Statistical Analysis of Dispersion and Geochemical Patterns of Sedimentary System...
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chemical analysis. The geochemical data of 248 sampling stations include concentrations of nine compounds (N, P, Mg, Fe, Mn, Ti, organic carbon, CaC0 3 ,
and AI 2 0 3 ,) obtained by chemical analysis. The average density of geochemical
data is about one station per 36 km 2 •
4
Grain-Size Classification of Sediments
The statistical procedure for sediment classification includes two basic steps: (1)
recognition of statistical correlations between attributes (grain-size fractions or
chemical concentrations) and statistical associations between objects (sediment
specimen) by means of RQ-mode principal components analysis; (2) classification of the objects by means of cluster analysis based on selected principal components.
The method of RQ-mode principal component analysis is used to examine
the correlations between variables (grain-size fractions), the clustering of objects (sediment specimens), and the correspondence between object clusters
and variables (Zhou et al.1983). Robust procedures were used to reduce the bias
caused by outliers.
As the grain-size data are compositional in nature, they are 'closed' in the
sense that entries in each row of the data sum to unity. This will induce negative
correlation and spurious correlation between variables and thus mask the true
picture of covariance structure (Aitchison 1982). Another problem is that compositional data are confined to the range of [0,1] and thus do not have a normal
distribution, which is the prerequisite of many classical statistical procedures.
Aitchison (l982, 1986) proposes logratio transformation to overcome the
problems of compositional data analysis. In this study, we transformed the raw
grain-size data to their centered logratios before performing RQ-mode principal
component analysis. For the entry Xjj the centered logratio transform has the following form
Zjj = log[xjj /g(Xj)], for i=1,2, ... ,n; j=1,2, ... ,D,
where g(Xj) is the geometric mean for the ith row.
As the data have zero entries but one can not take logarithms of zeros, we follow Aitchison (l986) by replacing the zeros with a small positive number
b(C+ l)(D-C)/D2, where 0 is the maximum rounding-off error, C the number of
zeros in the row, and D the number of entries in the row. Meanwhile, each positive entries in the row is reduced by oC(C+ l)!D 2 to keep the row sum to l. For
our data, 0=0.005, D=12, and C varies between 0 and 5. This procedure implies
that we regard the zeros in the data as traces under a given detection limit.
For comparison, we also conducted robust principal component analysis
without logratio transformation. The program ROPCA (Zhou 1989) was used to
complete both tasks. Figure 2 shows the loadings of the first four principal components from the two runs. For the logratio ROPCA the first four principal components represent 94% of total variance. Clear clustering of sediments is seen in
403
chemical analysis. The geochemical data of 248 sampling stations include concentrations of nine compounds (N, P, Mg, Fe, Mn, Ti, organic carbon, CaC0 3 ,
and AI 2 0 3 ,) obtained by chemical analysis. The average density of geochemical
data is about one station per 36 km 2 •
4
Grain-Size Classification of Sediments
The statistical procedure for sediment classification includes two basic steps: (1)
recognition of statistical correlations between attributes (grain-size fractions or
chemical concentrations) and statistical associations between objects (sediment
specimen) by means of RQ-mode principal components analysis; (2) classification of the objects by means of cluster analysis based on selected principal components.
The method of RQ-mode principal component analysis is used to examine
the correlations between variables (grain-size fractions), the clustering of objects (sediment specimens), and the correspondence between object clusters
and variables (Zhou et al.1983). Robust procedures were used to reduce the bias
caused by outliers.
As the grain-size data are compositional in nature, they are 'closed' in the
sense that entries in each row of the data sum to unity. This will induce negative
correlation and spurious correlation between variables and thus mask the true
picture of covariance structure (Aitchison 1982). Another problem is that compositional data are confined to the range of [0,1] and thus do not have a normal
distribution, which is the prerequisite of many classical statistical procedures.
Aitchison (l982, 1986) proposes logratio transformation to overcome the
problems of compositional data analysis. In this study, we transformed the raw
grain-size data to their centered logratios before performing RQ-mode principal
component analysis. For the entry Xjj the centered logratio transform has the following form
Zjj = log[xjj /g(Xj)], for i=1,2, ... ,n; j=1,2, ... ,D,
where g(Xj) is the geometric mean for the ith row.
As the data have zero entries but one can not take logarithms of zeros, we follow Aitchison (l986) by replacing the zeros with a small positive number
b(C+ l)(D-C)/D2, where 0 is the maximum rounding-off error, C the number of
zeros in the row, and D the number of entries in the row. Meanwhile, each positive entries in the row is reduced by oC(C+ l)!D 2 to keep the row sum to l. For
our data, 0=0.005, D=12, and C varies between 0 and 5. This procedure implies
that we regard the zeros in the data as traces under a given detection limit.
For comparison, we also conducted robust principal component analysis
without logratio transformation. The program ROPCA (Zhou 1989) was used to
complete both tasks. Figure 2 shows the loadings of the first four principal components from the two runs. For the logratio ROPCA the first four principal components represent 94% of total variance. Clear clustering of sediments is seen in