Techniques are described for performing cluster analysis on a set of data points using tri-point arbitration. In one embodiment, a first cluster that includes a set of data points is generated within volatile and/or non-volatile storage of a computing device. A set of tri-point arbitration similarity values are computed where each similarity value in the set of similarity values corresponds to a respective data point pair and is computed based, at least in part, on a distance between the respective data point pair and a set of one or more arbiter data points. The first cluster is partitioned within volatile and/or non-volatile storage of the computing device into a set of two or more clusters. A determination is made, based at least in part on the set of similarity values in the tri-arbitration similarity matrix, whether to continue partitioning the set of data points.