MULTIVARIATE MIXTURE OF NORMALS WITH UNKNOWN NUMBER OF COMPONENTS: AN APPLICATION TO CLUSTER NEOLITHIC CERAMICS FROM AEGEAN AND ASIA MINOR USING PORTABLE XRF*

Multivariate techniques and especially cluster analysis have been commonly used in archaeometry. Exploratory and model‐based techniques of clustering have been applied to geochemical (continuous) data of archaeological artefacts for provenance studies. Model‐based clustering techniques such as classification maximum likelihood and mixture maximum likelihood have been used to a lesser extent in this context and, although they seem to be suitable for such data, they either present practical difficulties—such as high dimensionality of the data—or their performance gives no evidence that they are superior to standard methods. In this paper standard statistical methods (hierarchical clustering, principal components analysis) and the recently developed model‐based multivariate mixture of normals with an unknown number of components, are applied and compared. The data set provides chemical compositions of 188 ceramic samples derived from the Aegean islands and surrounding areas.     

Spatial Characteristics and Comparisons of Interaction and Median Clustering Models

Cluster analysis has been pursued from a number of directions for identifying interesting relationships and patterns in spatial information. A major emphasis is currently on the development and refinement of optimization‐based clustering models for the purpose of exploring spatially referenced data. Within this context, two basic methods exist for identifying clusters that are most similar. An interesting feature of these two approaches is that one method approximates the relationships inherent in the other method. This is significant given that the approximation approach is invariably utilized for cluster detection in spatial and aspatial analysis. A number of spatial applications are investigated which highlight the differences in clusters produced by each model. This is an important contribution because the differences are in fact quite significant, yet these contrasts are not widely known or acknowledged.     

A REVIEW OF SUPERVISED AND UNSUPERVISED PATTERN RECOGNITION IN ARCHAEOMETRY*

Principal component, cluster and discriminant analysis are multivariate statistical methods that are widely used in archaeometry. They are examples of what are known in some literatures as unsupervised and supervised learning methods. Over the past 20 years or so, a wide variety of other learning methods have been developed that take advantage of modern computing power and, in some cases, have been designed to handle data sets more complex than those often used in archaeometric data analysis. To date, these methods have had little impact on archaeometry. This paper reviews, in a largely non‐technical manner, the ideas behind these newer methods; illustrates their use on a variety of data sets; and attempts to assess their potential for future archaeometric use.     

Model‐based Cluster Analysis of Artefact Compositional Data

Cluster analysis is the most widely used multivariate technique in archaeometry, with the majority of applications being exploratory in nature. Model‐based methods of clustering have their advocates, but have seen little application to archaeometric data. The paper investigates two such methods. They have potential advantages over exploratory techniques, if successful. Mixture maximum‐likelihood worked well using low‐dimensional lead isotope data, but had problems coping with higher‐dimensional ceramic compositional data. For our most challenging example, classification maximum‐likelihood performed comparably with more standard methods, but we find no evidence to suggest that it should supplant these.     

Local Indicators of Network-Constrained Clusters in Spatial Point Patterns

The detection of clustering in a spatial phenomenon of interest is an important issue in spatial pattern analysis. While traditional methods mostly rely on the planar space assumption, many spatial phenomena defy the logic of this assumption. For instance, certain spatial phenomena related to human activities are inherently constrained by a transportation network because of our strong dependence on the transportation system. This article thus introduces an exploratory spatial data analysis method named l ocal i ndicators of n etwork-constrained c luster s (LINCS), for detecting local-scale clustering in a spatial phenomenon that is constrained by a network space. The LINCS method presented here applies to a set of point events distributed over the network space. It is based on the network K -function, which is designed to determine whether an event distribution has a significant clustering tendency with respect to the network space. First, an incremental K -function is developed so as to identify cluster size more explicitly than the original K -function does. Second, to enable identification of cluster locations, a local K -function is derived by decomposing and modifying the original network K -function. The local K -function LINCS, which is referred to as KLINCS, is tested on the distribution of 1997 highway vehicle crashes in the Buffalo, NY area. Also discussed is an adjustment of the KLINCS method for the nonuniformity of the population at risk over the network. As traffic volume can be seen as a surrogate of the population exposed to a risk of vehicle crashes, the spatial distribution of vehicle crashes is examined in relation to that of traffic volumes on the network. The results of the KLINCS analysis are validated through a comparison with priority investigation locations (PILs) designated by the New York State Department of Transportation.     

Geography, Spatial Data Analysis, and Geostatistics: An Overview

Geostatistics is a distinctive methodology within the field of spatial statistics. In the past, it has been linked to particular problems (e.g., spatial interpolation by kriging) and types of spatial data (attributes defined on continuous space). It has been used more by physical than human geographers because of the nature of their types of data. The approach taken by geostatisticians has several features that distinguish it from the methods typically used by human geographers for analyzing spatial variation associated with regional data, and we discuss these. Geostatisticians attach much importance to estimating and modeling the variogram to explore and analyze spatial variation because of the insight it provides. This article identifies the benefits of geostatistics, reviews its uses, and examines some of the recent developments that make it valuable for the analysis of data on areal supports across a wide range of problems.     

FUZZY PATTERN CLASSIFICATION OF STRONG GROUND MOTION RECORDS

Classification of earthquake strong ground motion (SGM) records is performed using fuzzy pattern recognition to exploit knowledge in the data that is utilised in a genetic algorithm (GA) search and scaling program. SGM records are historically treated as “fingerprints” of certain event magnitude and mechanism of faulting systems recorded at different distances on different soil types. Therefore, databases of SGM records of today present data of complex nature in high dimensions (many of the dimensions—or SGM parameters in time and frequency domain—are presently available from different archives). In this study, simple ground motion parameters were used but were combined and scaled nonlinearly such that the physical properties of the data could be preserved while reducing its dimensionality. The processed data was then analysed using fuzzy c-means (FCM) clustering method to explore the possibility of meaningfully representing earthquake SGM data in lower dimensions through finding subsets of mathematically similar vectors in a benchmark database. This representation can be used in practical applications and has a direct influence on the processes of synthesising ground motion records, identifying unknown ground motion parameters (e.g. soil type in this study), improving the quality of matching SGM records to design target spectra, and in rule generalisation for response. The results showed that the stochastic behaviour of earthquake ground motion records can be accurately simplified by having only a few of motion parameters. The very same parameters may also be utilised to derive unknown characteristics of the motion when the classification task on “training” records is performed carefully. The clusters are valid and stable in time and frequency domain and are meaningful even with respect to seismological features that were not included in the classification task.     

Hatching seeds before they’re counted

Like other analytic aspects of archaeology, archaeobotany has been growing progressively more quantitative in the past few decades. This may be a sign of the proliferation of increasingly mature and sophisticated methodologies for analyzing botanical data, but associated with the sophistication of quantitative methods is their inherent opacity: the value and applicability of anthropological conclusions drawn from quantitative archaeobotanical data are not only limited by the amount of information that can be extracted from data by sophisticated statistical tools, but also by our ability to draw reasonable anthropological—as opposed to merely statistical—conclusions. Even the words “classification” and “significance” have different meanings in statistics and in anthropology. In this paper, I propose the use of graphical analysis for archaeobotanical data in addition to, or instead of, typical statistical tools like significance tests, variable reduction, and clustering. Applied to data from charred seed assemblages from the ancient Near East, the visual representation of quantitative data has the advantage of handling semiquantitative data better and being interpretable without reliance on the paradigm of a formal statistical test.     

基于模糊关系识别的多要素空间离散化方法——以江苏阜宁人口与经济分析为例

社会、经济要素的空间离散化是精细化县级主体功能区划的重要需求,本文提出了一种基于模糊关系识别的空间数据离散化方法。该方法利用广义权距离实现对专家知识与多系统分层要素的综合集成,并通过建立待离散化要素与其影响指标的模糊关系识别模型,获得空间离散化权重。以2009年江苏省阜宁县人口、GDP以及经济发展水平的空间离散化为例进行实例分析。结果显示,本文提出的空间离散化方法具有较好的准确性与可信度,可较好揭示各影响要素对待离散要素的空间影响。     

国际旅游研究前沿的知识图谱分析——基于对TM和ATM所载文献的考察

本文运用科学计量学中的作者共引分析、多维尺度分析、聚类分析和因子分析,对国际旅游研究领域中的两本具有代表性的期刊——Tourism Management和Annals of Tourism Research进行科学计量分析,绘制出旅游研究前沿热点主流学术群体及其代表人物的知识图谱。该图谱显示出当前国际旅游研究存在4个主流学术群体和研究领域,且旅游研究从以往的以经济学为基础向跨学科的综合研究发展。     

Where is Helvellyn? Fuzziness of multi-scale landscape morphometry

The landscape in which people live is made up of many features, which are named and have importance for cultural reasons. Prominent among these are the naming of upland features such as mountains, but mountains are an enigmatic phenomenon which do not bear precise and repeatable definition. They have a vague spatial extent, and recent research has modelled such classes as spatial fuzzy sets. We take a specifically multi-resolution approach to the definition of the fuzzy set membership of morphometric classes of landscape. We explore this idea with respect to the identification of culturally recognized landscape features of the English Lake District. Discussion focuses on peaks and passes, and the results show that the landscape elements identified in the analysis correspond to well-known landmarks included in a place name database for the area, although many more are found in the analysis than are named in the available database. Further analysis shows that a richer interrogation of the landscape can be achieved with Geographical Information Systems when using this method than using standard approaches.     

An Empirical Comparison of Edge Effect Correction Methods Applied to K‐function Analysis

This paper explores various edge correction methods for K‐function analysis via Monte Carlo simulation. The correction methods discussed here are Ripley's circumference correction, a toroidal correction, and a guard area correction. First, simulation envelopes for a random point pattern are constructed for each edge correction method. Then statistical powers of these envelopes are analyzed in terms of the probability of detecting clustering and regularity in simulated clustering/regularity patterns. In addition to the K‐function, K(h), determined for individual distances, h, an overall statistic k is also examined. A major finding of this paper is that the K‐function method adjusted by either the Ripley or toroidal edge correction method is more powerful than what is not adjusted or adjusted by the guard area method. Another is that the overall statistic k outperforms the individual K(h) across almost the entire range of potential distances h.     

Controlling the False Discovery Rate: A New Application to Account for Multiple and Dependent Tests in Local Statistics of Spatial Association

Assessing the significance of multiple and dependent comparisons is an important, and often ignored, issue that becomes more critical as the size of data sets increases. If not accounted for, false-positive differences are very likely to be identified. The need to address this issue has led to the development of a myriad of procedures to account for multiple testing. The simplest and most widely used technique is the Bonferroni method, which controls the probability that a true null hypothesis is incorrectly rejected. However, it is a very conservative procedure. As a result, the larger the data set the greater the chances that truly significant differences will be missed. In 1995, a new criterion, the false discovery rate (FDR), was proposed to control the proportion of false declarations of significance among those individual deviations from null hypotheses considered to be significant. It is more powerful than all previously proposed methods. Multiple and dependent comparisons are also fundamental in spatial analysis. As the number of locations increases, assessing the significance of local statistics of spatial association becomes a complex matter. In this article we use empirical and simulated data to evaluate the use of the FDR approach in appraising the occurrence of clusters detected by local indicators of spatial association. Results show a significant gain in identification of meaningful clusters when controlling the FDR, in comparison to more conservative approaches. When no control is adopted, false clusters are likely to be identified. If a conservative approach is used, clusters are only partially identified and true clusters are largely missed. In contrast, when the FDR approach is adopted, clusters are fully identified. Incorporating a correction for spatial dependence to conservative methods improves the results, but not enough to match those obtained by the FDR approach.     

On the similarity of tree‐ring patterns: Assessing the influence of semi‐synchronous growth changes on the Gleichläufigkeitskoeffizient for big tree‐ring data sets

The Gleichläufigkeitskoeffizient (GLK), or the percentage of parallel variation (%PV), is an often used non‐parametric similarity measure in dendrochronological research. However, when analysing big data sets using the GLK, this measure has some issues. The main problem is that it includes not only synchronous but also semi‐synchronous growth changes. These are years in which the growth in one of the compared series does not change in two subsequent years. This influences the GLK, often only slightly, but the larger the data set the stronger the effect. The similarity between tree‐ring series can be more objectively expressed by replacing the GLK with the synchronous (SGC) and semi‐synchronous growth changes (SSGC). The calculation is similar, since GLK = SGC + SSGC/2. Large values of the SSGC are indicative of possible anomalies or even errors. The SGC is much better suited than the GLK to describe similarity. The SGC should therefore be used to analyse big data sets, for clustering and/or dendroprovenance studies. It is recommended to combine the SGC with parametric measures.     

Methods of Mapping and Identifying Small Clusters of Rare Diseases with Applications to Geographical Epidemiology

Geographical variation operates at a variety of scales. Methods of mapping variation in disease incidence between different countries or even counties are relatively well developed. When, however, the question relates to much smaller aggregations (that is, “clustering”), attention has mainly been restricted to areas near putative point hazards; the majority of cases are excluded from such an investigation. In this study we show how clustering may be investigated and displayed in such a way that it becomes a powerful tool in epidemiological research. As examples we use incidence data from the Yorkshire health region for selected childhood cancers and adult haematopoietic malignancies. The methods would readily extend to any small clusters of rare events.     

Between Large-N and Small-N Analyses: Historical Comparison of Thirty Insurgency Case Studies

Abstract

The authors study the 30 insurgencies occurring between 1978 and 2008 using four methods crossing the qualitative/quantitative divide. The four approaches are narrative, bivariate comparison, comparative qualitative analysis, and K-medoids clustering. The quantification of qualitative data allows the authors to compare more cases than they could “hold in their heads” under a traditional small-n qualitative approach, improving the quality of the overall narrative and helping to ensure that the quantitative analyses respected the nuance of the detailed case histories. Structured data-mining reduces the dimensionality of possible explanatory factors relative to the available observations to expose patterns in the data in ways more common in large-n studies. The four analytic approaches produced similar and mutually supporting findings, leading to robust conclusions.     

Thinking Through Networks: A Review of Formal Network Methods in Archaeology

This review aims to expose the potential of formal network methods for archaeology by tracing the origins of the academic traditions, network models, and techniques that have been most influential to archaeologists. A brief discussion of graph theoretic applications in archaeology reveals how graph visualization and analysis was used since the 1960s in a very similar way to later network analysis applications, but did not seem to have influenced the more widespread adoption of network techniques over the past decade. These recent archaeological applications have been strongly influenced by two academic traditions, social network analysis and sociophysics. The most influential and promising techniques and models adopted from these traditions are critically discussed. This review reveals some general trends which are considered to be the result of two critical issues that will need to be addressed in future archaeological network analysis: (1) a general unawareness of the historicity and diversity of formal network methods both within and outside the archaeological discipline has resulted in a very limited methodological scope; (2) the adoption or development of network methods has very rarely been driven by specific archaeological research questions and is dominated by a few popular models and techniques, which has in some cases resulted in a routinized explanatory process. This review illustrates, however, the great potential of formal network methods for archaeology and argues that, if this potential is to be applied in a critical way, a broad multidisciplinary scope is necessary and specific archaeological research contexts should dominate applications.     

Regional cleavages in African politics: Persistent electoral blocs and territorial oppositions

Do socio-economic cleavages shape electoral dynamics in African countries? Previous individual-level and party systems research on African politics has de-emphasized socio-economic factors, contributing to the common view that ethnic cleavages and short-term ethnic alliances define politics both locally and nationally. Focusing on Kenya, Zambia, and Malawi, we draw on methods in electoral geography to offer a spatial analysis of geographic patterns in constituency-level electoral returns over three decades that reveals the existence of persistent regional voting blocs that, in their temporal stability and multiethnic character, are not well explained by prevailing theory. The anomalies open the door to a reinterpretation national electoral structure and dynamics in the three countries that takes the geographic clustering of the persistent voting blocs as a clue to their etiology. We propose an interpretation that focuses on core-periphery cleavages in national electorates, following Lipset and Rokkan's (1967) classic model of territorial oppositions in countries undergoing political and economic integration and modernization. DHS data and proxies for regional economic activity support this interpretation. Socio-economic cleavages of the type explored in comparative political economy literatures on spatial inequality and territorial politics may be more salient in African electoral politics than previously thought.     

A Comparative Analysis of Wet and Dry Ashing Techniques for the Extraction of Phytoliths from Plant Material

Two methods are commonly used for the extraction of phytoliths from plant material to be used as reference in the analysis of archaeological phytolith samples: (1) spodograms or dry ashings; and (2) acid digestions or wet ashing. It has been suggested that these techniques may modify the resultant samples in different ways. Dry ashing, in particular, has been implicated as a cause of shrinkage and warping in phytolith assemblages when incineration occurs at ≥450°C. The results of a morphometric comparative analysis between the dry ashing and wet ashing methods do not support these claims. This study establishes that differences in patterns of dimension and curvature of short bilobate phytoliths and of elongate phytoliths both subjected to dry and wet ash preparation are not statistically significant. There is, therefore, no detectable evidence of morphological impact as a result of these methods. This finding implies that any differences that do occur in phytolith size and curvature are typical, possibly random permutation within assemblages, or that they are the result of variation in leaf cell structure rather than the consequence of a particular extraction procedure. This suggests that the practice of using different methods of preparation of reference samples for fossil analysis can be reliably continued.