Bing Liu
ABSTRACT
Because the Aitchison simplex spatial data is limited by bounded and definite sum constraints, the data generally does not meet the multivariate normal distribution, and there is a strict or approximate linear relationship between some variables, it is very difficult to establish its data model. In multiple regression analysis, a small change in the sample attribute value will greatly disturb the estimated value of the regression coefficient, resulting in the extremely unstable regression coefficient, and the existing general statistical analysis methods cannot be used to properly interpret and process the data. To solve this problem, based on the relevant definitions of complete algebraic operations in Aitchison simplex space, this paper proposes a filling method based on missing data in simplex space: firstly, the k-means method is used for initial filling in simplex space, then the equidistant logarithm ratio transformation is carried out, and finally the principal component method is used to correct the initial filling value. The example results show that the effect of using the principal component correction filling method based on the proposed complete algebraic operation system of simplex space is better than that of other filling methods.
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Index Terms
- Missing data filling method based on Aitchison simplex space
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