🍩 Database of Original & Non-Theoretical Uses of Topology

(found 4 matches in 0.001961s)

  1. A Topological Framework for Deep Learning (2020)

    Mustafa Hajij, Kyle Istvan
    Abstract We utilize classical facts from topology to show that the classification problem in machine learning is always solvable under very mild conditions. Furthermore, we show that a softmax classification network acts on an input topological space by a finite sequence of topological moves to achieve the classification task. Moreover, given a training dataset, we show how topological formalism can be used to suggest the appropriate architectural choices for neural networks designed to be trained as classifiers on the data. Finally, we show how the architecture of a neural network cannot be chosen independently from the shape of the underlying data. To demonstrate these results, we provide example datasets and show how they are acted upon by neural nets from this topological perspective.

  2. CCF-GNN: A Unified Model Aggregating Appearance, Microenvironment, and Topology for Pathology Image Classification (2023)

    Hongxiao Wang, Gang Huang, Zhuo Zhao, Liang Cheng, Anna Juncker-Jensen, Máté Levente Nagy, Xin Lu, Xiangliang Zhang, Danny Z. Chen
    Abstract Pathology images contain rich information of cell appearance, microenvironment, and topology features for cancer analysis and diagnosis. Among such features, topology becomes increasingly important in analysis for cancer immunotherapy. By analyzing geometric and hierarchically structured cell distribution topology, oncologists can identify densely-packed and cancer-relevant cell communities (CCs) for making decisions. Compared to commonly-used pixel-level Convolution Neural Network (CNN) features and cell-instance-level Graph Neural Network (GNN) features, CC topology features are at a higher level of granularity and geometry. However, topological features have not been well exploited by recent deep learning (DL) methods for pathology image classification due to lack of effective topological descriptors for cell distribution and gathering patterns. In this paper, inspired by clinical practice, we analyze and classify pathology images by comprehensively learning cell appearance, microenvironment, and topology in a fine-to-coarse manner. To describe and exploit topology, we design Cell Community Forest (CCF), a novel graph that represents the hierarchical formulation process of big-sparse CCs from small-dense CCs. Using CCF as a new geometric topological descriptor of tumor cells in pathology images, we propose CCF-GNN, a GNN model that successively aggregates heterogeneous features (e.g., appearance, microenvironment) from cell-instance-level, cell-community-level, into image-level for pathology image classification. Extensive cross-validation experiments show that our method significantly outperforms alternative methods on H&E-stained; immunofluorescence images for disease grading tasks with multiple cancer types. Our proposed CCF-GNN establishes a new topological data analysis (TDA) based method, which facilitates integrating multi-level heterogeneous features of point clouds (e.g., for cells) into a unified DL framework.

  3. Topologically Densified Distributions (2020)

    Christoph Hofer, Florian Graf, Marc Niethammer, Roland Kwitt
    Abstract We study regularization in the context of small sample-size learning with over-parametrized neural networks. Specifically, we shift focus from architectural properties, such as norms on the network weights, to properties of the internal representations before a linear classifier. Specifically, we impose a topological constraint on samples drawn from the probability measure induced in that space. This provably leads to mass concentration effects around the representations of training instances, i.e., a property beneficial for generalization. By leveraging previous work to impose topological constrains in a neural network setting, we provide empirical evidence (across various vision benchmarks) to support our claim for better generalization.

  4. Topology-Informed Machine Learning for Efficient Prediction of Solid Oxide Fuel Cell Electrode Polarization (2025)

    Maksym Szemer, Szymon Buchaniec, Tomasz Prokop, Grzegorz Brus
    Abstract Machine learning has emerged as a potent computational tool for expediting research and development in solid oxide fuel cell electrodes. The effective application of machine learning for performance prediction requires transforming electrode microstructure into a format compatible with artificial neural networks. Input data may range from a comprehensive digital material representation of the electrode to a selected set of microstructural parameters. The chosen representation significantly influences the performance and results of the network. Here, we show a novel approach utilizing persistence representation derived from computational topology. Using 500 microstructures and current–voltage characteristics obtained with three-dimensional first-principles simulations, we have prepared an artificial neural network model that can replicate current–voltage characteristics of unseen microstructures based on their persistent image representation. The artificial neural network can accurately predict the polarization curve of solid oxide fuel cell electrodes. The presented method incorporates complex microstructural information from the digital material representation while requiring substantially less computational resources (preprocessing and prediction time ≈1min) compared to our high-fidelity simulations (simulation time ≈1h) to obtain a single current-potential characteristic for one microstructure.

    Community Resources