On some classification methods for high dimensional and functional data

[摘要] In this study, we propose classification method based on multivariate rank. We show that this classifier is Bayes rule under suitable conditions. Multivariate ranks are not invariant under affine transformation of the data and so, the effect of deviation from property of spherical symmetry is investigated. Based on this, we construct affine invariant version of this classifier. When the distributions of competing populations have different covariance matrices, minimum rank classifier performs poorly irrespective of affine invariance. To overcome this limitation, we propose a classifier based on multivariate rank region. The asymptotic properties of this method and its associated probability of misclassification are studied. Also, we propose classifiers based on the distribution of the spatial rank and establish some theoretical results for this classification method. For affine invariant version of this method, two invariants are proposed. Many multivariate techniques fail to perform well when data are curves or functions. We propose classification method based on L\(_2\) distance to spatial median and later generalise it to Lp distance to Lpmedian. The optimal choice of p is determined by cross validation of misclassification errors. The performances of our propose methods are examined by using simulation and real data set and the results are compared with the results from existing methods.

[发布机构] University:University of Birmingham;Department:School of Mathematics

[关键词] Q Science;QA Mathematics