Clustering of temporal event processes

A temporal point process is a sequence of points, each representing the occurrence time of an event. Each temporal point process is related to the behavior of an entity. As a result, clustering of temporal point processes can help differentiate between entities, thereby revealing patterns of behaviors. This study proposes a hierarchical cluster method for clustering temporal point processes based on the discrete Fréchet (DF) distance. The DF cluster method is divided into four steps: (1) constructing a DF similarity matrix between temporal point processes; (2) constructing a complete linkage hierarchical tree based on the DF similarity matrix; (3) clustering the point processes with a threshold determined by locating the local maxima on the curve of the pseudo-F statistic (an index which measures the separability between clusters and the compactness in clusters); and (4) identifying inner patterns for each cluster formed by a series of dense intervals, each of which contains at least one event of all processes of the cluster. The contributions of the article are: (1) the proposed DF cluster method can cluster temporal point processes into different groups and (2) more importantly, it can identify the inner pattern of each cluster. Two synthetic data sets were created to illustrate the DF distance between temporal point process clusters (the first data set) and validate the proposed DF cluster method (the second data set), respectively. An experiment and a comparison with a method based on dynamic time warping show that DF cluster successfully identifies the preconfigured patterns in the second synthetic data set. The cluster method was then applied to a population migration history data set for the Northern Plains of the United States, revealing some interesting population migration patterns.     

COVID-19期间国家关系交互网络时空分析研究

COVID-19疫情不断蔓延为国际政治、外交关系等带来深刻影响。目前基于复杂网络方法的国际关系研究较少考虑节点的空间属性,难以探索国际关系的动态演化模式及其空间分布特征。该文提出一种结合时间序列聚类与空间统计的国家关系交互网络演化模式探测方法。基于2020年1月-2021年3月的GDELT数据构建国家关系交互网络,基于节点的演化特征,应用K-means聚类算法将节点划分为6种类型,结合局部连接统计方法分析节点演化模式的空间分布特征。研究表明:面对疫情冲击,各国为控制疫情蔓延倾向于参与合作交互事件;国家关系交互网络中的不同时序演化模式总体按照节点的点度中心性强度由高到低分布;疫情防控期间网络中始终处于边缘地位的节点在空间分布上呈现聚集特征,而核心节点空间分布较分散。通过研究网络节点的时序演化模式及空间分布特征可为公共卫生危机事件期间国际关系与地缘政治研究提供新思路,对于危机事件期间制定外交政策与应对策略具有一定参考价值。     

Exploring spatiotemporal clusters based on extended kernel estimation methods

We examined three different ways to integrate spatial and temporal data in kernel density estimation methods (KDE) to identify space–time clusters of geographic events. Spatial data and time data are typically measured in different units along respective dimensions. Therefore, spatial KDE methods require special extensions when incorporating temporal data to detect spatiotemporal clusters of geographical event. In addition to a real-world data set, we applied the proposed methods to simulated data that were generated through random and normal processes to compare results of different kernel functions. The comparison is based on hit rates and values of a compactness index with considerations of both spatial and temporal attributes of the data. The results show that the spatiotemporal KDE (STKDE) can reach higher hit rates while keeping identified hotspots compact. The implementation of these STKDE methods is tested using the 2012 crime event data in Akron, Ohio, as an example. The results show that STKDE methods reveal new perspectives from the data that go beyond what can be extracted by using the conventional spatial KDE.     

The Use of Comaps to Explore the Spatial and Temporal Dynamics of Fire Incidents: A Case Study in South Wales,United Kingdom*

This article reports on the results from a spatiotemporal analysis of disaggregate fire incident data. The innovative analysis presented here focuses on the exploration of spatial and temporal patterns for four principal fire incident categories: property, vehicle, secondary fires, and malicious false alarms. This research extends previous work on spatial exploration of spatiotemporal patterns by demonstrating the benefits of comaps and kernel density estimation in examining temporal and spatiotemporal dynamics in calls for services. Results indicate that fire incidents are not static in either time or space and that spatiotemporal variation is related to incident type. The application of these techniques has the potential to inform policy decisions both from a reactive, resource‐allocation perspective and from a more proactive perspective, such as through spatial targeting of preventive measures.     

Flow Cross K-function: a bivariate flow analytical method

Spatial flow data represent meaningful interaction activities between pairs of corresponding locations, such as daily commuting, animal migration, and merchandise shipping. Despite recent advances in flow data analytics, there is a lack of literature on detecting bivariate or multivariate spatial flow patterns. In this paper we introduce a new spatial statistical method called Flow Cross K-function, which combines the Cross K-function that detects marked point patterns and the Flow K-function that detects univariate flow clustering patterns. Flow Cross K-function specifically assesses spatial dependence of two types of flow events, in other words, whether one type of flows is spatially associated with the other, and if so, whether this is according to a clustering or dispersion trend. Both a global version and a local version of Flow Cross K-function are developed. The former measures the overall bivariate flow patterns in the study area, while the latter can identify anomalies at local scales that may not follow the global trend. We test our method with carefully designed synthetic data that simulate the extreme situations. We exemplify the usefulness of this method with an empirical study that examines the distributions of taxi trip flows in New York City.     

Leveraging correlation across space and time to interpolate geophysical data via CoKriging

Managing geophysical data generated by emerging spatiotemporal data sources (e.g. geosensor networks) presents a growing challenge to Geographic Information System science. The presence of correlation poses difficulties with respect to traditional spatial data analysis. This paper describes a novel spatiotemporal analytical scheme that allows us to yield a characterization of correlation in geophysical data along the spatial and temporal dimensions. We resort to a multivariate statistical model, namely CoKriging, in order to derive accurate spatiotemporal interpolation models. These predict unknown data by utilizing not only their own geosensor values at the same time, but also information from near past data. We use a window-based computation methodology that leverages the power of temporal correlation in a spatial modeling phase. This is done by also fitting the computed interpolation model to data which may change over time. In an assessment, using various geophysical data sets, we show that the presented algorithm is often able to deal with both spatial and temporal correlations. This helps to gain accuracy during the interpolation phase, compared to spatial and spatiotemporal competitors. Specifically, we evaluate the efficacy of the interpolation phase by using established machine-learning metrics (i.e. root mean squared error, Akaike information criterion and computation time).     

Two-stage permutation tests for determining homogeneity within a spatial cluster

The discovery of spatial clusters formed by proximal spatial units with similar non-spatial attribute values plays an important role in spatial data analysis. Although several spatial contiguity-constrained clustering methods are currently available, almost all of them discover clusters in a geographical dataset, even though the dataset has no natural clustering structure. Statistically evaluating the significance of the degree of homogeneity within a single spatial cluster is difficult. To overcome this limitation, this study develops a permutation test approach Specifically, the homogeneity of a spatial cluster is measured based on the local variance and cluster member permutation, and two-stage permutation tests are developed to determine the significance of the degree of homogeneity within each spatial cluster. The proposed permutation tests can be integrated into the existing spatial clustering algorithms to detect homogeneous spatial clusters. The proposed tests are compared with four existing tests (i.e., Park’s test, the contiguity-constrained nonparametric analysis of variance (COCOPAN) method, spatial scan statistic, and q-statistic) using two simulated and two meteorological datasets. The comparison shows that the proposed two-stage permutation tests are more effective to identify homogeneous spatial clusters and to determine homogeneous clustering structures in practical applications.     

Space–time interaction of residential burglaries in Wuhan,China

Borrowing methods from epidemiology, studies of spatiotemporal regularities of crime have been booming in various industrialized countries. However, few such attempts are empirical studies using crime data in developing countries due to a lack of data availability. Utilizing a recent burglary dataset in Wuhan, the fourth largest city in China, current research applied the sequential kernel density estimation and the space–time K-function methods to analyze the spatiotemporal changes of hotspots of residential burglaries. The results show that, both spatial and spatiotemporal clustering exists. The hotspots were relatively stable over time. The space–time clustering, however, shows significant concentrations both in space and over time. In addition, analytic results show significant effects of distance decay in terms of occurrences of burglary incidents along the spatial and temporal dimensions. Moreover, findings from the research provide critical information on the space–time rhythm of crime, and therefore can be utilized in crime prevention practice. Finally, the implications of the findings and limitations are discussed.     

Detecting ethnic residential clusters using an optimisation clustering method

To understand residential clustering of contemporary immigrants and other ethnic minorities in urban areas, it is important to first identify where they are clustered. In recent years, increasing attention has been given to the use of local statistics as a tool for finding the location of racial/ethnic residential clusters. However, since many existing local statistics are primarily developed for epidemiological studies where clustering is associated with relatively rare events, its application in studies of residential segregation may not always yield satisfactory results. This article proposes an optimisation clustering method for delineating the boundaries of ethnic residential clusters. The proposed approach uses a modified greedy algorithm to find the most likely extent of clusters and employs total within-group absolute deviations as a clustering criterion. To demonstrate the effectiveness of the method, we applied it to a set of synthetic landscapes and to two empirical data sets in Auckland, New Zealand. The results show that the proposed method can detect ethnic residential clusters effectively and that it has potential for use in other disciplines as it offers an ability to detect large, arbitrarily shaped clusters.     

A method for discovery and analysis of temporal patterns in complex event data

Pattern analysis techniques currently common within geography tend to focus either on characterizing patterns of spatial and/or temporal recurrence of a single event type (e.g., incidence of flu cases) or on comparing sequences of a limited number of event types where relationships between events are already represented in the data (e.g., movement patterns). The availability of large amounts of multivariate spatiotemporal data, however, requires new methods for pattern analysis. Here, we present a technique for finding associations among many different event types where the associations among these varying event types are not explicitly represented in the data or known in advance. This pattern discovery method, known as T-pattern analysis, was first developed within the field of psychology for the purpose of finding patterns in personal interactions. We have adapted and extended the T-pattern method to take the unique characteristics of geographic data into account and implemented it within a geovisualization toolkit for an integrated computational-geovisual environment we call STempo. To demonstrate how T-pattern analysis can be employed in geographic research for discovering patterns in complex spatiotemporal data, we describe a case study featuring events from news reports about Yemen during the Arab Spring of 2011–2012. Using supplementary data from the Global Database of Events, Language, and Tone, we briefly summarize and reference a separate validation study, then evaluate the scalability of the T-pattern approach. We conclude with ideas for further extensions of the T-pattern technique to increase its utility for spatiotemporal analysis.     

A statistical method for detecting spatiotemporal co-occurrence patterns

Spatiotemporal co-occurrence patterns (STCOPs) are subsets of Boolean features whose instances frequently co-occur in both space and time. The detection of STCOPs is crucial to the investigation of the spatiotemporal interactions among different features. However, prevalent STCOPs reported by available methods do not necessarily indicate the statistically significant dependence among different features, which is likely to result in highly erroneous assessments in practice. To improve the reliability of results, this paper develops a statistical method to detect STCOPs and discern their statistical significance. The proposed method detects STCOPs against the null hypothesis that the spatiotemporal distributions of different features are independent of each other. To construct the null hypothesis, suitable spatiotemporal point-process models considering spatiotemporal autocorrelation are employed to model the distributions of different features. The performance of the proposed statistical method is assessed by synthetic experiments and a case study aimed at identifying crime patterns among multiple crime types in Portland City. The experimental results demonstrate that the proposed method is more effective for detecting meaningful STCOPs than the available alternative methods.     

A Typology of Socio-Economic Advantage and Disadvantage in Australia's Large Non-Metropolitan Cities,Towns and Regions

Australia's large regional cities and towns display a wide variation in their adjustment to the socio-economic transitions that have occurred over the past decade. In terms of socio-economic advantage and disadvantage, these changes, often associated with globalisation, wider economic and technological restructuring, the changing demographics of the population and shifts in public policy, are not evenly dispersed across non-metropolitan regions. Such outcomes have been discussed across a variety of academic disciplines using a variety of data and methods, and the research undertaken has provided a useful grounding for contemporary studies both theoretically and methodologically. Analysis of new data provides an opportunity to extend and update our understanding. This paper presents an analysis of secondary data aimed at analysing non-metropolitan cities, towns and regions based on differential levels of socio-economic performance. Using an alternative clustering method, this paper groups non-metropolitan cities, towns and regions according to the degree to which they share similar socio-economic and demographic outcomes. These clusters form the basis of a typology representing the range of socio-economic and demographic outcomes at the non-metropolitan level.     

基于大数据的西安市国内游客情感体验时空变化研究

大数据时代,社交媒体的大量应用为研究游客情感体验以及探索其时空变化提供了新的数据源。采集3 a间西安市国内游客微博签到数据,运用热点格网图法、Getis-Ord Gi*方法和X-means聚类方法,从积极情感和消极情感2个维度研究西安市国内游客情感体验时空变化和演化规律。结果表明：（1） 城市中心、城市主轴线、主要商圈以及景区景点附近游客情感相对较高且稳定,高情感体验区域主要分布在曲江新区和西安古城旅游区。（2） 消极情感体验在西安的交通枢纽和城市边缘的空间占比高,交通枢纽主要以车站、城市进出口为主。（3） 整体上来看,3 a间西安市游客情感较为平稳,积极情感呈现“中心—边缘”的空间格局,消极情感和积极情感的呈现具有相似性,主要以3种类型为主：稳定型、相对稳定型和剧烈波动型。在3种类型中,稳定型的主要聚集地在城市中心、商圈附近、交通干线周边以及景区景点附近,相对稳定型占据西安市大面积区域,剧烈波动型处于距离城市中心较远的边缘。     

Mapping spatiotemporal patterns of events using social media: a case study of influenza trends

Tracking spatial and temporal trends of events (e.g. disease outbreaks and natural disasters) is important for situation awareness and timely response. Social media, with increasing popularity, provide an effective way to collect event-related data from massive populations and thus a significant opportunity to dynamically monitor events as they emerge and evolve. While existing research has demonstrated the value of social media as sensors in event detection, estimating potential time spans and influenced areas of an event from social media remains challenging. Challenges include the unstable volumes of available data, the spatial heterogeneity of event activities and social media data, and the data sparsity. This paper describes a systematic approach to detecting potential spatiotemporal patterns of events by resolving these challenges through several interrelated strategies: using kernel density estimation for smoothed social media intensity surfaces; utilizing event-unrelated social media posts to help map relative event prevalence; and normalizing event indicators based on historical fluctuation. This approach generates event indicator maps and significance maps explaining spatiotemporal variations of event prevalence to identify space-time regions with potentially abnormal event activities. The approach has been applied to detect influenza activity patterns in the conterminous US using Twitter data. A set of experiments demonstrated that our approach produces high-resolution influenza activity maps that could be explained by available ground truth data.     

沈阳市部门企业地理集聚与城市结构

基于产业空间聚集分布情况探寻城市结构特征,是当前大都市区实证研究中的聚焦点所在,但由于方法论的限制而无法真正揭示产业地理集聚之间的内在关联性。基于已有研究基础,试图通过完善潜力模型、设置距离参数、结合主成分分析法实现对产业地理集聚测度方法论的完善与发展,并选取极具代表性大都市区核心城市——沈阳市为样本单元,以2008年的经济普查部门企业数据开展实证检验。结果表明：沈阳市部门企业之间除了交通运输、仓储和邮政中心产业属于地方化经济外,其余的均为企业关联;水利、环境和公共设施管理业产业依附于制造业呈临街抑或隔街集聚,而与公共管理和组织产业之间同街道集聚;支配主角之间,存在中心CBD主宰制造业的布局,而制造业又在很大程度上影响着交通运输、仓储和邮政中心的布局;企业地理集聚形成的城市结构依然是一个明显的“单中心圈层”结构,没有表现出“去中心化”抑或多极化或分散化演变趋势。研究成果与现实情况基本吻合,侧面说明该模式对揭示城市产业地理集聚模式以及由此形成的城市结构特征具有一定的解释力。     

Multi-level method for discovery of regional co-location patterns

Regional 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.     

Aoristic analysis: the spatial interpretation of unspecific temporal events

Temporal limitations of GIS databases are never more apparent than when the time of a change to any spatial object is unknown. This paper examines an unusual type of spatiotemporal imprecision where an event occurs at a known location but at an unknown time. Aoristic analysis can provide a temporal weight and give an indication of the probability that the event occurred within a defined period. Visualisation of temporal weights can be enhanced by modifications to existing surface generation algorithms and a temporal intensity surface can be created. An example from burglaries in Central Nottingham (UK) shows that aoristic analysis can smooth irregularities arising from poor database interrogation, and provide an alternative conceptualisation of space and time that is both comprehensible and meaningful.     

基于圈层结构的游客活动空间边界提取新方法

准确刻画游客活动空间边界对于优化景区结构、实施界限管控、提高资源利用效益均有重要意义.由于游客行为的复杂性与边界模糊性,利用传统地理边界提取方法难以有效识别游客活动空间边界.基于层次聚类算法优化后的Delaunay三角网进行核密度估计,解决了多尺度下点核密度对空间边界拟合不精确的问题,同时借鉴圈层结构理论,依据游客空间...     

Local Spatiotemporal Modeling of House Prices: A Mixed Model Approach

The real estate market has long provided an active application area for spatial–temporal modeling and analysis and it is well known that house prices tend to be not only spatially but also temporally correlated. In the spatial dimension, nearby properties tend to have similar values because they share similar characteristics, but house prices tend to vary over space due to differences in these characteristics. In the temporal dimension, current house prices tend to be based on property values from previous years and in the spatial–temporal dimension, the properties on which current prices are based tend to be in close spatial proximity. To date, however, most research on house prices has adopted either a spatial perspective or a temporal one; relatively little effort has been devoted to situations where both spatial and temporal effects coexist. Using ten years of house price data in Fife, Scotland (2003–2012), this research applies a mixed model approach, semiparametric geographically weighted regression (GWR), to explore, model, and analyze the spatiotemporal variations in the relationships between house prices and associated determinants. The study demonstrates that the mixed modeling technique provides better results than standard approaches to predicting house prices by accounting for spatiotemporal relationships at both global and local scales.