  As the size $n$ of datasets become massive, many commonly-used clustering
algorithms (for example, $k$-means or hierarchical agglomerative clustering
(HAC) require prohibitive computational cost and memory. In this paper, we
propose a solution to these clustering problems by extending threshold
clustering (TC) to problems of instance selection. TC is a recently developed
clustering algorithm designed to partition data into many small clusters in
linearithmic time (on average). Our proposed clustering method is as follows.
First, TC is performed and clusters are reduced into single "prototype" points.
Then, TC is applied repeatedly on these prototype points until sufficient data
reduction has been obtained. Finally, a more sophisticated clustering algorithm
is applied to the reduced prototype points, thereby obtaining a clustering on
all $n$ data points. This entire procedure for clustering is called iterative
hybridized threshold clustering (IHTC). Through simulation results and by
applying our methodology on several real datasets, we show that IHTC combined
with $k$-means or HAC substantially reduces the run time and memory usage of
the original clustering algorithms while still preserving their performance.
Additionally, IHTC helps prevent singular data points from being overfit by
clustering algorithms.
