Detection of Outliers in Multivariate Data: A Method Based on Influence Eigen

Outliers can be defined simply as an observation (or a subset of observations) that is isolated from the other observations in the data set. There are two main reasons that motivate people to find outliers; the first is the researchers intention. The second is the effects of an outlier on analyses. This article does not differentiate between the various justifications for outlier detection. The aim is to advise the analyst of observations that are considerably different from the majority. This article focuses on the identification of outliers using the eigenstructure of S and S(i) in terms of eigenvalues, eigenvectors and principle component. Note that S(i) is the sample covariance matrix of data matrix X(i), where the subscript i in parentheses is read as ”with observation i removed from X”. The idea of using the eigenstructure as a tool for identification of outliers is motivated by Maximum Eigen Difference (MED). MED is the method for identification of outliers proposed by [1]. This method utilises the maximum eigenvalue and the corresponding eigenvector. It is noted that examination of observations effect on the maximum eigenvalue is very significant. The technique for identification of outliers discuss in this article is applicable to a wide variety of settings. In this article, observations that are located far away from the remaining data are considered to be outliers.