Scholarlink

<p>Recently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved significant success in processing point-cloud data and has emerged as a promising paradigm in data science. However, TDL has not been extended to differentiable-manifold data, including images, due to the challenges introduced by differential topology. We address this challenge by introducing a manifold topological deep learning (MTDL) framework. To apply Hodge theory, we integrate it into a streamlined convolutional neural network within the MTDL framework. In this framework, original images are represented as smooth manifolds with vector fields that are decomposed into three orthogonal components based on Hodge theory. These components are then concatenated to form an input image for the convolutional neural network architecture. The performance of MTDL is evaluated using the MedMNIST v2 benchmark database, which comprises 717,287 biomedical images from eleven 2D and six 3D datasets. MTDL significantly outperforms other competing methods, extending TDL to a wide range of data on smooth manifolds.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Manifold topological deep learning for biomedical data

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月1日

查看全文
  • Xiang Liu,
  • Zhe Su,
  • Yongyi Shi,
  • Yiying Tong,
  • Ge Wang,
  • Guo-Wei Wei

摘要

Recently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved significant success in processing point-cloud data and has emerged as a promising paradigm in data science. However, TDL has not been extended to differentiable-manifold data, including images, due to the challenges introduced by differential topology. We address this challenge by introducing a manifold topological deep learning (MTDL) framework. To apply Hodge theory, we integrate it into a streamlined convolutional neural network within the MTDL framework. In this framework, original images are represented as smooth manifolds with vector fields that are decomposed into three orthogonal components based on Hodge theory. These components are then concatenated to form an input image for the convolutional neural network architecture. The performance of MTDL is evaluated using the MedMNIST v2 benchmark database, which comprises 717,287 biomedical images from eleven 2D and six 3D datasets. MTDL significantly outperforms other competing methods, extending TDL to a wide range of data on smooth manifolds.