### An R Library for Compositional Data Analysis in Archaeometry

"... Compositional data naturally arises from the scientific analysis of the chemical composition of archaeological material such as ceramic and glass artefacts. Data of this type can be explored using a variety of techniques, from standard multivariate methods such as principal components analysis and c ..."

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Compositional data naturally arises from the scientific analysis of the chemical composition of archaeological material such as ceramic and glass artefacts. Data of this type can be explored using a variety of techniques, from standard multivariate methods such as principal components analysis and cluster analysis, to methods based upon the use of log-ratios. The general aim is to identify groups of chemically similar artefacts that could potentially be used to answer questions of provenance. This paper will demonstrate work in progress on the development of a documented library of methods, implemented using the statistical package R, for the analysis of compositional data. R is an open source package that makes available very powerful statistical facilities at no cost. We aim to show how, with the aid of statistical software such as R, traditional exploratory multivariate analysis can easily be used alongside, or in combination with, specialist techniques of compositional data analysis. The library has been developed from a core of basic R functionality, together with purpose-written routines arising from our own research (for example that reported at CoDaWork'03). In addition, we have included other appropriate publicly available techniques and libraries that have been implemented in R by other authors. Available functions range from standard multivariate techniques through to various approaches to log-ratio analysis and zero replacement. We also discuss and demonstrate a small selection of relatively new techniques that have hitherto been little-used in archaeometric applications involving compositional data. The application of the library to the analysis of data arising in archaeometry will be demonstrated; results from different analyses will be compared; and the utility of the various methods discussed. Key words: archaeometry; compositional data; multivariate analysis; R.

### c © International Statistical Institute Simple Correspondence Analysis: A Bibliographic Review

"... Over the past fewdecades correspondence analysis has gained an international reputation as a powerful statistical tool for the graphical analysis of contingency tables. This popularity stems from its development and application inmany European countries, especially France, and its use has spread to ..."

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Over the past fewdecades correspondence analysis has gained an international reputation as a powerful statistical tool for the graphical analysis of contingency tables. This popularity stems from its development and application inmany European countries, especially France, and its use has spread to English speaking nations such as the United States and the United Kingdom. Its growing popularity amongst statistical practitioners, andmore recently those disciplineswhere the role of statistics is less dominant, demonstrates the importance of the continuing research and development of the methodology. The aim of this paper is to highlight the theoretical, practical and computational issues of simple correspondence analysis and discuss its relationship with recent advances that can be used to graphically display the association in two-way categorical data.

### DOI: 10.1007/s00357 Dealing with Distances and Transformations for Fuzzy C-Means Clustering of Compositional Data

, 2012

"... Abstract: Clustering techniques are based upon a dissimilarity or distance mea-sure between objects and clusters. This paper focuses on the simplex space, whose elements—compositions—are subject to non-negativity and constant-sum constraints. Any data analysis involving compositions should fulfill t ..."

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Abstract: Clustering techniques are based upon a dissimilarity or distance mea-sure between objects and clusters. This paper focuses on the simplex space, whose elements—compositions—are subject to non-negativity and constant-sum constraints. Any data analysis involving compositions should fulfill two main principles: scale invariance and subcompositional coherence. Among fuzzy clustering methods, the FCM algorithm is broadly applied in a variety of fields, but it is not well-behaved when dealing with compositions. Here, the adequacy of different dissimilarities in the simplex, together with the behavior of the common log-ratio transformations, is dis-cussed in the basis of compositional principles. As a result, a well-founded strategy for FCM clustering of compositions is suggested. Theoretical findings are accom-panied by numerical evidence, and a detailed account of our proposal is provided. Finally, a case study is illustrated using a nutritional data set known in the clustering literature.

### Detailed guide to CoDaPack: a freeware compositional software

"... Abstract: Suitable statistical methods for compositional data based on log-ratio methodology are not included in standard statistical packages. This work presents a detailed guide to freeware Excel for Windows-based package, named CoDaPack, which implements most of the basic statistical methods of t ..."

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Abstract: Suitable statistical methods for compositional data based on log-ratio methodology are not included in standard statistical packages. This work presents a detailed guide to freeware Excel for Windows-based package, named CoDaPack, which implements most of the basic statistical methods of this methodology. The web site

### In situ Laser Induced Breakdown Spectroscopy as a tool to discriminate volcanic rocks and magmatic series, Iceland

"... This study evaluates the potentialities of a lab-made pLIBS (portable Laser-Induced Breakdown Spectroscopy) to sort volcanic rocks belonging to various magmatic series. An in-situ chemical analysis of 19 atomic lines, including Al, Ba, Ca, Cr, Cu, Fe, Mg, Mn, Na, Si, Sr and Ti, from 21 sampled rock ..."

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This study evaluates the potentialities of a lab-made pLIBS (portable Laser-Induced Breakdown Spectroscopy) to sort volcanic rocks belonging to various magmatic series. An in-situ chemical analysis of 19 atomic lines, including Al, Ba, Ca, Cr, Cu, Fe, Mg, Mn, Na, Si, Sr and Ti, from 21 sampled rocks was performed during a field exploration in Iceland. Iceland was chosen both for the various typologies of volcanic rocks and the rugged conditions in the field in order to test the sturdiness of the pLIPS. Elemental compositions were also measured using laboratory ICP-AES measurements on the same samples. Based on these latter results, which can be used to identify three different groups of volcanic rocks, a classification model was built in order to sort pLIBS data and to categorize unknown samples. Using a reliable statistical scheme applied to LIBS compositional data, the classification capability of the pLIBS system is clearly demonstrated (90-100% success rate). Although this prototype does not provide quantitative measurements, its use should be of particular interest for future geological field investigations.

### New Features of CoDaPack. An Userfriendly Compositional Data Package

"... Abstract The statistical analysis of compositional data is commonly used in geological studies. As is well-known, compositions should be treated using logratios of parts, which are difficult to use correctly in standard statistical packages. In this paper we describe the new features of our freewar ..."

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Abstract The statistical analysis of compositional data is commonly used in geological studies. As is well-known, compositions should be treated using logratios of parts, which are difficult to use correctly in standard statistical packages. In this paper we describe the new features of our freeware package, named CoDaPack, which implements most of the basic statistical methods suitable for compositional data. An example using real data is presented to illustrate the use of the package.

### P_TOS05_Isotope.doc

"... Abstract Isotopic data are currently becoming an important source of information regarding sources, evolution and mixing processes of water in hydrogeologic systems. However, it is not clear how to treat with statistics the geochemical data and the isotopic data together. We propose to introduce th ..."

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Abstract Isotopic data are currently becoming an important source of information regarding sources, evolution and mixing processes of water in hydrogeologic systems. However, it is not clear how to treat with statistics the geochemical data and the isotopic data together. We propose to introduce the isotopic information as new parts, and apply compositional data analysis with the resulting increased composition. Results are equivalent to downscale the classical isotopic delta variables, because they are already relative (as needed in the compositional framework) and isotopic variations are almost always very small. This methodology is illustrated and tested with the study of the Llobregat River Basin (Barcelona, NE Spain), where it is shown that, though very small, isotopic variations comp lement geochemical principal components, and help in the better identification of pollution sources.

### Characterisation and distribution of deposited trace elements transported over long and intermediate distances in north-eastern France using Sphagnum peatlands as a sentinel ecosystem

"... h i g h l i g h t s First characterisation of long-range deposition using sphagnum peatlands in France. Cd, Zn, Pb and Cu are predominantly of anthropogenic origin. A new synthetic indicator describes the deposition of anthropogenic elements. Vosges and Alps are the most affected by anthropogenic d ..."

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h i g h l i g h t s First characterisation of long-range deposition using sphagnum peatlands in France. Cd, Zn, Pb and Cu are predominantly of anthropogenic origin. A new synthetic indicator describes the deposition of anthropogenic elements. Vosges and Alps are the most affected by anthropogenic deposition. Trace elements in the form of particulate matter can be transported downwind from their emission sources and may have negative effects on human health and ecosystems. The transport of trace elements is often studied by monitoring their accumulation in mosses. The aim of this study was to characterise and describe the distribution of deposited trace elements transported over long and intermediate distances in north-eastern France, a location far from the main emission sources. We analysed the trace element accumulation in Sphagnum capillifolium in 54 ombrotrophic peatlands distributed in six regions of France (Alps, Jura, Massif Central, Morvan, Rhône corridor and Vosges). The concentrations of Al, Cd, Cr, Cu, Fe, Pb, Ti, V, and Zn in the surface were determined in three replicate samples of Sphagnum within each peatland. The enrichment factors calculated using Ti as the element of reference clearly exhibited a predominant anthropogenic origin for Cd, Cu, Pb, and Zn, although the concentrations were relatively low compared to those found in other studies. The isolation of the peatlands from any fixed and traffic emission source suggests an intermediate and/or long-distance transport of the pollutants from their emission sources. The structure of the compositional dataset was explored using a covariance biplot. The first score was used as a synthetic indicator of the origin of the deposits and the degree of contamination of each peatland. This new index showed that the Vosges and the Alps were the regions most affected by high enrichment of trace elements, particularly Pb and Cd. The erosion of soils highly contaminated by former mining and smelting activities in the Vosges and the polluted cities and busy highways in the Alps may account for these distributions. The Jura was the least affected region sampled, and the other regions presented intermediate anthropogenic deposits. This study provides valuable information concerning the management and protection of these ecosystems. a r t i c l e i n f o