Persistent Homology for Structural Characterization in Disordered Systems

• URL: http://arxiv.org/abs/2411.14390v3
• Date: Thu, 09 Jan 2025 00:17:04 GMT
• Title: Persistent Homology for Structural Characterization in Disordered Systems
• Authors: An Wang, Li Zou,
• Abstract summary: We propose a unified framework based on persistent homology (PH) to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data structure. It has shown to be highly effective and interpretable in predicting particle rearrangements and classifying global phases.
• Score: 3.3033726268021315
• License:
• Abstract: We propose a unified framework based on persistent homology (PH) to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data structure, and has shown to be highly effective and interpretable in predicting particle rearrangements and classifying global phases. We also demonstrated that using a single variable enables a linear SVM to achieve nearly perfect three-phase classification. Inspired by this discovery, we define a non-parametric metric, the Separation Index (SI), which not only achieves this classification without sacrificing significant performance but also establishes a connection between particle environments and the global phase structure. Our methods provide an effective framework for understanding and analyzing the properties of disordered materials, with broad potential applications in materials science and even wider studies of complex systems.

Related papers

• Unraveling the Localized Latents: Learning Stratified Manifold Structures in LLM Embedding Space with Sparse Mixture-of-Experts [3.9426000822656224]
  We conjecture that in large language models, the embeddings live in a local manifold structure with different dimensions depending on the perplexities and domains of the input data. By incorporating an attention-based soft-gating network, we verify that our model learns specialized sub-manifolds for an ensemble of input data sources.
  arXiv  Detail & Related papers  (2025-02-19T09:33:16Z)
• Scalable manifold learning by uniform landmark sampling and constrained locally linear embedding [0.6144680854063939]
  We propose a scalable manifold learning (scML) method that can manipulate large-scale and high-dimensional data in an efficient manner. We empirically validated the effectiveness of scML on synthetic datasets and real-world benchmarks of different types. scML scales well with increasing data sizes and embedding dimensions, and exhibits promising performance in preserving the global structure.
  arXiv  Detail & Related papers  (2024-01-02T08:43:06Z)
• Efficient Multi-View Graph Clustering with Local and Global Structure Preservation [59.49018175496533]
  We propose a novel anchor-based multi-view graph clustering framework termed Efficient Multi-View Graph Clustering with Local and Global Structure Preservation (EMVGC-LG) Specifically, EMVGC-LG jointly optimize anchor construction and graph learning to enhance the clustering quality. In addition, EMVGC-LG inherits the linear complexity of existing AMVGC methods respecting the sample number.
  arXiv  Detail & Related papers  (2023-08-31T12:12:30Z)
• Exploring The Potential Of GANs In Biological Sequence Analysis [0.966840768820136]
  We propose a novel approach to handle the data imbalance issue based on Generative Adversarial Networks (GANs) GANs are utilized to generate synthetic data that closely resembles the real one. We perform 3 distinct classification tasks by using 3 different sequence datasets.
  arXiv  Detail & Related papers  (2023-03-04T13:46:45Z)
• Feature construction using explanations of individual predictions [0.0]
  We propose a novel approach for reducing the search space based on aggregation of instance-based explanations of predictive models. We empirically show that reducing the search to these groups significantly reduces the time of feature construction. We show significant improvements in classification accuracy for several classifiers and demonstrate the feasibility of the proposed feature construction even for large datasets.
  arXiv  Detail & Related papers  (2023-01-23T18:59:01Z)
• Scalable Intervention Target Estimation in Linear Models [52.60799340056917]
  Current approaches to causal structure learning either work with known intervention targets or use hypothesis testing to discover the unknown intervention targets. This paper proposes a scalable and efficient algorithm that consistently identifies all intervention targets. The proposed algorithm can be used to also update a given observational Markov equivalence class into the interventional Markov equivalence class.
  arXiv  Detail & Related papers  (2021-11-15T03:16:56Z)
• Structure-Aware Feature Generation for Zero-Shot Learning [108.76968151682621]
  We introduce a novel structure-aware feature generation scheme, termed as SA-GAN, to account for the topological structure in learning both the latent space and the generative networks. Our method significantly enhances the generalization capability on unseen-classes and consequently improve the classification performance.
  arXiv  Detail & Related papers  (2021-08-16T11:52:08Z)
• Spatio-Temporal Representation Factorization for Video-based Person Re-Identification [55.01276167336187]
  We propose Spatio-Temporal Representation Factorization module (STRF) for re-ID. STRF is a flexible new computational unit that can be used in conjunction with most existing 3D convolutional neural network architectures for re-ID. We empirically show that STRF improves performance of various existing baseline architectures while demonstrating new state-of-the-art results.
  arXiv  Detail & Related papers  (2021-07-25T19:29:37Z)
• Unveiling the Potential of Structure-Preserving for Weakly Supervised Object Localization [71.79436685992128]
  We propose a two-stage approach, termed structure-preserving activation (SPA), towards fully leveraging the structure information incorporated in convolutional features for WSOL. In the first stage, a restricted activation module (RAM) is designed to alleviate the structure-missing issue caused by the classification network. In the second stage, we propose a post-process approach, termed self-correlation map generating (SCG) module to obtain structure-preserving localization maps.
  arXiv  Detail & Related papers  (2021-03-08T03:04:14Z)
• Joint Characterization of Multiscale Information in High Dimensional Data [0.0]
  We propose a multiscale joint characterization approach designed to exploit synergies between global and local approaches to dimensionality reduction. We show that joint characterization is capable of detecting and isolating signals which are not evident from either PCA or t-sne alone.
  arXiv  Detail & Related papers  (2021-02-18T23:33:00Z)
• Towards Uncovering the Intrinsic Data Structures for Unsupervised Domain Adaptation using Structurally Regularized Deep Clustering [119.88565565454378]
  Unsupervised domain adaptation (UDA) is to learn classification models that make predictions for unlabeled data on a target domain. We propose a hybrid model of Structurally Regularized Deep Clustering, which integrates the regularized discriminative clustering of target data with a generative one. Our proposed H-SRDC outperforms all the existing methods under both the inductive and transductive settings.
  arXiv  Detail & Related papers  (2020-12-08T08:52:00Z)

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.