophthora megakarya Epidemic in Newly Established Cacao Plantations.

Studying spatial and temporal plant disease dynamics helps us to understand pathogen dispersal processes and improve disease control recommendations. In this study, three cacao plots devoid of primary inoculum of Phytophthora megakarya (causal agent of cacao black pod rot disease) upon establishment in 2006 were monitored for presence of disease on a weekly basis from 2009 to 2016. Ripley's K(r) function, join count statistics, and Fisher's Exact test were used to analyze spatial and temporal disease dynamics. Disease distribution maps showed aggregated disease patterns in all plots; however, for the years of disease onset, exogenous primary infections were mostly randomly distributed. The K(r) function confirmed these results indicating that inoculum generally disperses only over short distances. Moreover, significant positive spatial autocorrelations showed that diseased trees were often clustered up to a distance of 3 to 9 m. Temporal disease progression was low, meaning that endogenous inoculum failed to establish itself, which is partly explained by rigorous phytosanitation and partly by unfavorable microclimatic conditions for disease development. Because P. megakarya had difficulty establishing itself in the plots, proximity to already infected cacao plantations drove infection dynamics. Thus, isolation of newly established cacao plantations from infected ones and rigorous phytosanitation as a preventive strategy appears to be an effective approach to control cacao black pod rot disease for newly established cacao plantations.

Spatial dynamics of alpine tree lines under global warming: What explains the mismatch between tree densification and elevational upward shifts at the tree line ecotone?

AbstractAimMost studies focusing on the alpine tree line responses to climate warming have used either the tree densification within the ecotone or its elevational upshift as indicators. However, it is acknowledged that the relationship between densification and upshift is spatially heterogeneous, making inferences and comparability among studies tricky. The lack of consistent empirical evidence on this potential mismatch and its drivers leads us to focus on this issue in this study. The aim was twofold: (a) to quantify the mismatch between the two processes at a regional scale, and (b) to identify its site‐specific determinants.TaxonPinus uncinata (Ramond ex DC.)LocationFrench eastern Pyrenees.MethodsAn object‐oriented supervised classification procedure was performed on historical (1953) and current (2015) aerial photographs. Based on the resulting rasters, densification of the tree line ecotone and upward shift of the tree line were estimated at the two dates in 191 sites, then standardized, before finally being compared. Three site clusters were derived (no mismatch, densification prevalence and upshift prevalence). After having characterized their spatial patterns through join count statistics, a multinomial logistic regression model was computed to identify the correlates of these clusters among a list of site variables.ResultsNo spatial pattern among the categories of responses emerges at a local scale, but buffers with no mismatch tend to aggregate at a larger scale. Changes in minimum air temperatures, site elevation, mean slope, slope morphometry and lithology appear as significant drivers of the observed mismatch, implying that the relationship between densification and elevational upshift is context specific.Main conclusionsOur findings suggest that both densification and upshift should be considered in quantitative analyses of tree line spatial dynamics, since these two ecological processes are not controlled by the same drivers.

Evaluating possible intraspecific variation in resistance of western hemlock (Pinaceae) toAdelges tsugae(Hemiptera: Adelgidae)

AbstractWestern hemlock,Tsuga heterophylla(Rafinesque) Sargent (Pinaceae), trees growing in a clonal, commercial seed orchard on Whidbey Island, Washington, United States of America were assessed forAdelges tsugae(Annand) (Hemiptera: Adelgidae) infestation levels to determine whether there was any evidence of resistance to this herbivore. Join-count statistics revealed thatA. tsugaeinfested trees were not clumped, but instead were randomly distributed throughout the seed orchard. Chi-square analyses suggested that there is a genetic basis for different levels ofA. tsugaeinfestation among the genets represented in the orchard. However, since none of the genets were completely free ofA. tsugaeinfestation, differences among genets seem to be related more to susceptibility or tolerance than complete resistance. Among the 17 genets that had five or more ramets in the seed orchard, only one had more than one ramet free ofA. tsugae. That genet had four of five ramets that were free ofA. tsugae. However, it is not possible to say whether that was due to chance or inherent tree characteristics that make it less susceptible toA. tsugaeinfestation.

Operational Local Join Count Statistics for Cluster Detection.

This paper operationalizes the idea of a local indicator of spatial association (LISA) for the situation where the variables of interest are binary. This yields a conditional version of a local join count statistic. The statistic is extended to a bivariate and multivariate context, with an explicit treatment of co-location. The approach provides an alternative to point pattern based statistics for situations where all potential locations of an event are available (e.g., all parcels in a city). The statistics are implemented in the open source GeoDa software and yield maps of local clusters of binary variables, as well as co-location clusters of two (or more) binary variables. Empirical illustrations investigate local clusters of house sales in Detroit in 2013 and 2014, and urban design characteristics of Chicago census blocks in 2017.

Spatial autocorrelation for massive spatial data: verification of efficiency and statistical power asymptotics

Being a hot topic in recent years, many studies have been conducted with spatial data containing massive numbers of observations. Because initial developments for classical spatial autocorrelation statistics are based on rather small sample sizes, in the context of massive spatial datasets, this paper presents extensions to efficiency and statistical power comparisons between the Moran coefficient and the Geary ratio for different variable distribution assumptions and selected geographic neighborhood definitions. The question addressed asks whether or not earlier results for small n extend to large and massively large n, especially for non-normal variables; implications established are relevant to big spatial data. To achieve these comparisons, this paper summarizes proofs of limiting variances, also called asymptotic variances, to do the efficiency analysis, and derives the relationship function between the two statistics to compare their statistical power at the same scale. Visualization of this statistical power analysis employs an alternative technique that already appears in the literature, furnishing additional understanding and clarity about these spatial autocorrelation statistics. Results include: the Moran coefficient is more efficient than the Geary ratio for most surface partitionings, because this index has a relatively smaller asymptotic as well as exact variance, and the superior power of the Moran coefficient vis-a-vis the Geary ratio for positive spatial autocorrelation depends upon the type of geographic configuration, with this power approaching one as sample sizes become increasingly large. Because spatial analysts usually calculate these two statistics for interval/ration data, this paper also includes comments about the join count statistics used for nominal data.

Spatial Correlation Analysis on Physical Unclonable Functions

The evaluation of the quality of physical unclonable functions (PUFs) is still under research. Most state-of-the-art metrics are found to measure only bias, while correlations, e.g., within the PUF response of a single device, remain unnoticed. In this paper, we introduce spatial autocorrelation analysis (SPACA), which is used in other fields of research, as a method to reveal correlations in the response of single-challenge PUFs. The presented statistics—Moran’s I, Geary’s c, and Join Count statistic—can be used to test the quality of an implementation using a set of sample devices as well as monitor ongoing production. Their results are also important for selecting an appropriate post-processing of the raw PUF response. Experiments on data sets from three different PUF implementations on field-programmable gate array and application-specific integrated circuit using SPACA show the capabilities of the introduced statistics. An efficient implementation of SPACA in MATLAB was developed to conduct the experiments. We discuss how SPACA can be used in practical testing and suggest to consider SPACA for a future test suite for PUFs.

Spatial and Temporal Pattern Analyses of Esca Grapevine Disease in Vineyards in France.

To assess the capacity of esca to spread within vineyards of the Bordeaux region, over 8 years of annual records, containing between 1,200 and 2,300 contiguous Cabernet Sauvignon vines from 15 mature vineyards, were used for spatial statistical analyses. A group of nonparametric tests, based on join count statistics and on permutation methods, was developed to characterize the spatial structure of esca-symptomatic vines in terms of spread in any direction or within-row only. Among vineyards, a large range of spatial patterns, from random to strongly structured, associated with various prevalence rates that increased over time were observed. In four vineyards, the complex esca distribution pattern indicated different levels of clustering. By contrast, in other vineyards, only small clusters of two adjacent symptomatic vines were observed, and they were localized along rows, without enlargement over time, except in one vineyard. An analysis of spatial dependence between previously and newly symptomatic vines within k-order neighborhoods (k = 1 to 5), showed, for 5 of the 15 vineyards, that the newly symptomatic vines were located close to previously infected vines, without a favored orientation or neighbor order. All the results together suggested a limited potential for secondary local spread from neighboring symptomatic vines.

Post-fire morel (Morchella) mushroom abundance, spatial structure, and harvest sustainability

Morel mushrooms are globally distributed, socially and economically important reproductive structures produced by fungi of the genus Morchella. Morels are highly prized edible mushrooms and significant harvests are collected throughout their range, especially in the first year after fire, when some morel species fruit prolifically. Few studies have quantified post-fire morel mushroom abundance, despite their widespread human use. The purpose of this study is to provide the first ever estimate of post-fire morel mushroom abundance in Sierra Nevada mixed-conifer forest. Specifically, we estimate the abundance and spatial variability of morel mushrooms across an intensively mapped and measured forest research site during the first growing season following fire.We conducted this study in the Yosemite Forest Dynamics Plot, a long-term forest research installation located in old-growth mixed-conifer forest of Yosemite National Park, California, USA. We surveyed for morel mushrooms in n=1119 contiguous circular 3.14m2 plots arranged along 2240m of permanently marked, georeferenced transects. We characterized the spatial correlation of morel plots using k category (multicolor) join count statistics. We analyzed spatial correlations at interplot distances up to 9.0m.There were 595 morel mushrooms in the 1119 plots we measured. Mushrooms occurred in 17.8% of plots. We estimated a mean standing crop of 1693morelsha−1 (SE=155.4morelsha−1). Morel-occupied plots were strongly and significantly spatially autocorrelated. Most of the spatial correlation among morel-occupied plots was apparent at scales up to 7.0m, and was strongest at scales <3.0m.This study is one of only four that provide unbiased estimates of post-fire morel abundance. Our morel abundance estimates are generally consistent with prior work in high-latitude North American conifer forests. The strong spatial autocorrelation of morel-occupied microsites at scales <7m indicates that key factors controlling post-fire morel productivity are heterogeneous at small spatial scales. We propose a simple conceptual model to explain this spatial structure that includes spatial variability of pre-fire Morchella colonies; pre-fire vegetation community and fuelbed; fire behavior, intensity, and effects; and soil moisture and temperature. Relatively liberal harvest limits for recreational and subsistence harvesters appear appropriate and sustainable, at least for coniferous forests in the first year following fire. However, intensive commercial harvest, in jurisdictions where it is allowed, may warrant monitoring to assess potential impacts to long-term morel productivity, conflict with recreational harvesters, and non-target effects.

Utilizing spatial association analysis to determine the number of multiple grids for multiple-point statistics

Scale selection is a fundamental issue of spatial analysis. Based on spatial association analysis, this paper proposes a quantitative method for estimating the scale, which is represented using the minimal number of multiple grids in a single normal equation simulation. First, the largest scale structural information that a data template can consider for the finest grid is computed using the distance between the central cell and the border of the data template. The maximum distance at which cells are associated with each other in the training image is then analyzed using join count statistics. Finally, the minimal number of multiple grids is estimated based on the criterion that the data template used on the largest grid should account for the maximum distance between associated cells. The proposed method is validated using two- and three-dimensional experiments. The results show that increasing the number of multiple grids does not significantly improve the simulation quality when the number of multiple grids used is larger than that estimated. A sensitivity analysis demonstrates that the proposed method adapts to the configuration of the data template, the geometric structure of the target surface objects, and a re-scaled training image if it adequately represents the large-scale structural information of the target surface objects.

Classifying multidimensional trajectories of neighbourhood change: a self-organizing map and k-means approach

ABSTRACTUnderstanding the dynamic nature of how urban neighbourhoods evolve through time has been a critical issue both in the literature and in public policy practice for decades. Methodological limitations in understanding change across the multiple attribute dimensions that define a neighbourhood, through time and for spatially situated units, have largely reduced empirical analyses to two points in time or for a singular attribute dimension. This paper demonstrates a two-layered approach to classifying neighbourhoods according to their multidimensional, temporal trajectories. The method first projects data onto a two-dimensional output space using a self-organizing map, then constructs temporal trajectories of change across this space and, finally, classifies the resulting trajectories with a k-means algorithm. The resulting typology of neighbourhood trajectories are then mapped in the geographic space to visualize the space–time, multidimensional dynamics. A case study of neighbourhood change from 1970 to 2010 in eight US cities demonstrates the effectiveness approach for grouping neighbourhoods according to the similarity of their temporal pathways of change. Ten processes are uncovered ranging from various forms of suburbanization to revitalization and a suburban densification trend in the newest, rapidly growing cities in the study. Finally, we calculated a join-count statistic to quantify the observed spatial pattern of each of these neighbourhood types in each city.

Local Indicator of Colocation Quotient with a Statistical Significance Test: Examining Spatial Association of Crime and Facilities

Most existing point-based colocation methods are global measures (e.g., join count statistic, cross K function, and global colocation quotient). Most recently, a local indicator such as the local colocation quotient has been proposed to capture the variability of colocation across areas. Our research advances this line of work by developing a simulation-based statistical test for the local indicator of colocation quotient (LCLQ). The study applies the indicator to examine the association of land use facilities with crime patterns. Moreover, we use the street network distance in addition to the traditional Euclidean distance in defining neighbors because human activities (including facilities and crimes) usually occur along a street network. The method is applied to analyze the colocation of three types of crimes and three categories of facilities in a city in Jiangsu Province, China. The findings demonstrate the value of the proposed method in colocation analysis of crime and facilities and, in general, colocation analysis of point data.

Detecting nominal variables’ spatial associations using conditional probabilities of neighboring surface objects’ categories

How to automatically mining the spatial association patterns in spatial data is a challenging task in spatial data mining. In this paper, we propose three indices that represent the per-class, inter-class, and overall spatial associations of a nominal variable, which are based on the conditional probabilities of surface object categories. These indices represent relative quantities and are normalized to the region [−1,1], which more accord with the intuitive cognition of people. We present some algorithms for detecting spatial associations that are based on these indices. The proposed method can be regarded as an extension of join count statistics and Transiogram. Several constructive examples were used to illustrate the advantages of the new method. Using two real data sets, vegetation types in Qingxian, Shanxi, China and neural tube birth defects in Heshun, Shanxi, China, we ran comparative experiments with other commonly used methods, including join count statistics, co-location quotient, and Q(m) statistics. The experimental results show that the proposed method can detect more subtle spatial associations, and is not sensitive to the sequence of neighbors.

Spatial autocorrelation of communes websites: A case study of the region Stredné Považie in Slovakia

AbstractSince its origination the Internet has been the basic communication channel through which e-Government processes in our society are carried out. The basic element of such processes is an existing website. This paper is the result of long-term research during which the authors collected information on the presence or absence of websites of self-governments in Slovakia. The output can be divided into two main parts. The first one, on the basis of the acquired data, evaluates the overall trend of self-government websites between 2008-2012. The results were distributed in the form of a website devoted to communes of Slovakia, using technology enabling the graphical and cartographic interpretation of the results. In the second part, on the basis of the gathered data, the authors applied spatial autocorrelation, specifically the ‘join count statistics’ method with the subsequent application to selected phenomenon in society, in particular the occurrence of websites of a selected region of Stredné Považie in Slovakia at the same time interval. This way the authors wanted to point out the interaction of communes in the development of websites, whether through inspiration or rivalry among neighbouring communes. From this point of view, mainly in the first period under review (2008), positive spatial autocorrelation is apparent in the occurrence of communes with websites.