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.
arXiv:2601.16427v3 Announce Type: replace-cross Abstract: We study exact community recovery in sparse directed stochastic block models using neighborhood smoothing of connection-probability profiles....
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
arXiv:2608.21466v1 Announce Type: new Abstract: We develop spectral algorithms for selecting state-space partitions that define averaging kernels for finite, ergodic and reversible Markov chains. For...
arXiv:2607. 24237v1 Announce Type: new Abstract: Many existing clustering methods are designed based on a set-oriented definition---a cluster is a set of similar points---relying a point-to-point similarity function to find similar points.
arXiv:2608. 06276v1 Announce Type: cross Abstract: Persistence diagrams (PDs) provide stable and interpretable summaries of multiscale topological structure.
The paper formalizes a geometric tradeoff between ambient separation and sampling gaps to determine when distinct manifold components can be reliably separated in clustering. It introduces a threshold phenomenon for mutual‑k‑nearest‑neighbor graphs, defining an uncertainty zone where the number of clusters cannot be identified. The authors propose Manifold‑Based Clustering (MBC), which outputs a bracket interval quantifying this uncertainty rather than forcing a single cluster count.
arXiv:2607. 24537v1 Announce Type: new Abstract: In the Big Data era, the scalability of clustering algorithms constitutes a key challenge.
arXiv:2607. 05469v1 Announce Type: cross Abstract: Unsupervised graph clustering is a fundamental technique for uncovering underlying semantic patterns in large-scale networks.
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.
arXiv:2602. 08542v3 Announce Type: replace-cross 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.
arXiv:2606. 28268v1 Announce Type: cross Abstract: Test-time adaptation (TTA) has emerged as a promising paradigm for mitigating distribution shifts in deep models.
arXiv:2607. 03329v1 Announce Type: new Abstract: Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks.