The forward search and data visualization
The forward search procedure is based on the Mahalonobis norm of \(n\) data vectors \(y_i\), \[ d_i^2(m)=(y_i-\widehat\mu(m))^\top \widehat\Sigma^{-1}(m)(y_i-\widehat\mu(m)), \] where the means \(\widehat\mu(m)\) and covariances \(\widehat\Sigma(m)\) are estimated by a subset \(S(m)\) of \(m\) observations. At the \(m\)-th step of the procedure \(m+1\) observations with the smallest \(d_i^2(m)\) are taken as new \(S(m+1)\). The trajectories of \(d_i^2(m)\), \(m=m_0\), \(m_0+1,\dots,n\), are depicted at one display for all \(i=1,\dots m\). The authors discuss the use of such ``forward plots'' for the investigation of cluster structure and outlier detection. Applications to different real life and simulated examples are presented.
scientific article; zbMATH DE number 2118525