Comments on "A self-organizing network for hyperellipsoidal clustering (HEC)" [with reply]

In the above paper by Mao-Jain (ibid., vol.7 (1996)), the Mahalanobis distance is used instead of Euclidean distance as the distance measure in order to acquire the hyperellipsoidal clustering. We prove that the clustering cost function is a constant under this condition, so hyperellipsoidal clustering cannot be realized. We also explains why the clustering algorithm developed in the above paper can get some good hyperellipsoidal clustering results. In reply, Mao-Jain state that the Wang-Xia failed to point out that their HEC clustering algorithm used a regularized Mahalanobis distance instead of the standard Mahalanobis distance. It is the regularized Mahalanobis distance which plays an important role in realizing hyperellipsoidal clusters. In conclusion, the comments made by Wang-Xia together with this response provide some new insights into the behavior of their HEC clustering algorithm. It further confirms that the HEC algorithm is a useful tool for understanding the structure of multidimensional data.