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Abstract

The classification of Western European flanged axes dating to the Middle Bronze Age (1650–1350 BC) is very complex. Many types of axe have been identified, some of which have numerous variant forms. In the current French terminology, all axes are divided into two generic groups: namely " Atlantic " (Atlantique) and " Eastern " (Orientale). Each of these generic groups, however, is highly polymorphic, so that it is often very difficult for the operator to classify individual axes with absolute confidence and certainty. In order to overcome such problems , a new shape classification is proposed, using morphometric analysis (Elliptic Fourier Analysis) followed by unsupervised model-based clustering and discriminant analysis, both based on Gaussian mixture modelling. Together , these methods produce a clearer pattern, which is independently validated by the spatial distribution of the findings, and multinomial scan statistics. This approach is fast, reproducible, and operator-independent, allowing artefacts of unknown membership to be classified rapidly. The method is designed to be amendable by the introduction of new artefacts, in the light of future discoveries. This method can be adapted to suit many other archaeological artefacts, providing information about the material, social and cultural relations of ancient populations.

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... Analyses of lithic shape are neither new or novel, and it is not surprising that geometric morphometrics (GM) (sensu Corti, 1993) has captivated analysts of material culture due to the substantive contribution of morphology to lithic typologies (Fox, 2015;Thulman, 2012;Wilczek et al., 2015). The first application of GM to archaeologically-recovered artefacts was an analysis of irregular shapes by elliptic Fourier analysis (EFA) (Gero and Mazzullo, 1984), and the adoption of the method by the archaeological community has continued. ...
... EFA has been increasingly employed in lithic analyses, where analysts continue are developing novel approaches that advance archaeological applications (Cardillo, 2010;Fox, 2015;Iovita, 2009Iovita, , 2010Iovita, , 2011Iovita and McPherron, 2011;Smith et al., 2014;Gingerich et al., 2014;Sholts et al., 2012;Wilczek et al., 2015). Numerous creative research designs have also been presented that address some of the very real challenges associated with the oft-fractured and incomplete specimens abundant in the archaeological record (Byrne et al., 2016;Rezek et al., 2011;Smith, 2010;Smith and DeWitt, 2016). ...
Preprint
This analysis of Gahagan biface morphology enlists the three largest samples of Gahagan bifaces, to include that of the type site (Gahagan Mound) as well as the Mounds Plantation and George C. Davis sites. Results indicate a significant difference in Gahagan biface morphology at the Mounds Plantation site when compared with Gahagan bifaces from the Gahagan Mound and George C. Davis sites. Tests for allometry and asymmetry were not significant. The test of morphological disparity indicates that Gahagan bifaces produced at the Mounds Plantation site occupy a more restricted range of morphospace than those produced at Gahagan Mound, providing evidence for standardisation and diversity in Caddo biface production. While the sample includes a wide range of variability, the test of morphological integration indicates that Gahagan bifaces are significantly integrated, meaning that those traits used to characterise their shape (blade and base) vary in a coordinated manner. These results articulate with a shift in Caddo bottle morphology over the same geography, potentially indicating two previously unrecognised and morphologically-distinct lithic and ceramic production areas.
... At the same time, no directly applicable methodology is available for the Bronze Age mould-cast tools which were subject to further deformations due to their wear. Studies devoted to the morphometric differentiation of bronze axes are noteworthy (Monna et al. 2013;Wilczek et al. 2015), although based on two-dimensional cross-sections. ...
... W świetle publikowanych przykładów metody te wykorzystują przede wszystkim badacze epoki kamienia do analizy cech metrycznych artefaktów krzemiennych (Chacón et al. 2016;Herzlinger, Grosman 2018), jednak trudno o znalezienie metodologii wprost aplikowanej dla analizy narzędzi wykonanych z brązu, odlewanych w formach, podlegających dalszym deformacjom wskutek użytkowana. Dla tej problematyki z pewnością warte odnotowania są prace poświęcone zróżnicowaniu morfometrii brązowych siekierek, bazujące jednak na dwuwymiarowych przekrojach (Monna et al. 2013;Wilczek et al. 2015). ...
Book
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The volume presents results of two-year project : multi-aspect analysis of four late Bronze Age deposits placed in ceramic vessels and containing metal tools, weapons and ornaments. The linear arrangement of the hoards is extraordinary and the landscape studies in the deposit area indicate that they were related to the place of forcing the wide Barycz Valley, marked and narrative route towards its narrowing. All are of similar chronology, that is HaB2-3 – Montelius V – 950-800/750 BC.
... Différentes techniques sont employées ; en premier lieu, il s'agit d'analyses de contours ouverts qui vont comparer l'arête faciale interne de chaque hache par la méthode de la Transformée en Cosinus Discrète (Forel et al. 2009, fig. 3 ;Gabillot et al. 2015) ou par les polynômes orthogonaux de Legendre (Monna et al. 2012 ;Gabillot et al. 2015). En second lieu, des analyses de contours fermés mobilisent la silhouette entière des haches (Wilczek et al. 2015). Les résultats de ces méthodes sont placés dans un graphique correspondant à une analyse multivariée qui permet de visualiser l'organisation des individus les uns par rapport aux autres (Forel et al. 2009, fig. ...
... Une autre analyse a été menée sur des haches à rebords, avec la méthode de l'analyse de Fourrier elliptique (Wilczek et al. 2015). Le corpus est constitué cette fois par 250 haches à rebords attribuées à des types atlantiques et orientaux mal définis à l'oeil nu, si bien que la comparaison de leur silhouette seule permet difficilement de les attribuer à des types précis. ...
... Chacón et al., 2016;Serwatka, 2014) and elsewhere (Lycett, 2007), Holocene forager tools in South America (e.g. Charlin & González-José, 2012;Okumura & Araujo, 2014;Suárez & Cardillo, 2019) and later prehistoric metal axes (Wilczek et al., 2015), lances (Birch & Martinón-Torres, 2019) and adornments (Vestergaard & Hoggard, 2019) have all been subjected to geometric morphometric assessments, often leading to a substantial critique of established typologies. There is little methodological consistency across these emerging case studies, however, and rarely have such studies re-analysed different datasets comparatively (see Monnier & McNulty, 2010, for an exception), making it difficult to evaluate their conclusions independently of their methodological choices. ...
Article
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The identification of material culture variability remains an important goal in archaeology, as such variability is commonly coupled with interpretations of cultural transmission and adaptation. While most archaeological cultures are defined on the basis of typology and research tradition, cultural evolutionary reasoning combined with computer-aided methods such as geometric morphometrics (GMM) can shed new light on the validity of many such entrenched groupings, especially in regard to European Upper Palaeolithic projectile points and their classification. Little methodological consistency, however, makes it difficult to compare the conclusions of such studies. Here, we present an effort towards a benchmarked, case-transferrable toolkit that comparatively explores relevant techniques centred on outline-based GMM. First, we re-analyse two previously conducted landmark-based analyses of stone artefacts using our whole-outline approach, demonstrating that outlines can offer an efficient and reliable alternative. We then show how a careful application of clustering algorithms to GMM outline data is able to successfully discriminate between distinctive tool shapes and suggest that such data can also be used to infer cultural evolutionary histories matching already observed typo-chronological patterns. Building on this baseline work, we apply the same methods to a dataset of large tanged points from the European Final Palaeolithic (ca. 15,000–11,000 cal BP). Exploratively comparing the structure of design space within and between the datasets analysed here, our results indicate that Final Palaeolithic tanged point shapes do not fall into meaningful regional or cultural evolutionary groupings but exhibit an internal outline variance comparable to spatiotemporally much closer confined artefact groups of post-Palaeolithic age. We discuss these contrasting results in relation to the architecture of lithic tool design spaces and technological differences in blank production and tool manufacture.
... The spatial scan statistic and its variants within the SaTScan 2 toolkit have remained extremely Figure 1: An illustration of hot spots of Low Educational Achievement in India popular for detecting spatial hot spots over the past two decades. While health and communicable diseases form the most popular application area of SSS (e.g., [30]), they have been used within domains as diverse as archaeology [35] and urban planning [16]. ...
Preprint
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Pervasiveness of tracking devices and enhanced availability of spatially located data has deepened interest in using them for various policy interventions, through computational data analysis tasks such as spatial hot spot detection. In this paper, we consider, for the first time to our best knowledge, fairness in detecting spatial hot spots. We motivate the need for ensuring fairness through statistical parity over the collective population covered across chosen hot spots. We then characterize the task of identifying a diverse set of solutions in the noteworthiness-fairness trade-off spectrum, to empower the user to choose a trade-off justified by the policy domain. Being a novel task formulation, we also develop a suite of evaluation metrics for fair hot spots, motivated by the need to evaluate pertinent aspects of the task. We illustrate the computational infeasibility of identifying fair hot spots using naive and/or direct approaches and devise a method, codenamed {\it FiSH}, for efficiently identifying high-quality, fair and diverse sets of spatial hot spots. FiSH traverses the tree-structured search space using heuristics that guide it towards identifying effective and fair sets of spatial hot spots. Through an extensive empirical analysis over a real-world dataset from the domain of human development, we illustrate that FiSH generates high-quality solutions at fast response times.
... In this specific example, as in many other situations of this kind, a rapid and accurate procedure to extract, at least semi-automatically, stone boundaries from the data acquired by UAV would be a valuable improvement in the acquisition speed of archaeological documentation. The problem, in a nutshell, consists of a binary pixel classification (stone vs non-stone), and solutions can be sought in the numerous machine learning algorithms increasingly used in archaeology [12][13][14][15]. Colour information is an obvious candidate for input data, as stones are clearly visible in the images. ...
Article
The present study proposes a workflow to extract from orthomosaics the enormous amount of dry stones used by past societies to construct funeral complexes in the Mongolian steppes. Several different machine learning algorithms for binary pixel classification (i.e. stone vs non-stone) were evaluated. Input features were extracted from high-resolution orthomosaics and digital elevation models (both derived from aerial imaging). Comparative analysis used two colour spaces (RGB and HSV), texture features (contrast, homogeneity and entropy raster maps), and the topographic position index, combined with nine supervised learning algorithms (nearest centroid, naive Bayes, k-nearest neighbours, logistic regression, linear and quadratic discriminant analyses, support vector machine, random forest, and artificial neural network). When features are processed together, excellent output maps, very close to or outperforming current standards in archaeology, are observed for almost all classifiers. The size of the training set can be drastically reduced (to ca. 300 samples) by majority voting, while maintaining performance at the highest level (about 99.5% for all performance scores). Note, however, that if the training set is inadequate or not fully representative, the classification results are poor. That said, the methods applied and tested here are extremely rapid. Extensive mapping, which would have been difficult with traditional, manual, or semi-automatic delineation of stones using a vector graphics editor, now becomes possible. This workflow generally surpasses pedestrian surveys using differential GPS or a total station.
... It has also been useful in studying ceramic typologies (Wilczek et al., 2014) as well as temporal and technological investigations of lithic technologies (Archer and Braun, 2010;de Azevedo et al., 2014;Okumura and Araujo, 2014), with recent developments towards 3-dimensional GMM analysis (Lycett et al., 2010;Lycett and von Cramon-Taubadel, 2013). However, only a few GMM studies exist for metal artefacts (Odler, 2016, p. 248;Wilczek et al., 2015). ...
Article
Traditionally, standardisation of manufacture has been investigated using metrics (e.g. length and width) and compared in terms of the coefficient of variation (CV). This paper argues that standardisation should not only be investigated via metrics, but also in terms of shape. An Iron Age lance head type ('Havor'), known from three main weapon depositions in Southern Scandinavia, is used as a case study to test the effectiveness of shape analysis against traditional metric analysis for investigating standardisation. Geometric morphometric (GMM) analysis is used to measure the overall shape variation and to test shape difference of the same lance type coming from three different archaeological sites. The results demonstrate GMM to complement the traditional metric approach. Whilst metric measurements offer insights into Havor lance standardisation, the results from multivariate analysis of GMM data provides further explanation about the source of variation in terms of shape, including an assessment of object symmetry. This paper represents the first known methodological application of GMM analysis to iron weapons and demonstrates it to be an effective method for studying product standardisation in terms of shape variation.
... Les Nouvelles de l'archéologie n o 149 -Septembre 2017 morpho métrique ont démontré leur large supériorité sur les typo logies traditionnelles. En effet, celles-ci ne tiennent compte que d'une partie des données du profil ou de la silhouette des objets, alors que la morphométrie intègre la totalité de l'information (Wilczek et al. 2014(Wilczek et al. , 2015. Une voie de recherche prometteuse consiste alors à combiner la morphométrie en 3D et la phylomémétique, suivant l'exemple proposé pour les céramiques Caddo du Texas par Robert Selden, Thimotty Perttula et Michael O'Brien (2014) (fig. ...
Article
This investigation aggregates intact or reconstructed Gahagan bifaces from the southern Caddo area and central Texas to test the hypothesis that Gahagan biface morphology differs between the regions. The Gahagan bifaces (n=102) were scanned, then analyzed using a novel landmarking protocol and the tools of geometric morphometrics. Results provide a preview of the significant differences in Gahagan biface morphology expressed between the southern Caddo area and central Texas regions. The size discrepancy represents an inversion of current theoretical constructs that posit a decrease in tool size thought to articulate with an increase in distance from the raw material source. It is posited that the contrasting morphologies represent two discrete communities of practice; one (emergent Caddo horticulturalists) where Gahagan bifaces were enlisted primarily for burial and ritualistic activities, and the other (central Texas hunter-gatherers) where Gahagan bifaces were utilized over a longer time span in more practical and utilitarian contexts.
Article
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Bronze is the defining metal of the European Bronze Age and has been at the center of archaeological and science-based research for well over a century. Archaeometallurgical studies have largely focused on determining the geological origin of the constituent metals, copper and tin, and their movement from producer to consumer sites. More recently, the effects of recycling, both temporal and spatial, on the composition of the circulating metal stock have received much attention. Also, discussions of the value and perception of bronze, both as individual objects and as hoarded material, continue to be the focus of scholarly debate. Here, we bring together the sometimes-diverging views of several research groups on these topics in an attempt to find common ground and set out the major directions of the debate, for the benefit of future research. The paper discusses how to determine and interpret the geological provenance of new metal entering the system; the circulation of extant metal across time and space, and how this is seen in changing compositional signatures; and some economic aspects of metal production. These include the role of metal-producing communities within larger economic settings, quantifying the amount of metal present at any one time within a society, and aspects of hoarding, a distinctive European phenomenon that is less prevalent in the Middle Eastern and Asian Bronze Age societies.
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Analyses of ceramic vessel shape are neither new or novel; however, the relatively recent adoption of geometric morphometric (GM) methods by archaeologists provides a preview of the contribution of GM to the systematic and rigorous study of morphology as applied to material culture. This study is focused upon an analysis of Caddo bottle shapes for Belcher Engraved, Hickory Fine Engraved, Keno Trailed, Smithport Plain, and Taylor Engraved vessels from the Allen Plantation, Belcher Mound, Gahagan Mound, and Smithport Landing sites in the Clarence H. Webb collections from northwest Louisiana. Results indicate some significant relationships between bottle shape and size (allometry), bottle shape and type, and bottle shape and site. A test of morphological integration indicates that the bottles are significantly integrated, meaning that those discrete traits used to characterise their shape (rim, neck, body, and base) vary in a coordinated manner, highlighting significant integration between suites of attributes. The Smithport Plain and Hickory (Fine) Engraved bottles found at the Belcher Mound, Smithport Landing, and Gahagan Mound sites also provide evidence for two discrete (north–south) base and body shapes.
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Bronze is the defining metal of the European Bronze Age and has been at the center of archaeological and science-based research for well over a century. Archaeo-metallurgical studies have largely focused on determining the geological origin of the constituent metals, copper and tin, and their movement from producer to consumer sites. More recently, the effects of recycling, both temporal and spatial, on the composition of the circulating metal stock have received much attention. Also, discussions of the value and perception of bronze, both as individual objects and as hoarded material, continue to be the focus of scholarly debate. Here, we bring together the sometimes-diverging views of several research groups on these topics in an attempt to find common ground and set out the major directions of the debate, for the benefit of future research. The paper discusses how to determine and interpret the geological provenance of new metal entering the system; the circulation of extant metal across time and space, and how this is seen in changing compositional signatures; and some economic aspects of metal production. These include the role of metal-producing communities within larger economic settings, quantifying the amount of metal present at any one time within a society, and aspects of hoarding, a distinctive European phenomenon that is less prevalent in the Middle Eastern and Asian Bronze Age societies.
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We introduce here Momocs, a package intended to ease and popularize modern mor- phometrics with R, and particularly outline analysis, which aims to extract quantitative variables from shapes. It mostly hinges on the functions published in the book entitled Modern Morphometrics Using R by Claude (2008). From outline extraction from raw data to multivariate analysis, Momocs provides an integrated and convenient toolkit to students and researchers who are, or may become, interested in describing the shape and its variation. The methods implemented so far in Momocs are introduced through a simplistic case study that aims to test if two sets of bottles have different shapes.
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In this age of ever-increasing data set sizes, especially in the natural sciences, visualisation becomes more and more important. Self-organizing maps have many features that make them attractive in this respect: they do not rely on distributional assumptions, can handle huge data sets with ease, and have shown their worth in a large number of applications. In this paper, we highlight the kohonen package for R, which implements self-organizing maps as well as some extensions for supervised pattern recognition and data fusion.
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Conference Paper
Parmi les productions métalliques connues de l'âge du Bronze en Europe, certaines sont considérées comme des productions en série et sont nommées comme telles. Il s'agit en particulier des lames de haches à talon du Bronze moyen au milieu du deuxième millénaire avant notre ère, produites et utilisées massivement en Europe occidentale. Ces objets sont le plus souvent retrouvés en contexte de dépôt, c'est-à-dire qu'ils ont été retirés du circuit de production, qu’ils ont échappé à un éventuel recyclage, puis ont été volontairement rassemblés et enfouis sous terre. On les retrouve entiers, bruts ou prêts à l'emploi. Ils forment des ensembles homogènes de quelques objets ou de plusieurs dizaines, voire de centaines de pièces. De tels ensembles ont d'emblée suscité de nombreuses questions d'interprétation mais de toute évidence, les artisans bronziers protohistoriques ont cherché à reproduire à l'identique les modèles qu'ils avaient conçus. Une simple observation macroscopique montre une recherche des mêmes formes et des mêmes décors, ce qui donne souvent l'impression d'une grande homogénéité de la production de cette période. Il existe même de nombreux exemples de lames de haches dont on peut affirmer qu'elles ont été produites dans le même moule. Pourtant, si l'on examine la production d'un type dans son ensemble, c'est-à-dire tous les exemplaires considérés comme appartenant à ce même type, il existe, même à l'oeil nu, des disparités – notamment de forme – assez importantes. La question est alors de savoir dans quelle mesure les types identifiés à l'oeil nu sont réellement cohérents, autrement dit de mesurer le degré de précision dans la reproduction à l'identique des objets si nombreux et ce, au sein d'un territoire très vaste (plusieurs milliers de km2). Au-delà de cette question, il s'agit de comprendre les processus de fabrication des objets métalliques au milieu du deuxième millénaire avant notre ère, entre la Manche et les Alpes. Pour répondre à cette problématique, l'observation macroscopique ne suffisant plus, nous nous sommes attachés à mettre en oeuvre des méthodes issues des sciences du vivant, qui utilisent depuis longtemps des outils et des analyses mathématiques permettant de comparer des populations entre elles à partir des formes des individus qui les composent. Jusqu'à présent, nous avons sélectionné deux méthodes principales : la transformée en cosinus discrète (TCD) et les polynômes orthogonaux. L'emploi de ces techniques d'analyse nous permet de quantifier ce que l'on observe à l'oeil nu. Ces études ont tout d'abord montré que pour une même famille d'objets, ici les lames de haches dites « à talon », les deux types différents – distingués par leur répartition géographique (type normand et type breton) – avaient une réelle validité statistique en termes de forme, avec toutefois un chevauchement dans l'espace morphométrique. Ce fait prouve que les populations protohistoriques avaient conscience de leur appartenance territoriale, ici la péninsule armoricaine (type dit « breton ») et la vallée de la Seine (type dit « normand ») et qu'elles cherchaient à reproduire un modèle établi. Ces méthodes statistiques permettent également de quantifier la variabilité de forme présente dans chacun des types ; on voit donc bien que l'important est de se rapprocher d'une forme qui porte une signification spatiale et donc culturelle, même s'il ne s'agit pas d'exactes reproductions. Dès lors que l'on s'éloigne des zones de plus grande concentration géographique, on trouve des exemplaires qui ont l'aspect des modèles standards, mais qui se retrouvent en périphérie des espaces morphométriques formés par ces derniers. C'est alors que se pose la question de l'existence de productions locales d'imitations (et de transfert de technologie) dans les secteurs qui ne sont pas censés être des pôles majeurs de fabrication. Ainsi, à travers l'exemple des productions métalliques de haches, la règle de fabrication semble résider dans la volonté de se rapprocher au maximum d'un modèle de référence, sans pour autant que l'imitation soit forcément parfaite. Le degré de conformité ne semble pas être la notion la plus importante, tant que, à l'oeil nu, les objets se ressemblent.
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We analyzed interspecific wing outline shape variations of 5 species of antlion: Myrmeleon bore (Tjeder, 1941), M. immanis Walker, 1853, M. fuscus Yang, 1999, Euroleon coreanus Okamoto, 1926, and E. flavicorpus Wang, 2009. In total, 98 forewings and 98 hindwings from the 5 species were sampled and subjected to an elliptic Fourier analysis. Twenty 1st Fourier harmonics were summarized via a principal component analysis and the 1st 8 principal components of shape variation were considered for statistical tests (multivariate analysis of variance, canonical variate analysis, and cluster analysis). Euroleon coreanus and E. flavicorpus were recognized as a group, while M. bore, M. immanis, and M. fuscus comprised a separate group. Results of the analysis of wing outline shapes of the 5 species agree with the current taxonomic system.
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In 2010, in doubtful circumstances, a bronze axe blade was fortuitously discovered in the forest of Étaules. The artefact has been studied as detailed as possible in order to suggest its former cultural context, thus allowing to give a brief review of the Early Bronze Age in Burgundy. This flanged axe, close to the Neyruz type, can be attributed to the mid-Early Bronze Age. In an excellent state of preservation, it was carefully prepared after having been cast in a split mould; although worn by use, it remains fully functional. Despite the lack of the archaeological context at the precise place where it was discovered, its presence strengthens the idea of a developed human occupation in Burgundy at the time of the early second millennium B.C.
Chapter
Principal component analysis has often been dealt with in textbooks as a special case of factor analysis, and this tendency has been continued by many computer packages which treat PCA as one option in a program for factor analysis—see Appendix A2. This view is misguided since PCA and factor analysis, as usually defined, are really quite distinct techniques. The confusion may have arisen, in part, because of Hotelling’s (1933) original paper, in which principal components were introduced in the context of providing a small number of ‘more fundamental’ variables which determine the values of the p original variables. This is very much in the spirit of the factor model introduced in Section 7.1, although Girschick (1936) indicates that there were soon criticisms of Hotelling’s method of PCs, as being inappropriate for factor analysis. Further confusion results from the fact that practitioners of ‘factor analysis’ do not always have the same definition of the technique (see Jackson, 1981). The definition adopted in this chapter is, however, fairly standard.
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Leaflet shape of thirty-nine soybean cultivars/strains selected to cover the possible diversity of leaf shape, was quantitatively evaluated by principal components scores based on the elliptic Fourier descriptor of contours. After central leaflets of fully expanded compound-leaves of the cultivars/strains were videotaped, binary images of the leaflets were obtained from those video images by image processing. Then, the closed contour of each leaflet was extracted from the binary images and chain-coded by image processing. Because the first twenty harmonics could sufficiently represent soybean leaf contours, 77 elliptic Fourier coefficients were calculated for each chain-coded contour. Then, the Fourier coefficients were standardized so that the coefficients were invariant of the size, rotation, shift and chain-code starting-point of any contour. The principal component analysis about the standardized Fourier coefficients, showed that the cumulative contribution at the fifth principal component was about 96 o/o' Moreover, the effect of each principal component on the leaf shape was clarified by drawing the contours of leaflets using the Fourier coefficients inversely estimated under some typical values of the principal component scores. Consequently, it was indicated that the principal components scores about the standardized elliptic Fourier coefficients gave us powerful quantitative measures to evaluate soybean leaf shape. The analysis of variance and multiple comparison indicated that the genotypic differences on the first, the second and the fifth principal components were significantly large. Because the variations of those principal components were con-tinuous, the effects of the polygenes on the (size-invariant) shape were also suggested.
Book
The chapter introduces the idea that the relationships between natural conditions and the outcome of an observation may be deterministic, random, strategic or chaotic, and that numerical ecology addresses the second type of data; it describes the role of numerical ecology among the various phases of an ecological research. The chapter includes discussion of the following topics: spatial structure, spatial dependence, and spatial correlation (independent observations, independent descriptors, linear independence, independent variable of a model, independent samples, origin of spatial structures, tests of significance in the presence of spatial correlation, and classical sampling and spatial structure), statistical testing by permutation (classical tests of significance, permutation tests, alternative types of permutation tests), computer programs and packages, ecological descriptors (i.e. variables: mathematical types of descriptors, and intensive, extensive, additive, and non-additive descriptors), descriptor coding (linear transformation, nonlinear transformations, combining descriptors, ranging and standardization, implicit transformation in association coefficients, normalization, dummy variable coding, and treatment of missing data (delete rows or columns, accommodate algorithms to missing data, estimate missing values). The chapter ends on a description of relevant software implemented in the R language.
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Cambridge Core - Quantitative Biology, Biostatistics and Mathematical Modeling - Fourier Descriptors and their Applications in Biology - edited by Pete E. Lestrel
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Geometric Morphometrics for Biologists is an introductory textbook for a course on geometric morphometrics, written for graduate students and upper division undergraduates, covering both theory of shape analysis and methods of multivariate analysis. It is designed for students with minimal math background; taking them from the process of data collection through basic and more advanced statistical analyses. Many examples are given, beginning with simple although realistic case-studies, through examples of complex analyses requiring several different kinds of methods. The book also includes URLâs for free software and step-by-step instructions for using the software.
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Cluster analysis is the automated search for groups of related observations in a dataset. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures, and most clustering methods available in commercial software are also of this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as how many clusters are there, which clustering method should be used, and how should outliers be handled. We review a general methodology for model-based clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, minefield detection, cluster recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology and discuss recent developments in model-based clustering for non-Gaussian data, high-dimensional datasets, large datasets, and Bayesian estimation.
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In the Proceedings of the Prehistoric Society for 1964, the writer presented (Roe, 1964) an interim report on his programme of research on the British Lower and Middle Palaeolithic material, describing methods of studying assemblages of handaxes by metrical and statistical analysis, and outlining the first results obtained. The present paper offers a summary of the final results obtained for certain aspects of the same research project, in particular the discerning of various groupings among the 38 handaxe assemblages considered. The Groups which emerge are clusters of sites whose industries are similar in terms of the morphological range and usual degree of refinement of their handaxes. The Thesis for which the research was undertaken was completed in March, 1967 (Roe, 1967), and is available for consultation. It is of course quite impossible to quote in the present paper more than a small part of the evidence upon which the final conclusions depend.
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The Self-Organising Map (SOM) algorithm was introduced by the author in 1981. Its theory and many applications form one of the major approaches to the contemporary artificial neural networks field, and new technologies have already been based on it. The most important practical applications are in exploratory data analysis, pattern recognition, speech analysis, robotics, industrial and medical diagnostics, instrumentation, and control, and literally hundreds of other tasks. In this monograph the mathematical preliminaries, background, basic ideas, and implications are expounded in a manner which is accessible without prior expert knowledge.
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A generalized procedure, elliptical Fourier analysis, for accurately characterizing the shape of complex morphological forms of the type commonly encountered in the biological sciences, is described. Elliptical Fourier functions are derived as a parametric formulation from conventional Fourier analysis, i.e., as a pair of equations that are functions of a third variable. The use of elliptical Fourier functions circumvents three restrictions that have limited conventional Fourier analysis to certain classes of shapes. These restrictions are (1) equal divisions over the interval or period; (2) dependency on the coordinate system, i.e., conventional Fourier functions are not “coordinate free”; and (3) the presence of shapes with outlines that curve back on themselves, a common occurrence. These three limitations are effectively removed with the utilization of elliptical Fourier functions, facilitating the analysis of a much larger class of two-dimensional forms.
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The first edition of Geometric Morphometrics for Biologists has been the primary resource for teaching modern geometric methods of shape analysis to biologists who have a stronger background in biology than in multivariate statistics and matrix algebra. These geometric methods are appealing to biologists who approach the study of shape from a variety of perspectives, from clinical to evolutionary, because they incorporate the geometry of organisms throughout the data analysis. The second edition of this book retains the emphasis on accessible explanations, and the copious illustrations and examples of the first, updating the treatment of both theory and practice. The second edition represents the current state-of-the-art and adds new examples and summarizes recent literature, as well as provides an overview of new software and step-by-step guidance through details of carrying out the analyses. Contains updated coverage of methods, especially for sampling complex curves and 3D forms and a new chapter on applications of geometric morphometrics to forensics Offers a reorganization of chapters to streamline learning basic concepts Presents detailed instructions for conducting analyses with freely available, easy to use software Provides numerous illustrations, including graphical presentations of important theoretical concepts and demonstrations of alternative approaches to presenting results. Sorry not available as a full text download!
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Principal component analysis is central to the study of multivariate data. Although one of the earliest multivariate techniques it continues to be the subject of much research, ranging from new model- based approaches to algorithmic ideas from neural networks. It is extremely versatile with applications in many disciplines. The first edition of this book was the first comprehensive text written solely on principal component analysis. The second edition updates and substantially expands the original version, and is once again the definitive text on the subject. It includes core material, current research and a wide range of applications. Its length is nearly double that of the first edition. Researchers in statistics, or in other fields that use principal component analysis, will find that the book gives an authoritative yet accessible account of the subject. It is also a valuable resource for graduate courses in multivariate analysis. The book requires some knowledge of matrix algebra. Ian Jolliffe is
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The respective roles of the phylogenetic and ecological components in an adaptive radiation are tested on a sample of Old World rats and mice (Muridae, Murinae). Phylogeny was established on nuclear and mitochondrial genes and reconstructed by maximum likelihood and Bayesian methods. This phylogeny is congruent with previous larger scale ones recently published, but includes some new results: Bandicota and Nesokia are sister taxa and Micromys would be closely related to the Rattus group. The ecological diversification is investigated through one factor, the diet, and the mandible outline provides the morphological marker. Elliptic and radial Fourier transforms are used for quantifying size and shape differences among species. Univariate size and shape parameters indicate that phylogeny is more influential on size than diet, and the reverse occurs for shape and robust patterns are recognized by multivariate analyses of the data sets provided by the Fourier methods. Omnivorous and herbivorous groups are well separated despite some overlapping, as well as are other Murinae with a specialized diet (insects, seeds). Phylogeny is also influential as shown by the segregation of several groups (Praomys, Arvicanthini, Rattus, Apodemus). Allometric shape variation was investigated, and although present it does not overwhelm effects of either phylogeny or diet. Massive mandibles characterize herbivorous Murinae and slender mandibles, the insectivorous ones. A strong angular process relative to the coronoid process characterizes seedeaters, and the reverse characterized Murinae with a diet based largely on animal matter. Such changes in morphology are clearly in relation with the functioning of the mandible, and with the forces required by the nature of the food: the need of a stronger occlusal force in herbivorous species would explain massive mandibles, and an increase of the grasping and piercing function of incisors in insectivorous species would explain slender mandibles.
Article
Fourier analysis applied to the outlines of the first upper and lower molars of European Miocene murine rodents was used to quantify the size and shape variations associated with their radiation and to determine the evolutionary relationships among the taxa. The results suggested the occurrence of two lineages involving different evolutionary patterns. Size exhibits a rapid diversification in both lineages, probably because of selective pressures related to increasing competition among species. With regard to shape, one of the lineages is characterized by a conservative morphology, and the other by a tooth evolution oriented toward broader molars, which is interpreted as an adaptive specialization. Size and shape evolution are diversely associated during the radiation, and they may be related to the morphological differentiation of co-existing species and the avoidance of interspecific competition.
Article
Kernel density estimates, which at their simplest can be viewed as a smoothed form of histogram, have been widely studied in the statistical literature in recent years but used hardly at all within archaeology. They provide an eeective method of data presentation for univariate and particularly bivariate data and this is illustrated with a range of examples. The methodology can be used as an informal approach to spatial cluster analysis, and one example suggests that it is competitive with other approaches in this area. A reason for the lack of use of kernel density estimates by archaeologists may be the lack of accessible software. The analyses described here were undertaken in the MATLAB package using routines developed by the second author, and are available on request.
Article
Ten morphometric descriptors (five pairs of form and shape parameters) are used to describe the complex morphology of the first lower molar of two morphologically similar species, Microtus arvalis and M. agrestis. These descriptors are derived either from linear measurements or from outline analysis. The effects of these different descriptors on classical analysis as used in biology or palaeobiology are explored. First, the reliability of results in statistical classification is assessed. All of the descriptors discriminate well between the two species. The initial morphometric scheme (linear or outline) does not induce marked differences in statistical classification and the major discrepancies are between standardized and non-standardized versions of descriptors, and between amplitude- and coefficient-based or linear-based descriptors. Subsequently, the similarity of morphospaces based on partial least squares analysis and of intraspecific variance (estimated from the morphospace analysis) are observed. This is done within a morphospace-disparity framework and procedures used here for testing are directed at this research area. Similarities between morphospaces are relatively high. In this case, the initial morphometric scheme is a major factor inducing dissimilarity. However, the patterns of intraspecific dispersion inferred from morphospaces are roughly similar. Major differences in results correspond to the two classes of form or shape descriptors. Similarity of intraspecific variance is obtained when standardized descriptors are used (except for amplitude-based descriptors); conversely, dissimilarity is obtained when non-standardized descriptors are used. In many cases, the results of the various analyses are robust despite changes in descriptor. Moreover, the developmental pathway of vole teeth can frequently explain major dissimilarity or even similarity. © 2004 The Linnean Society of London, Biological Journal of the Linnean Society, 2004, 83, 243–260.