Tootfinder

Clustering in Varying Metrics
Deeparnab Chakrabarty, Jonathan Conroy, Ankita Sarkar
https://arxiv.org/abs/2510.07860 https://arxiv.org/pdf/2510.07860

Clustering in Varying Metrics
We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the clustering costs -- e.g., the average or maximum -- where the cost is measured via $k$-center/median/means objectives. More generally, we minimize a norm $Ψ$ over the $T$ cost values. We show that for $T \geq 3$, the problem is inapproximable to any finite facto…

Kernel K-means clustering of distributional data
Amparo Ba\'illo, Jose R. Berrendero, Mart\'in S\'anchez-Signorini
https://arxiv.org/abs/2509.18037 https://

Kernel K-means clustering of distributional data
We consider the problem of clustering a sample of probability distributions from a random distribution on $\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing kernel Hilbert space (RKHS) $\mathcal H$. By mapping each distribution to its corresponding kernel mean embedding in $\mathcal H$, we obtain a sample in this RKHS where we carry out the $K$-means clustering procedure, which provides an unsupervised classifica…

Characterizing failure morphologies in fiber-reinforced composites via k-means clustering based multiscale framework
Harpreet Singh
https://arxiv.org/abs/2509.20011 https://

Characterizing failure morphologies in fiber-reinforced composites via k-means clustering based multiscale framework
A novel homogenization methodology is proposed for analyzing the failure of fiber-reinforced composite materials, utilizing elastic and eigen influence tensors within a damage informed transformation field analysis (D-TFA) framework. This approach includes a technique for calculating macroscopic damage under uniform stress and strain conditions, offering more realistic simulations. Computational efficiency is enhanced through a reduced-order modeling strategy, while elastic and eigen strain dis…

Hybrid Quantum-Classical Optimisation of Traveling Salesperson Problem
Christos Lytrosyngounis, Ioannis Lytrosyngounis
https://arxiv.org/abs/2509.26229 https://

Hybrid Quantum-Classical Optimisation of Traveling Salesperson Problem
The Traveling Salesperson Problem (TSP), a quintessential NP-hard combinatorial optimisation challenge, is vital for logistics and network design but limited by exponential complexity in large instances. We propose a hybrid quantum-classical framework integrating variational quantum eigensolver (VQE) optimisation with classical machine learning, using K-means clustering for problem decomposition and a RandomForestRegressor for path refinement. Evaluated on 80 European cities (from 4 to 80 citie…

Geographic Characterisation of Children's Health and Wellbeing through Vulnerability Indices Using Principal Component Analysis (PCA) and K-Means Clustering
Harriette Phillips, Aiden Price, Kerrie Mengersen
https://arxiv.org/abs/2509.14236

Geographic Characterisation of Children's Health and Wellbeing through Vulnerability Indices Using Principal Component Analysis (PCA) and K-Means Clustering
Using Australian children as a case study, this paper aims to develop vulnerability indices to characterise the health and well-being of children aged 0-5 years old. The indices are used to identify differences in children's health and well-being across geographic regions and identify clusters of regions with similar characteristics. The approach is underpinned by two well-known statistical methods, namely Principal Component Analysis and K-Means Clustering. The identification of these regions …

Model-free algorithms for fast node clustering in SBM type graphs and application to social role inference in animals
Bertrand Cloez, Adrien Cotil, Jean-Baptiste Menassol, Nicolas Verzelen
https://arxiv.org/abs/2509.15989

Model-free algorithms for fast node clustering in SBM type graphs and application to social role inference in animals
We propose a novel family of model-free algorithms for node clustering and parameter inference in graphs generated from the Stochastic Block Model (SBM), a fundamental framework in community detection. Drawing inspiration from the Lloyd algorithm for the $k$-means problem, our approach extends to SBMs with general edge weight distributions. We establish the consistency of our estimator under a natural identifiability condition. Through extensive numerical experiments, we benchmark our methods a…

Sublinear Time Quantum Sensitivity Sampling
Zhao Song, David P. Woodruff, Lichen Zhang
https://arxiv.org/abs/2509.16801 https://arxiv.org/pdf/2509.16801

Sublinear Time Quantum Sensitivity Sampling
We present a unified framework for quantum sensitivity sampling, extending the advantages of quantum computing to a broad class of classical approximation problems. Our unified framework provides a streamlined approach for constructing coresets and offers significant runtime improvements in applications such as clustering, regression, and low-rank approximation. Our contributions include: * $k$-median and $k$-means clustering: For $n$ points in $d$-dimensional Euclidean space, we give an algo…