Discordancy in reduced dimensions of outliers in high-dimensional datasets: application of an updating formula

Abstract

In multivariate outlier studies, the sum of squares and cross-product (SSCP) is an important property of the data matrix. For example, the much used Mahalanobis distance and the Wilk's ratio make use of SSCP matrices. One of the SSCP matrices involved in outlier studies is the matrix for the set of multiple outliers in the data. In this paper, an explicit expression for this matrix is derived. It has then been shown that in general the discordancy of multiple outliers is preserved along Multiple-Outlier Displaying Components with much lower dimensions than the original high-dimensional dataset