We introduce a fast and explainable clustering method called CLASSIX. It consists of two phases, namely a greedy aggregation phase of the sorted data into groups of nearby data points, followed by the merging of groups into clusters. The algorithm is controlled by two scalar parameters, namely a distance parameter for the aggregation and another parameter controlling the minimal cluster size. Extensive experiments are conducted to give a comprehensive evaluation of the clustering performance on synthetic and real-world datasets, with various cluster shapes and low to high feature dimensionality. Our experiments demonstrate that CLASSIX competes with state-of-the-art clustering algorithms. The algorithm has linear space complexity and achieves near linear time complexity on a wide range of problems. Its inherent simplicity allows for the generation of intuitive explanations of the computed clusters.

Quickshift is a popular algorithm for image segmentation, used as a preprocessing step in many applications. Unfortunately, it is quite challenging to understand the hyperparameters' influence on the number and shape of superpixels produced by the method. In this paper, we study theoretically a slightly modified version of the quickshift algorithm, with a particular emphasis on homogeneous image patches with i.i.d. pixel noise and sharp boundaries between such patches. Leveraging this analysis, we derive a simple heuristic to scale quickshift hyperparameters when dealing with real images, which we check empirically.

We provide initial seedings to the Quick Shift clustering algorithm, which approximate the locally high-density regions of the data. Such seedings act as more stable and expressive cluster-cores than the singleton modes found by Quick Shift. We establish statistical consistency guarantees for this modification. We then show strong clustering performance on real datasets as well as promising applications to image segmentation.