Finally, we develop an efficient implementation that translates these computational savings into actual wall-clock speedup.

In this paper, we initiate the study of Euclidean clustering with Distance-based privacy. Distance-based privacy is motivated by the fact that it is often only needed to protect the privacy of exact, rather than approximate, locations.

We show experimentally that the algorithm clarans of Ng and Han (1994) finds better K -medoids solutions than the V oronoi iteration algorithm of Hastie et al. (2001). This finding, along with the similarity between the V oronoi iteration algorithm and Lloyd's K -means algorithm, motivates us to use clarans as a K -means initializer. We show that clarans outperforms other algorithms on 23/23 datasets with a mean decrease over k-means-++ (Arthur and V assilvitskii, 2007) of 30% for initialization mean squared error (MSE) and 3% for final MSE. We introduce algorithmic improvements to clarans which improve its complexity and runtime, making it a viable initialization scheme for large datasets.

Finally, we develop an efficient implementation that translates these computational savings into actual wall-clock speedup.

In this paper, we initiate the study of Euclidean clustering with Distance-based privacy. Distance-based privacy is motivated by the fact that it is often only needed to protect the privacy of exact, rather than approximate, locations.

To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME) algorithm. By introducing ordinal distance to replace traditional Euclidean distances, we theoretically demonstrate that ordinal distance overcomes the constraints of the curse of dimensionality in high-dimensional spaces, effectively distinguishing heterogeneous samples. We design an adaptive neighborhood adjustment method to construct similarity graphs that simultaneously balance intra-cluster compactness and inter-cluster separability. Furthermore, we develop a two-stage embedding framework: the first stage achieves preliminary cluster separation while preserving connectivity between structurally similar clusters via the similarity graph, and the second stage enhances inter-cluster separation through a label-driven distance reweighting. Experimental results demonstrate that AMSME significantly preserves intra-cluster topological structures and improves inter-cluster separation on real-world datasets. Additionally, leveraging its multi-resolution analysis capability, AMSME discovers novel neuronal subtypes in the mouse lumbar dorsal root ganglion scRNA-seq dataset, with marker gene analysis revealing their distinct biological roles.

Monitoring forest dynamics at an individual tree scale is essential for accurately assessing ecosystem responses to climate change, yet traditional methods relying on field-based forest inventories are labor-intensive and limited in spatial coverage. Advances in remote sensing using drone-acquired RGB imagery combined with deep learning models have promised precise individual tree crown (ITC) segmentation; however, existing methods are frequently validated against human-annotated images, lacking rigorous independent ground truth. In this study, we generate high-fidelity validation labels from co-located Terrestrial Laser Scanning (TLS) data for drone imagery of mixed unmanaged boreal and Mediterranean forests. We evaluate the performance of two widely used deep learning ITC segmentation models - DeepForest (RetinaNet) and Detectree2 (Mask R-CNN) - on these data, and compare to performance on further Mediterranean forest data labelled manually. When validated against TLS-derived ground truth from Mediterranean forests, model performance decreased significantly compared to assessment based on hand-labelled from an ecologically similar site (AP50: 0.094 vs. 0.670). Restricting evaluation to only canopy trees shrank this gap considerably (Canopy AP50: 0.365), although performance was still far lower than on similar hand-labelled data. Models also performed poorly on boreal forest data (AP50: 0.142), although again increasing when evaluated on canopy trees only (Canopy AP50: 0.308). Both models showed very poor localisation accuracy at stricter IoU thresholds, even when restricted to canopy trees (Max AP75: 0.051). Similar results have been observed in studies using aerial LiDAR data, suggesting fundamental limitations in aerial-based segmentation approaches in closed canopy forests.