🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.001101s)
  1. Hyperparameter Optimization of Topological Features for Machine Learning Applications (2019)

    Francis Motta, Christopher Tralie, Rossella Bedini, Fabiano Bini, Gilberto Bini, Hamed Eramian, Marcio Gameiro, Steve Haase, Hugh Haddox, John Harer, Nick Leiby, Franco Marinozzi, Scott Novotney, Gabe Rocklin, Jed Singer, Devin Strickland, Matt Vaughn
    Abstract This paper describes a general pipeline for generating optimal vector representations of topological features of data for use with machine learning algorithms. This pipeline can be viewed as a costly black-box function defined over a complex configuration space, each point of which specifies both how features are generated and how predictive models are trained on those features. We propose using state-of-the-art Bayesian optimization algorithms to inform the choice of topological vectorization hyperparameters while simultaneously choosing learning model parameters. We demonstrate the need for and effectiveness of this pipeline using two difficult biological learning problems, and illustrate the nontrivial interactions between topological feature generation and learning model hyperparameters.
  2. Topological Eulerian Synthesis of Slow Motion Periodic Videos (2018)

    Christopher Tralie, Matthew Berger
    Abstract We consider the problem of taking a video that is comprised of multiple periods of repetitive motion, and reordering the frames of the video into a single period, producing a detailed, single cycle video of motion. This problem is challenging, as such videos often contain noise, drift due to camera motion and from cycle to cycle, and irrelevant background motion/occlusions, and these factors can confound the relevant periodic motion we seek in the video. To address these issues in a simple and eļ¬ƒcient manner, we introduce a tracking free Eulerian approach for synthesizing a single cycle of motion. Our approach is geometric: we treat each frame as a point in high-dimensional Euclidean space, and analyze the sliding window embedding formed by this sequence of points, which yields samples along a topological loop regardless of the type of periodic motion. We combine tools from topological data analysis and spectral geometric analysis to estimate the phase of each window, and we exploit the sliding window structure to robustly reorder frames. We show quantitative results that highlight the robustness of our technique to camera shake, noise, and occlusions, and qualitative results of single-cycle motion synthesis across a variety of scenarios.