The influence function of the TCLUST robust clustering procedure

The TCLUST procedure performs robust clustering with the aim of finding clusters with different scatter structures and weights. An Eigenvalues Ratio constraint is considered by TCLUST in order to achieve a wide range of clustering alternatives depending on the allowed differences among cluster scatter matrices. Moreover, this constraint avoids finding uninteresting spurious clusters. In order to guarantee the robustness of the method against the presence of outliers and background noise, the method allows for trimming of a given proportion of observations self-determined by the data. Based on this “impartial trimming”, the procedure is assumed to have good robustness properties. As it was done for the trimmed k-means method, this article studies robustness properties of the TCLUST procedure in the univariate case with two clusters by means of the influence function. The conclusion is that the TCLUST has a robustness behavior close to that of the trimmed k-means in spite of the fact that it addresses a more general clustering approach.