Stochastic Approximation on Manifolds and Topological Data Analysis
Open Access DepositedWe study stochastic gradient descents on manifolds with deterministic, semi-adaptive and adaptive learning rates. To guarantee the convergence of the stochastic gradient descents, we establish convergence theorems on manifolds for retraction-based stochastic gradient descents admitting certain confinements. We then apply stochastic gradient descent algorithms to the weighted low-rank approximation problem and compare the performance of these algorithms. We also study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field, which are used in topological data analysis. Our method is based on a decomposition of the persistent homology. We demonstrate that, under fairly general assumptions, these two algebraic structures capture the same information from the filtered chain complex.
- All rights reserved
Notice to Authors
If you are the author of this work and you have any questions about the information on this page, please use the Contact form to get in touch with us.