🍩 Database of Original & Non-Theoretical Uses of Topology

(found 3 matches in 0.000959s)
  1. A Machine-Learning-Based Early Warning System Boosted by Topological Data Analysis (2019)

    Devraj Basu, Tieqiang Li
    Abstract We propose a novel early warning system for detecting financial market crashes that utilizes the information extracted from the shape of financial market movement. Our system incorporates Topological Data Analysis (TDA), a new set of data analytics techniques specialised in profiling the shape of data, into a more traditional machine learning framework. Incorporating TDA leads to substantial improvements in timely detecting the onset of a sharp market decline. Our framework is both able to generate new features and also unlock more value from existing factors. Our results illustrate the importance of understanding the shape of financial market data and suggest that incorporating TDA into a machine learning framework could be beneficial in a number of financial market settings.
  2. Using Persistent Homology and Dynamical Distances to Analyze Protein Binding (2016)

    Violeta Kovacev-Nikolic, Peter Bubenik, Dragan Nikolić, Giseon Heo
    Abstract Persistent homology captures the evolution of topological features of a model as a parameter changes. The most commonly used summary statistics of persistent homology are the barcode and the persistence diagram. Another summary statistic, the persistence landscape, was recently introduced by Bubenik. It is a functional summary, so it is easy to calculate sample means and variances, and it is straightforward to construct various test statistics. Implementing a permutation test we detect conformational changes between closed and open forms of the maltose-binding protein, a large biomolecule consisting of 370 amino acid residues. Furthermore, persistence landscapes can be applied to machine learning methods. A hyperplane from a support vector machine shows the clear separation between the closed and open proteins conformations. Moreover, because our approach captures dynamical properties of the protein our results may help in identifying residues susceptible to ligand binding; we show that the majority of active site residues and allosteric pathway residues are located in the vicinity of the most persistent loop in the corresponding filtered Vietoris-Rips complex. This finding was not observed in the classical anisotropic network model.