Cycle Registration in Persistent Homology with Applications in Topological Bootstrap

• URL: http://arxiv.org/abs/2101.00698v1
• Date: Sun, 3 Jan 2021 20:12:00 GMT
• Title: Cycle Registration in Persistent Homology with Applications in Topological Bootstrap
• Authors: Yohai Reani, Omer Bobrowski
• Abstract summary: We propose a novel approach for comparing the persistent homology representations of two spaces (filtrations) We do so by defining a correspondence relation between individual persistent cycles of two different spaces. Our matching of cycles is based on both the persistence intervals and the spatial placement of each feature.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this article we propose a novel approach for comparing the persistent homology representations of two spaces (filtrations). Commonly used methods are based on numerical summaries such as persistence diagrams and persistence landscapes, along with suitable metrics (e.g. Wasserstein). These summaries are useful for computational purposes, but they are merely a marginal of the actual topological information that persistent homology can provide. Instead, our approach compares between two topological representations directly in the data space. We do so by defining a correspondence relation between individual persistent cycles of two different spaces, and devising a method for computing this correspondence. Our matching of cycles is based on both the persistence intervals and the spatial placement of each feature. We demonstrate our new framework in the context of topological inference, where we use statistical bootstrap methods in order to differentiate between real features and noise in point cloud data.

Related papers

• Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averaging [3.8623569699070353]
  Trajectory inference deals with the challenge of reconstructing continuous processes from such observations. We propose methods for B-spline approximation of point clouds through consecutive averaging that is instrinsic to the Wasserstein space. We rigorously evaluate our method by providing convergence guarantees and testing it on simulated cell data.
  arXiv  Detail & Related papers  (2024-05-30T04:19:20Z)
• From Charts to Atlas: Merging Latent Spaces into One [15.47502439734611]
  Models trained on semantically related datasets and tasks exhibit comparable inter-sample relations within their latent spaces. We introduce Relative Latent Space Aggregation, a two-step approach that first renders the spaces comparable using relative representations, and then aggregates them via a simple mean. We compare the aggregated space with that derived from an end-to-end model trained over all tasks and show that the two spaces are similar.
  arXiv  Detail & Related papers  (2023-11-11T11:51:41Z)
• Stochastic interpolants with data-dependent couplings [31.854717378556334]
  We use the framework of interpolants to formalize how to itcouple the base and the target densities. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting.
  arXiv  Detail & Related papers  (2023-10-05T17:46:31Z)
• Concrete Score Matching: Generalized Score Matching for Discrete Data [109.12439278055213]
  "Concrete score" is a generalization of the (Stein) score for discrete settings. "Concrete Score Matching" is a framework to learn such scores from samples.
  arXiv  Detail & Related papers  (2022-11-02T00:41:37Z)
• On topological data analysis for SHM; an introduction to persistent homology [0.0]
  The main tool within topological data analysis is persistent homology. persistent homology is a representation of how the homological features of the data persist over an interval. These results allow for topological inference and the ability to deduce features in higher-dimensional data.
  arXiv  Detail & Related papers  (2022-09-12T12:02:39Z)
• Ontology Matching Through Absolute Orientation of Embedding Spaces [1.5169370091868053]
  Ontology is a core task when creating interoperable and linked open datasets. In this paper, we explore a structure-based mapping approach which is based on knowledge graph embeddings. We find in experiments with synthetic data, that the approach works very well on similarly structured datasets.
  arXiv  Detail & Related papers  (2022-04-08T12:59:31Z)
• Learning Conditional Invariance through Cycle Consistency [60.85059977904014]
  We propose a novel approach to identify meaningful and independent factors of variation in a dataset. Our method involves two separate latent subspaces for the target property and the remaining input information. We demonstrate on synthetic and molecular data that our approach identifies more meaningful factors which lead to sparser and more interpretable models.
  arXiv  Detail & Related papers  (2021-11-25T17:33:12Z)
• Temporally-Consistent Surface Reconstruction using Metrically-Consistent Atlases [131.50372468579067]
  We propose a method for unsupervised reconstruction of a temporally-consistent sequence of surfaces from a sequence of time-evolving point clouds. We represent the reconstructed surfaces as atlases computed by a neural network, which enables us to establish correspondences between frames. Our approach outperforms state-of-the-art ones on several challenging datasets.
  arXiv  Detail & Related papers  (2021-11-12T17:48:25Z)
• Modelling Neighbor Relation in Joint Space-Time Graph for Video Correspondence Learning [53.74240452117145]
  This paper presents a self-supervised method for learning reliable visual correspondence from unlabeled videos. We formulate the correspondence as finding paths in a joint space-time graph, where nodes are grid patches sampled from frames, and are linked by two types of edges. Our learned representation outperforms the state-of-the-art self-supervised methods on a variety of visual tasks.
  arXiv  Detail & Related papers  (2021-09-28T05:40:01Z)
• Image Synthesis via Semantic Composition [74.68191130898805]
  We present a novel approach to synthesize realistic images based on their semantic layouts. It hypothesizes that for objects with similar appearance, they share similar representation. Our method establishes dependencies between regions according to their appearance correlation, yielding both spatially variant and associated representations.
  arXiv  Detail & Related papers  (2021-09-15T02:26:07Z)
• Spatial Pyramid Based Graph Reasoning for Semantic Segmentation [67.47159595239798]
  We apply graph convolution into the semantic segmentation task and propose an improved Laplacian. The graph reasoning is directly performed in the original feature space organized as a spatial pyramid. We achieve comparable performance with advantages in computational and memory overhead.
  arXiv  Detail & Related papers  (2020-03-23T12:28:07Z)

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.