using a line (one-dimensional hyperplane) that passes through the mean point ($92.026667$). Between the resulting two clusters, the one above the line has a greater SSE. In iteration $2$, this cluster is therefore split along the X axis at the mean point ($66.975000$). In the final iteration, the cluster with the greatest SSE, i.e., the bottom cluster, is split along the X axis at the mean point ($41.057143$). In Figure \[part\_d\], the centroids of the final four clusters are denoted by stars.

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Proposed Modification to Var-Part and PCA-Part {#sec_mod}
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Su and Dy [@Su07] demonstrated that, besides being computationally efficient, Var-Part and PCA-Part perform very well on a variety of data sets. Recall that in each iteration these methods select the cluster with the greatest SSE and then project the $D$-dimensional points in this cluster on a partitioning axis. The difference between the two methods is the choice of this axis. In Var-Part, the partitioning axis is the coordinate axis with the greatest variance, whereas in PCA-Part it is the major axis. After the projection operation, both methods use the *mean* point on the partitioning axis as a ‘threshold’ to divide the points between two clusters. In other words, 