Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams

• URL: http://arxiv.org/abs/2607.27126v1
• Date: Wed, 29 Jul 2026 16:52:45 GMT
• Title: Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams
• Abstract summary: Expected Persistence Diagram (EPD) has been developed to reduce the time cost by studying the topology of multiple subsets of a point cloud.<n>We study an alternative discretization based on Voronoi histograms, which trades smooth functional approximation for adaptive partition-based counting.
• Score: 8.430442259341715
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Persistence Diagram (PD) is known to capture point cloud topology effectively, but its computation has high time complexity. Expected Persistence Diagram (EPD) has been developed to reduce the time cost by studying the topology of multiple subsets of a point cloud and it serves as a distribution of topological features. Existing EPD vectorizations often rely on predefined point transformations, such as Gaussian or landscape functions. We study an alternative discretization based on Voronoi histograms, which trades smooth functional approximation for adaptive partition-based counting. We propose to use Voronoi Diagram-based histogram as the vectorization of EPD, without imposing an explicit smooth point transformation model. Under stated separation and normalization conditions, we establish stability bounds and characterize when the histogram representation preserves Wasserstein-scale variation. We demonstrate the effectiveness of our proposed representation on real-world datasets which have significant topological features for classification and dimensionality reduction tasks.

Related papers

• When Do Graph Foundation Models Transfer? A Data-Centric Theory [68.54337055801571]
  Graph foundation models (GFMs) aim to reuse a single backbone across diverse graph domains, yet their transfer is often uneven and can exhibit negative transfer.<n>We show that for both set-based and message-passing tokenizations, any Lipschitz backbone admits an explicit decomposition of cross-domain output shift.<n>A key ingredient is positional-encoding (PE) stability: we establish stability guarantees for spectral PEs and highlight contrasting behaviors of eigenvector- versus subspace-based PEs.
  arXiv  Detail & Related papers  (2026-05-28T12:07:27Z)
• Bridging Graph Drawing and Dimensionality Reduction with Stochastic Stress Optimization [0.22940141855172028]
  Dimensionality Reduction (DR) and Graph Drawing (GD) aim to visualize abstract, non-linear structures, yet rely on different optimization paradigms.<n>We bridge these domains by adapting Gradient Descent (SGD) techniques from graph drawing to vector data embedding.
  arXiv  Detail & Related papers  (2026-05-01T13:22:56Z)
• Forecasting as Rendering: A 2D Gaussian Splatting Framework for Time Series Forecasting [79.37674445572462]
  Time series forecasting (TSF) remains a challenging problem due to the intricate entanglement of intraperiod-fluctuations and interperiod-trends.<n>Treating reshaped tensors as static images results in a topological mismatch.<n> relying on uniform fixed-size representations allocates modeling capacity inefficiently.<n>TimeGS is a novel framework that fundamentally shifts the forecasting paradigm from regression to 2D generative rendering.
  arXiv  Detail & Related papers  (2026-02-10T14:13:36Z)
• ReDiSC: A Reparameterized Masked Diffusion Model for Scalable Node Classification with Structured Predictions [64.17845687013434]
  We propose ReDiSC, a structured diffusion model for structured node classification.<n>We show that ReDiSC achieves superior or highly competitive performance compared to state-of-the-art GNN, label propagation, and diffusion-based baselines.<n> Notably, ReDiSC scales effectively to large-scale datasets on which previous structured diffusion methods fail due to computational constraints.
  arXiv  Detail & Related papers  (2025-07-19T04:46:53Z)
• IMPaCT GNN: Imposing invariance with Message Passing in Chronological split Temporal Graphs [8.861995276194435]
  This paper addresses domain adaptation challenges in graph data resulting from chronological splits. We propose IMPaCT, a method that imposes invariant properties based on realistic assumptions derived from temporal graph structures. We show that IMPaCT achieves a 3.8% performance improvement over current SOTA method on the ogbn-mag graph dataset.
  arXiv  Detail & Related papers  (2024-11-17T04:23:25Z)
• Diffeomorphic interpolation for efficient persistence-based topological optimization [3.7550827441501844]
  Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. We show that our approach combines efficiently with subsampling techniques, as the diffeomorphism derived from the gradient computed on a subsample can be used to update the coordinates of the full input object. We also showcase the relevance of our approach for black-box autoencoder (AE) regularization, where we aim at enforcing topological priors on the latent spaces associated to fixed, pre-trained, blackbox AE models.
  arXiv  Detail & Related papers  (2024-05-29T07:00:28Z)
• A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics [51.147876395589925]
  A non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time. A fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance.
  arXiv  Detail & Related papers  (2024-02-26T04:39:01Z)
• Deep Manifold Graph Auto-Encoder for Attributed Graph Embedding [51.75091298017941]
  This paper proposes a novel Deep Manifold (Variational) Graph Auto-Encoder (DMVGAE/DMGAE) for attributed graph data. The proposed method surpasses state-of-the-art baseline algorithms by a significant margin on different downstream tasks across popular datasets.
  arXiv  Detail & Related papers  (2024-01-12T17:57:07Z)
• Sparse Training of Discrete Diffusion Models for Graph Generation [45.103518022696996]
  We introduce SparseDiff, a novel diffusion model based on the observation that almost all large graphs are sparse. By selecting a subset of edges, SparseDiff effectively leverages sparse graph representations both during the noising process and within the denoising network. Our model demonstrates state-of-the-art performance across multiple metrics on both small and large datasets.
  arXiv  Detail & Related papers  (2023-11-03T16:50:26Z)
• A fast topological approach for predicting anomalies in time-varying graphs [0.0]
  A persistence diagram (PD) from topological data analysis (TDA) has become a popular descriptor of shape of data with a well-defined distance between points. This paper introduces a computationally efficient framework to extract shape information from graph data. In a real data application, our approach provides up to 22% gain in anomalous price prediction for the cryptocurrency transaction networks.
  arXiv  Detail & Related papers  (2023-05-11T01:54:45Z)
• Articulated Shape Matching Using Laplacian Eigenfunctions and Unsupervised Point Registration [38.16866987817019]
  Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match shapes by aligning their embeddings. We derive a new formulation that finds the best alignment between two congruent $K$-dimensional sets of points by selecting the best subset of eigenfunctions of the Laplacian matrix.
  arXiv  Detail & Related papers  (2020-12-14T08:49:25Z)
• Block-Approximated Exponential Random Graphs [77.4792558024487]
  An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. We propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions. Our methods are scalable to sparse graphs consisting of millions of nodes.
  arXiv  Detail & Related papers  (2020-02-14T11:42:16Z)
• Supervised Learning for Non-Sequential Data: A Canonical Polyadic Decomposition Approach [85.12934750565971]
  Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks. To alleviate this issue, it has been proposed to implicitly represent the model parameters as a tensor. For enhanced expressiveness, we generalize the framework to allow feature mapping to arbitrarily high-dimensional feature vectors.
  arXiv  Detail & Related papers  (2020-01-27T22:38:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.