The paper investigates how adjusting the sharpness of t‑SNE’s affinity matrix influences neighborhood preservation across scales. By applying a row‑wise power transform parameterized by γ, the authors can smooth or sharpen each row while keeping sparsity and rank order intact, effectively rescaling the Gaussian bandwidth and altering local perplexities. Experiments show that sharpening enhances the retention of the very nearest neighbors, whereas smoothing improves the preservation of broader local neighborhoods, outperforming existing multiscale affinity methods in the mid‑local range.
By Shirin Mohebi, Guillaume Bied, Jefrey Lijffijt
The paper introduces T-ARC, a clustering algorithm that integrates topological information into the K‑means objective by coupling a data‑fidelity term with a graph‑cut penalty. The latent graph is modeled as a random realization from a Stochastic Block Model, whose parameter is optimized via Distributionally Robust Optimization, using a persistence‑based similarity matrix derived from zero‑dimensional persistent homology. Experiments on synthetic non‑convex data and Fashion‑MNIST subsets demonstrate that T‑ARC recovers latent topological structures and outperforms K‑means on curved and interleaved clusters while remaining competitive and more stable on real data.
By Serena Grazia De Benedictis, Andersen Ang, Nicoletta Del Buono, Flavia Esposito, Laura Selicato
arXiv:2607. 27000v1 Announce Type: cross Abstract: Optimization in non-convex neural network models is strongly influenced by the geometry of the solution space: sparse, isolated, point-like clusters are typically algorithmically inaccessible, whereas wide and flat regions can be found efficiently despite being relatively rare.
By Enrico M. Malatesta, Alessandra Passalacqua, Riccardo Zecchina
arXiv:2604. 18801v2 Announce Type: replace Abstract: Scientific particle simulations in cosmology, molecular dynamics, and fluid dynamics produce large-scale datasets whose storage, movement, and analysis increasingly rely on lossy compression.
By Congrong Ren, Sheng Di, Katrin Heitmann, Franck Cappello, Hanqi Guo
Gradient-Guided Density Peak Clustering (GGDPC) enhances traditional density peak clustering by performing a gradient ascent step before each nearest‑neighbor uphill search, aiming to stabilize uphill paths in low‑density regions. The authors develop a stability theory linking the GGDPC graph to the gradient ascent flow of the population density, and establish consistency across five criteria: recovery of local modes, adjusted Rand index, dendrogram (cluster tree), path length, and waterfall measure. These results offer new statistical, geometric, and topological insights into DPC‑type clustering algorithms.
By Yikun Zhang, Yen-Chi Chen
arXiv:2401. 10927v3 Announce Type: replace-cross Abstract: In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions in $\mathbb{R}^p$.
By Shuheng Zhou