Multivariate analysis of log-ratio transformed data and its priority in mining science, porphyry and polymetallic vein deposits case studies

Received Date: 20.11.2017 Accepted Date: 01.07.2018 ABSTRACT Each mineralization style is characterized by typical signature associations between elements due to elemental interactions, therefore the coherence and closure effects problem must be overcome in geochemical processing. The coherence indicates the ratios between two components (rows or columns) remains the same whether they are considered in a subcomposition or in the full composition. The log-ratio transformation (LRT) has recognized as a standard procedure to support subcompositional coherence. The log-transformed data is applicable for geochemical data to unveil such associations, prior to applying the multivariate analysis like correspondence analysis (CA) and principal component analysis (PCA). At the present study, subcompositional coherence is overcome by inverse iso-metric log-ratio transformation for geochemical compositional data at two polymetallic and porphyry deposits. Based on Ilr-transformed data, Ag, Au, As, Pb, Te, Mo and rather S, W, Cu are enriched as polymetallic elements at Glojeh, while Au-Cu-(Mo) compositions indicate a porphyry deposit occurred in Dalli deposit. The ability to handle zero values in the data matrix and determining an elemental eccentricity from the center of each axis based on Euclidean distances are the advantages of CA method, with compression to LRT. Whereas, loading factors which spread in every direction and providing subcompositional coherence are the competitive advantages of PCA based on LRT, for both case studies. Results with these techniques show signifi cant ability to draw an inference in such geochemical data, and in improving the performance of multivariate techniques using LRT.

[1]  Richard Darling,et al.  Progresses in R- and Q-Mode Analysis: Correspondence Analysis and its Application to the Study of Geological Processes , 1974 .

[2]  Richard J. Howarth,et al.  Duplicate analysis in geochemical practice. Part II. Examination of proposed method and examples of its use , 1976 .

[3]  Michael J. Thompson,et al.  Duplicate analysis in geochemical practice. Part I. Theoretical approach and estimation of analytical reproducibility , 1976 .

[4]  J. Aitchison.  Principal component analysis of compositional data , 1983 .

[5]  J. Kazmierczak,et al.  Analyse logarithmique: deux exemples d'application , 1985 .

[6]  John Aitchison,et al.  The Statistical Analysis of Compositional Data , 1986 .

[7]  M. Collins,et al.  Variability of Northwest Florida Soils by Principal Component Analysis , 1988 .

[8]  John Aitchison,et al.  Relative variation diagrams for describing patterns of compositional variability , 1990 .

[9]  M. Greenacre.  Correspondence analysis in practice , 1993 .

[10]  Hongjin Ji,et al.  Correspondence cluster analysis and its application in exploration geochemistry , 1995 .

[11]  L. B. Klaczko,et al.  Heritability, phenotypic and genetic correlations of size and shape of Drosophila mediopunctata wings , 1999, Heredity.

[12]  C. Croux,et al.  Principal Component Analysis Based on Robust Estimators of the Covariance or Correlation Matrix: Influence Functions and Efficiencies , 2000 .

[13]  J. Aitchison,et al.  Biplots of Compositional Data , 2002 .

[14]  V. Pawlowsky-Glahn,et al.  Dealing with Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation , 2003 .

[15]  G. Mateu-Figueras,et al.  Isometric Logratio Transformations for Compositional Data Analysis , 2003 .

[16]  James C. Hayton,et al.  Factor Retention Decisions in Exploratory Factor Analysis: a Tutorial on Parallel Analysis , 2004 .

[17]  J Sundell,et al.  Class separation of buildings with high and low prevalence of SBS by principal component analysis. , 2004, Indoor air.

[18]  J. A. Martín-Fernández,et al.  Dealing with Compositional Data: The Freeware CoDaPack , 2005 .

[19]  V. Pawlowsky-Glahn,et al.  Compositional data and their analysis: an introduction , 2006, Geological Society, London, Special Publications.

[20]  V. Yohai,et al.  Robust Statistics: Theory and Methods , 2006 .

[21]  H. Abdi,et al.  Multiple Correspondence Analysis , 2006 .

[22]  Clifford R. Stanley,et al.  On the special application of Thompson–Howarth error analysis to geochemical variables exhibiting a nugget effect , 2006, Geochemistry: Exploration, Environment, Analysis.

[23]  P. Filzmoser,et al.  Wahrscheinlichkeitstheorie Cluster analysis applied to regional geochemical data : Problems and possibilities , 2006 .

[24]  M. Greenacre,et al.  Multiple Correspondence Analysis and Related Methods , 2006 .

[25]  I. S. Scarminio,et al.  Q-mode curve resolution of UV-vis spectra for structural transformation studies of anthocyanins in acidic solutions. , 2007, Analytica chimica acta.

[26]  M. Greenacre.  Theory of Correspondence Analysis , 2007 .

[27]  B. Mazzilli,et al.  Chemical characterization and recent sedimentation rates in sediment cores from Rio Grande reservoir, SP, Brazil , 2007 .

[28]  Hongjin Ji,et al.  Semi-hierarchical correspondence cluster analysis and regional geochemical pattern recognition , 2007 .

[29]  Monique Noirhomme-Fraiture,et al.  Symbolic Data Analysis and the SODAS Software , 2008 .

[30]  Clemens Reimann,et al.  Statistical data analysis explained : applied environmental statics with R , 2008 .

[31]  Ingo Hotz,et al.  iPCA : An Interactive System for PCA-based Visual Analytics , 2008 .

[32]  P. Filzmoser,et al.  Outlier Detection for Compositional Data Using Robust Methods , 2008 .

[33]  P. Filzmoser,et al.  Principal component analysis for compositional data with outliers , 2009 .

[34]  E. Carranza.  Controls on mineral deposit occurrence inferred from analysis of their spatial pattern and spatial association with geological features , 2009 .

[35]  D. Karamanis,et al.  Environmental assessment of natural radionuclides and heavy metals in waters discharged from a lignite-fired power plant , 2009 .

[36]  Michael Greenacre,et al.  Log-Ratio Analysis Is a Limiting Case of Correspondence Analysis , 2009 .

[37]  Clemens Reimann,et al.  Robust factor analysis for compositional data , 2009, Comput. Geosci..

[38]  P. Filzmoser,et al.  Univariate Statistical Analysis of Environmental (compositional) Data: Problems and Possibilities , 2009 .

[39]  Thomas Olofsson,et al.  Building energy parameter investigations based on multivariate analysis , 2009 .

[40]  P. Filzmoser,et al.  The bivariate statistical analysis of environmental (compositional) data. , 2010, The Science of the total environment.

[41]  Yongfeng Zhu,et al.  Geochemistry of hydrothermal gold deposits: A review , 2011 .

[42]  E. Carranza.  Analysis and mapping of geochemical anomalies using logratio-transformed stream sediment data with c , 2011 .

[43]  M. Greenacre.  Measuring Subcompositional Incoherence , 2011 .

[44]  V. Pawlowsky-Glahn,et al.  Compositional data analysis : theory and applications , 2011 .

[45]  P. Filzmoser,et al.  The concept of compositional data analysis in practice--total major element concentrations in agricultural and grazing land soils of Europe. , 2012, The Science of the total environment.

[46]  Afshin Akbarpour,et al.  Cluster and R-mode factor analyses on soil geochemical data of Masjed-Daghi exploration area, northwestern Iran , 2013, Arabian Journal of Geosciences.

[47]  F. Darabi-Golestan,et al.  Alteration, zoning model, and mineralogical structure considering lithogeochemical investigation in Northern Dalli Cu–Au porphyry , 2013, Arabian Journal of Geosciences.

[48]  R. KhaloKakaie,et al.  Interpretation of lithogeochemical and geophysical data to identify the buried mineralized area in Cu-Au porphyry of Dalli-Northern Hill , 2013, Arabian Journal of Geosciences.

[49]  M. I. Ríos-Risquez,et al.  The relationship between psychosocial job stress and burnout in emergency departments: an exploratory study. , 2012, Nursing outlook.

[50]  G. Suresh,et al.  Assessment of spatial distribution and radiological hazardous nature of radionuclides in high background radiation area, Kerala, India. , 2013, Applied radiation and isotopes : including data, instrumentation and methods for use in agriculture, industry and medicine.

[51]  H. Abdi,et al.  Multiple factor analysis: principal component analysis for multitable and multiblock data sets , 2013 .

[52]  Interpretation of the Sources of Radioactive Elements and Relationship between them by Using Multivariate Analyses in Anzali Wetland Area , 2013 .

[53]  R. Zuo,et al.  Compositional data analysis in the study of integrated geochemical anomalies associated with mineralization , 2013 .

[54]  A. Çiçek,et al.  Assessment of the effects of large borate deposits on surface water quality by multi statistical approaches: A case study of Seydisuyu Stream (Turkey) , 2014 .

[55]  Sheng Wang,et al.  Feature extraction using adaptive slow feature discriminant analysis , 2015, Neurocomputing.

[56]  Qiuming Cheng,et al.  Multivariate analysis for geochemical process identification using stream sediment geochemical data: A perspective from compositional data , 2016 .

[57]  E. Carranza.  Geochemical Mineral Exploration: Should We Use Enrichment Factors or Log-Ratios? , 2017, Natural Resources Research.

[58]  A. Hezarkhani,et al.  High precision analysis modeling by backward elimination with attitude on interaction effects on Au (Ag)-polymetallic mineralization of Glojeh, Iran , 2016 .

[59]  Sayan Mukherjee,et al.  A phylogenetic transform enhances analysis of compositional microbiota data , 2016 .

[60]  A. Hezarkhani,et al.  Assessment of 226Ra, 238U, 232Th, 137Cs and 40K activities from the northern coastline of Oman Sea (water and sediments). , 2017, Marine pollution bulletin.

[61]  A. Hezarkhani,et al.  Evaluation of elemental mineralization rank using fractal and multivariate techniques and improving the performance by log-ratio transformation , 2017, Journal of Geochemical Exploration.

[62]  A. Hezarkhani,et al.  R- and Q-mode multivariate analysis to sense spatial mineralization rather than uni-elemental fractal modeling in polymetallic vein deposits , 2018 .