🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.001607s)

  1. Position: Topological Deep Learning Is the New Frontier for Relational Learning (2024)

    Theodore Papamarkou, Tolga Birdal, Michael M. Bronstein, Gunnar E. Carlsson, Justin Curry, Yue Gao, Mustafa Hajij, Roland Kwitt, Pietro Lio, Paolo Di Lorenzo, Vasileios Maroulas, Nina Miolane, Farzana Nasrin, Karthikeyan Natesan Ramamurthy, Bastian Rieck, Simone Scardapane, Michael T. Schaub, Petar Veličković, Bei Wang, Yusu Wang, Guowei Wei, Ghada Zamzmi
    Abstract Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

  2. PI-Net: A Deep Learning Approach to Extract Topological Persistence Images (2020)

    Anirudh Som, Hongjun Choi, Karthikeyan Natesan Ramamurthy, Matthew Buman, Pavan Turaga
    Abstract Topological features such as persistence diagrams and their functional approximations like persistence images (PIs) have been showing substantial promise for machine learning and computer vision applications. This is greatly attributed to the robustness topological representations provide against different types of physical nuisance variables seen in real-world data, such as view-point, illumination, and more. However, key bottlenecks to their large scale adoption are computational expenditure and difficulty incorporating them in a differentiable architecture. We take an important step in this paper to mitigate these bottlenecks by proposing a novel one-step approach to generate PIs directly from the input data. We design two separate convolutional neural network architectures, one designed to take in multi-variate time series signals as input and another that accepts multi-channel images as input. We call these networks Signal PI-Net and Image PINet respectively. To the best of our knowledge, we are the first to propose the use of deep learning for computing topological features directly from data. We explore the use of the proposed PI-Net architectures on two applications: human activity recognition using tri-axial accelerometer sensor data and image classification. We demonstrate the ease of fusion of PIs in supervised deep learning architectures and speed up of several orders of magnitude for extracting PIs from data. Our code is available at https://github.com/anirudhsom/PI-Net.