To analyse very high dimensional data, or large data volumes, we study random projection. Since hierarchically clustered data can be scaled in one dimension, seriation or unidimensional scaling is our primary objective. Having determined a unidimensional scaling of the multidimensional data cloud, this is followed by clustering. In many past case studies we carried out such clustering, using the Baire, or longest common prefix, metric and, simultaneously, ultrametric. In this paper, we examine properties of the seriation, and of the induction of the clustering on the data summarization, through seriation. Simulations are described as well as a small, illustrative example using Fisher’s iris data.