Improved Classification for Compositional Data Using the α-transformation

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• 作者：Michail Tsagris ; Simon Preston ; Andrew T. A. Wood
• 关键词：Compositional data ; Classification ; α ; transformation ; α ; metric ; Jensen ; Shannon divergence
• 刊名：Journal of Classification
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：33
• 期：2
• 页码：243-261
• 全文大小：366 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistical Theory and Methods
  Pattern Recognition
  Bioinformatics
  Signal,Image and Speech Processing
  Psychometrics
  Marketing
  
• 出版者：Springer New York
• ISSN：1432-1343
• 卷排序：33

文摘

In compositional data analysis, an observation is a vector containing nonnegative values, only the relative sizes of which are considered to be of interest. Without loss of generality, a compositional vector can be taken to be a vector of proportions that sum to one. Data of this type arise in many areas including geology, archaeology, biology, economics and political science. In this paper we investigate methods for classification of compositional data. Our approach centers on the idea of using the α-transformation to transform the data and then to classify the transformed data via regularized discriminant analysis and the k-nearest neighbors algorithm. Using the α-transformation generalizes two rival approaches in compositional data analysis, one (when α=1) that treats the data as though they were Euclidean, ignoring the compositional constraint, and another (when α = 0) that employs Aitchison’s centered log-ratio transformation. A numerical study with several real datasets shows that whether using α = 1 or α = 0 gives better classification performance depends on the dataset, and moreover that using an intermediate value of α can sometimes give better performance than using either 1 or 0.