  BIRCH clustering is a widely known approach for clustering, that has
influenced much subsequent research and commercial products. The key
contribution of BIRCH is the Clustering Feature tree (CF-Tree), which is a
compressed representation of the input data. As new data arrives, the tree is
eventually rebuilt to increase the compression. Afterward, the leaves of the
tree are used for clustering. Because of the data compression, this method is
very scalable. The idea has been adopted for example for k-means, data stream,
and density-based clustering.
  Clustering features used by BIRCH are simple summary statistics that can
easily be updated with new data: the number of points, the linear sums, and the
sum of squared values. Unfortunately, how the sum of squares is then used in
BIRCH is prone to catastrophic cancellation.
  We introduce a replacement cluster feature that does not have this numeric
problem, that is not much more expensive to maintain, and which makes many
computations simpler and hence more efficient. These cluster features can also
easily be used in other work derived from BIRCH, such as algorithms for
streaming data. In the experiments, we demonstrate the numerical problem and
compare the performance of the original algorithm compared to the improved
cluster features.
