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Identifying Important Pairwise Logratios in compositional data with Sparse Principal Component Analysis

MATHEMATICAL GEOSCIENCES 2025年第2期57卷 333-358页

作者： Nesrstova, Viktorie Wilms, Ines Hron, Karel Filzmoser, Peter Palacky Univ Olomouc Fac Sci Dept Math Anal & Applicat Math 17 Listopadu 12 Olomouc Czech Republic Univ Hradec Kralove Dept Informat & Quantitat Methods Fac Informat & Management Hradecka 1249-6 Hradec Kralove Czech Republic Maastricht Univ Dept Quantitat Econ Tongersestr 53 Maastricht Netherlands TU Wien Inst Stat & Math Methods Econ Wiedner Hauptstr 8-10 Vienna Austria

compositional data are characterized by the fact that their elemental information is contained in simple pairwise logratios of the parts that constitute the composition. While pairwise logratios are typically easy to interpret, the number of possible pairs to consider quickly becomes too large even for medium-sized compositions, which may hinder interpretability in further multivariate analysis. Sparse methods can therefore be useful for identifying a few important pairwise logratios (and parts contained in them) from the total candidate set. To this end, we propose a procedure based on the construction of all possible pairwise logratios and employ sparse principal component analysis to identify important pairwise logratios. The performance of the procedure is demonstrated with both simulated and real-world data. In our empirical analysis, we propose three visual tools showing (i) the balance between sparsity and explained variability, (ii) the stability of the pairwise logratios, and (iii) the importance of the original compositional parts to aid practitioners in their model interpretation.

关键词： compositional data Pairwise logratios Sparse PCA Geochemical data

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SVDD control charts based on MEWMA technique for monitoring compositional data

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COMPUTERS & INDUSTRIAL ENGINEERING 2025年 201卷

作者： Nguyen, Thi Thuy Van Heuchenne, Cedric Tran, Kim Duc Tartare, Guillaume Tran, Kim Phuc Univ Liege HEC Liege Management Sch B-4000 Liege Belgium Univ Lille ENSAIT GEMTEX Genie & Mat Text ULR 2461 F-59000 Lille France Dong A Univ IAD Da Nang 50000 Vietnam

Monitoring compositional data (CoDa) using control charts has become increasingly important in Statistical Process Control (SPC). This study introduces two approaches for CoDa monitoring, utilizing support vector data description (SVDD) control charts in conjunction with the multivariate exponentially weighted moving average (MEWMA) technique, specifically focusing on Phase II monitoring processes. The proposed approaches use two transformation methods: the Dirichlet density transformation and the isometric log-ratio transformation. We evaluate the effectiveness of the proposed SVDD control charts by computing the out-of-control zero-state Average Run Length ( ARL 1 ) using simulated data. Our results demonstrate that SVDD control charts detect anomalies more effectively than the traditional MEWMA control chart across various scenarios in monitoring CoDa. These findings contribute to the advancement of SPC and offer valuable insights for practitioners involved in CoDa monitoring across diverse applications.

关键词： Statistical process control compositional data Control chart Isometric log-ratio Dirichlet density Support vector data description

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Unveiling Land Use Dynamics: Insights from a Hierarchical Bayesian Spatio-Temporal Modelling of compositional data

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JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2025年 1-26页

作者： Figueira, Mario Guarner, Carmen Conesa, David Lopez-Quilez, Antonio Krisztin, Tamas Univ Valencia Dept Stat & Operat Res Carrer Dr Moliner 50 Burjassot 46100 Valencia Spain Int Inst Appl Syst Anal IIASA Schlosspl 1 A-2361 Laxenburg Austria

Changes in land use patterns have significant environmental and socio-economic impacts, making it crucial for policymakers to understand their causes and consequences. This study, part of the European LAMASUS (Land Management for Sustainability) project, aims to support the EU's climate neutrality target by developing a governance model through collaboration among policymakers, land users, and researchers. We present a methodological synthesis for treating land use data using a Bayesian approach within spatial and spatio-temporal modelling frameworks. The study tackles the challenges of analysing land use changes, particularly the presence of zero values and computational issues with large datasets. It introduces joint model structures to address zeros and employs sequential inference and consensus methods for Big data problems. Spatial downscaling models approximate smaller scales from aggregated data, circumventing high-resolution data complications. We explore Beta regression and compositional data Analysis (CoDa) for land use data, review relevant spatial and spatio-temporal models, and present strategies for handling zeros. The paper demonstrates the implementation of key models, downscaling techniques, and solutions to Big data challenges with examples from simulated data and the LAMASUS project, providing a comprehensive framework for understanding and managing land use changes.

关键词： Land use compositional data Spatio-temporal models Downscaling Big data INLA

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A comparison of methods for analysing compositional data with fixed and variable totals: a simulation study using the examples of time-use and dietary data

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BMC MEDICAL RESEARCH METHODOLOGY 2025年第1期25卷 1-14页

作者： Tomova, Georgia D. Walmsley, Rosemary Berrie, Laurie Morris, Michelle A. Tennant, Peter W. G. Alan Turing Inst British Lib 96 Euston Rd London NW1 2DB England Univ Leeds Leeds Inst Data Analyt Leeds LS2 9NL England Univ Leeds Sch Med Leeds LS2 9NL England Univ Edinburgh Inst Geog Sch Geosci Edinburgh EH8 9XP Scotland Univ Leeds Sch Food Sci & Nutr Leeds LS2 9JT England

Backgroundcompositional data comprise the parts of a 'whole' (or 'total'), which sum to that 'whole'. The 'whole' may vary between units of analyses, or it may be fixed (constant). For example, total energy intake (a variable total) is the sum of intake from all foods or macronutrients. Total time in a day (a fixed total) is the sum of time spent engaging in various activities. There exist different approaches to analysing compositional data, such as the isocaloric or isotemporal model, ratio variables, and compositional data analysis (CoDA). Although the performance of the different approaches has been compared previously, this has only been conducted in real data. Since the true relationships are unknown in real data, it is difficult to compare model performance in estimating a known effect. We use data simulations of different parametric relationships, to explore and demonstrate the performance of each approach under various possible *** simulated physical activity time-use and dietary data as examples of compositional data with fixed and variable totals, respectively, using different parametric relationships between the compositional components and the outcome (fasting plasma glucose): linear, log2, and isometric log-ratios. We evaluated the performance of a range of generalised linear and additive models as well as CoDA, in estimating a 1-unit and either 10-unit (for physical activity) or 100-unit (for dietary data) reallocations under each parametric scenario. We simulated 10,000 datasets with 1,000 observations in *** performance of each approach to analysing compositional data depends on how closely its parameterisation matches the true data generating process. Overall, we demonstrated that the consequences of using an incorrect parameterisation (e.g. using CoDA when the true relationship is linear) are more severe for larger reallocations (e.g. 10-min or 100-kcal) than for 1-unit reallocations. The implications of choosing an un

关键词： compositional data compositional data analysis Isotemporal model Ratio variables Leave-one-out model Physical activity Dietary intake

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Principal Components Analysis: Row Scaling and compositional data

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JOURNAL OF CHEMOMETRICS 2025年第3期39卷

作者： Brereton, Richard G. UNIV BRISTOL SCH CHEM BRISTOL England

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Graph convolutional network for compositional data

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INFORMATION FUSION 2025年 117卷

作者： Lu, Shan Wang, Huiwen Zhao, Jichang Cent Univ Finance & Econ Sch Stat & Math Beijing 100081 Peoples R China Beihang Univ Sch Econ & Management Beijing 100191 Peoples R China Beihang Univ Key Lab Complex Syst Anal Management & Decis Minist Educ Beijing 100191 Peoples R China

Graph convolutional network (GCN) has garnered significant attention and become a powerful tool for learning graph representations. However, when dealing with compositional data prevalent in various fields, the traditional GCN faces theoretical challenges due to the intrinsic constraints of such data. This paper generalizes the spectral graph theory in simplex space, aiming to address the graph structures among observations for compositional data analysis and to extend GCN by assigning mathematical objects of compositions to each vertex of a graph. We propose the graph Fourier transformation in simplex space, based on which a compositional graph convolutional network (CGCN) layer is introduced. This novel layer enables a GCN to appropriately capture the sample space of compositional data, allowing it to handle compositional features as model inputs. We then propose a new GCN architecture called COMP-GCN, incorporating the CGCN layer at the initial stage. We evaluate the effectiveness of COMP-GCN through simulation studies and two real- world applications: stock networks derived from co-investors in the Chinese stock market and student social networks based on co-locations in campus activities. The results demonstrate its superior performance over competitive methods with modest additional computational cost compared to traditional GCN. Our findings suggest the potential of the proposed model to inspire anew class of powerful algorithms for graph inference on compositional data in virtue of the generalization of graph convolution on simplex space.

关键词： Graph neural networks Graph convolutional network compositional data Spectral graph theory Graph inference

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compositional data in Geostatistics: A Log-Ratio Based Framework to Analyze Regionalized Compositions

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MATHEMATICAL GEOSCIENCES 2020年第8期52卷 1067-1084页

作者： Pawlowsky-Glahn, V. Egozcue, J. J. Univ Girona Dept Comp Sci Appl Math & Stat Girona Spain Tech Univ Catalonia Dept Civil & Environm Engn Barcelona Spain

Problems with compositional data, like spurious correlation and negative bias, are well known in the Geosciences. Not so well known is the fact that the same problems appear when dealing with regionalized compositions. Here, these problems are illustrated, and a solution, based on the principle of working in coordinates using orthonormal logratio representations, is presented. This approach offers a tool for standard geostatistical studies. One of the advantages the method has is that it allows the usual inconsistencies with indicator kriging to be overcome through simplicial indicator kriging. A general way of modelling crossvariograms of coordinates, based on the matrix valued variation variogram, is discussed. In summary, the main aspects related to the modelling and analysis of regionalized compositions have had satisfactory solutions found for them. The proposed methodology is illustrated with public data from a survey concerning arsenic contamination in underground water in Bangladesh.

关键词： compositional data Variation variogram Simplicial indikator kriging Multinomial logistic regression Crossvariogram compositional kriging

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compositional data analysis of Holocene sediments from the West Bengal Sundarbans, India: Geochemical proxies for grain-size variability in a delta environment

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APPLIED GEOCHEMISTRY 2016年 75卷 222-235页

作者： Flood, R. P. Bloemsma, M. R. Weltje, G. J. Barr, I. D. O'Rourke, S. M. Turner, J. N. Orford, J. D. Queens Univ Belfast Sch Geog Archaeol & Palaeoecol Belfast BT7 1NN Antrim North Ireland Tata Steel Netherlands Main Off Postbus 10000 NL-1970 CA IJmuiden Netherlands Univ Leuven Geol Div Dept Earth & Environm Sci Celestijnenlaan 200E B-3001 Leuven Heverlee Belgium Univ Coll Dublin Sch Biosyst Engn Dublin 4 Ireland Univ Coll Dublin Sch Geog Dublin 4 Ireland Univ Coll Dublin UCD Earth Inst Dublin 4 Ireland Trinity Coll Dublin Sch Nat Sci Dublin 2 Ireland

This paper is part of a special issue of Applied Geochemistry focusing on reliable applications of compositional multivariate statistical methods. This study outlines the application of compositional data analysis (CoDa) to calibration of geochemical data and multivariate statistical modelling of geochemistry and grain-size data from a set of Holocene sedimentary cores from the Ganges-Brahmaputra (G-B) delta. Over the last two decades, understanding near-continuous records of sedimentary sequences has required the use of core-scanning X-ray fluorescence (XRF) spectrometry, for both terrestrial and marine sedimentary sequences. Initial XRF data are generally unusable in 'raw-format', requiring data processing in order to remove instrument bias, as well as informed sequence interpretation. The applicability of these conventional calibration equations to core-scanning XRF data are further limited by, the constraints posed by unknown measurement geometry and specimen homogeneity, as well as matrix effects. Log ratio based calibration schemes have been developed and applied to clastic sedimentary sequences focusing mainly on energy dispersive-XRF (ED-XRF) core-scanning. This study has applied high resolution core-scanning XRF to Holocene sedimentary sequences from the tidal-dominated Indian Sundarbans, (Ganges-Brahmaputra delta plain). The Log-Ratio Calibration Equation (LRCE) was applied to a subset of core-scan and conventional ED-XRF data to quantify elemental composition. This provides a robust calibration scheme using reduced major axis regression of log-ratio transformed geochemical data. Through partial least squares (PLS) modelling of geochemical and grain-size data, it is possible to derive robust proxy information for the Sundarbans depositional environment. The application of these techniques to Holocene sedimentary data offers an improved methodological framework for unravelling Holocene sedimentation patterns. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： compositional data Ganges-Brahmaputra delta XRF Calibration Geochemistry Grain-size Partial least squares

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compositional data analysis of smoke emissions from debris piles with low-density polyethylene

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JOURNAL OF THE AIR & WASTE MANAGEMENT ASSOCIATION 2020年第8期70卷 834-845页

作者： Weise, David R. Jung, Heejung Palarea-Albaladejo, Javier Cocker, David R. US Forest Serv USDA Pacific Southwest Res Stn Riverside CA 92507 USA Univ Calif Riverside Dept Mech Engn Riverside CA 92521 USA Biomath & Stat Scotland Edinburgh Midlothian Scotland Univ Calif Riverside Dept Chem & Environm Engn Riverside CA 92521 USA

data describing the composition of smoke are inherently multivariate and always non-negative parts of a whole. The data are relative and the information is contained in the ratios between parts of the composition. A prior analysis of smoke emissions produced from the burning of manzanita wood mixed with low-density polyethylene plastic applied traditional statistical methods to the compositional data and found no effect. The current paper applies compositional data techniques to these smoke emissions to determine if the prior analysis was accurate. Analysis of variance of the isometric log-ratios showed that LDPE significantly affected the CO(2)emission ratio for 8 of the 191 trace gases;this analysis showed none of the gases identified in the previous analysis were affected by LDPE. LDPE did not affect the CO(2)emission ratios for the alkanes, alkenes, alkynes, aldehydes, cycloalkanes, cycloalkenes, diolefins, ketones, MAHs, and PAHs. compositional data analysis should be used to analyze smoke emissions data. Burning contaminant-free LDPE should produce emissions like wood. Implications Reanalysis of impact of burning LDPE plastic in silvicultural debris piles using appropriate statistical techniques confirmed previously published results from inappropriate techniques that LDPE did not change the composition of the smoke emissions. Being able to dispose of these LDPE-covered forest debris by burning can save thousands of dollars in labor costs annually. Disposal of pesticide-free agricultural LDPE plastic by burning should only produce wood-like smoke emissions. This applies to LDPE/total mass ratios of 0.25- 2.5% as studied.

关键词： Arctostaphylos LDPE Polyethylene compositional data log-ratio analysis particulate plastic smoke

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compositional data for Bi-Pb tellurosulfides

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CANADIAN MINERALOGIST 2007年第3期45卷 417-435页

作者： Cook, Nigel J. Ciobanu, Cristiana L. Stanley, Christopher J. Paar, Werner H. Sundblad, Krister Univ Oslo Nat Hist Museum N-0318 Oslo Norway S Australian Museum Adelaide SA 5000 Australia Univ Adelaide Dept Earth & Environm Sci Adelaide SA 5000 Australia Nat Hist Museum Dept Mineral London SW7 5BD England Salzburg Univ Inst Mineral A-5020 Salzburg Austria Univ Turku Dept Geol FIN-20014 Turku Finland

Compounds containing essential Bi, Ph, Te and S are rare in nature. Aleksite, PbBi2Te2S2, is known from less than ten localities worldwide, and the single other recognized mineral, saddlebackite, Pb2Bi2Te2S3, is known only from the type locality, the Boddington Au deposit, Western Australia. Another phase, unnamed PbBi4Te4S3, had earlier been recognized as homogeneous grains and lamellar intergrowths within an assemblage consisting of aleksite, tellurobismuthite and tetradymite from St. David's mine Clogau, Wales. U.K. Re-investigation of this assemblage, including careful micro-analysis to avoid obvious intergrowths of phases. reveals an almost continuous range of compositions between tetradymite and aleksite. Investigations of complex sulfosalt-telluride assemblages from lilijarvi, a satellite deposit within the Orijarvi orefield, southwest Finland, have revealed compositions approximating to the range Pb5Bi4Te4S7 - Pb7Bi4Te4S9. These occur as fine intergrowths, rarely as larger single lamellae. also with aleksite, within a matrix of giessenite, galena and cosalite. The samples contain abundant gold, seen also as symplectite intergrowths with rutile. Investigation of the microparagenesis of precious-metal -bearing galena - chalcopyrite - pyrite mineralization in quartz veins at Fragant ("Langenleiten"), Carinthia Province of Austria, revealed the presence of several compositionally different Bi-Pb tellurosulfides. Aleksite is the most abundant, followed by unnamed phases with compositions close to Pb3Bi4TC4S5, Pb5Bi4Te4S7 and Pb6Bi4Te4S8. They occur as inclusions in galena and are variably associated with sulfosalts such as lillianite. cosalite, felbertalite and aikinite. The compositional dataset from the above occurrences is difficult to interpret without accompanying structural data. The data, however, Suggest the existence of an incremental chemical series with the general formula PbNBi4Te4SN+2. Alternatively, these are not discrete, essentially immiscible pha

关键词： tellurosulfides aleksite compositional data unnamed phases Clogau Wales lilijarvi Finland fragant Austria

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