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Incremental (k, z)-Clustering on Graphs
Emilio Cruciani, Sebastian Forster, Antonis Skarlatos
https://arxiv.org/abs/2602.08542 https://arxiv.org/pdf/2602.08542 https://arxiv.org/html/2602.08542
arXiv:2602.08542v1 Announce Type: new
Abstract: Given a weighted undirected graph, a number of clusters $k$, and an exponent $z$, the goal in the $(k, z)$-clustering problem on graphs is to select $k$ vertices as centers that minimize the sum of the distances raised to the power $z$ of each vertex to its closest center. In the dynamic setting, the graph is subject to adversarial edge updates, and the goal is to maintain explicitly an exact $(k, z)$-clustering solution in the induced shortest-path metric.
While efficient dynamic $k$-center approximation algorithms on graphs exist [Cruciani et al. SODA 2024], to the best of our knowledge, no prior work provides similar results for the dynamic $(k,z)$-clustering problem. As the main result of this paper, we develop a randomized incremental $(k, z)$-clustering algorithm that maintains with high probability a constant-factor approximation in a graph undergoing edge insertions with a total update time of $\tilde O(k m^{1 o(1)} k^{1 \frac{1}{\lambda}} m)$, where $\lambda \geq 1$ is an arbitrary fixed constant. Our incremental algorithm consists of two stages. In the first stage, we maintain a constant-factor bicriteria approximate solution of size $\tilde{O}(k)$ with a total update time of $m^{1 o(1)}$ over all adversarial edge insertions. This first stage is an intricate adaptation of the bicriteria approximation algorithm by Mettu and Plaxton [Machine Learning 2004] to incremental graphs. One of our key technical results is that the radii in their algorithm can be assumed to be non-decreasing while the approximation ratio remains constant, a property that may be of independent interest.
In the second stage, we maintain a constant-factor approximate $(k,z)$-clustering solution on a dynamic weighted instance induced by the bicriteria approximate solution. For this subproblem, we employ a dynamic spanner algorithm together with a static $(k,z)$-clustering algorithm.
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You Only Train Once: Differentiable Subset Selection for Omics Data
Daphn\'e Chopard, Jorge da Silva Gon\c{c}alves, Irene Cannistraci, Thomas M. Sutter, Julia E. Vogt
https://arxiv.org/abs/2512.17678 https://arxiv.org/pdf/2512.17678 https://arxiv.org/html/2512.17678
arXiv:2512.17678v1 Announce Type: new
Abstract: Selecting compact and informative gene subsets from single-cell transcriptomic data is essential for biomarker discovery, improving interpretability, and cost-effective profiling. However, most existing feature selection approaches either operate as multi-stage pipelines or rely on post hoc feature attribution, making selection and prediction weakly coupled. In this work, we present YOTO (you only train once), an end-to-end framework that jointly identifies discrete gene subsets and performs prediction within a single differentiable architecture. In our model, the prediction task directly guides which genes are selected, while the learned subsets, in turn, shape the predictive representation. This closed feedback loop enables the model to iteratively refine both what it selects and how it predicts during training. Unlike existing approaches, YOTO enforces sparsity so that only the selected genes contribute to inference, eliminating the need to train additional downstream classifiers. Through a multi-task learning design, the model learns shared representations across related objectives, allowing partially labeled datasets to inform one another, and discovering gene subsets that generalize across tasks without additional training steps. We evaluate YOTO on two representative single-cell RNA-seq datasets, showing that it consistently outperforms state-of-the-art baselines. These results demonstrate that sparse, end-to-end, multi-task gene subset selection improves predictive performance and yields compact and meaningful gene subsets, advancing biomarker discovery and single-cell analysis.
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