Minimum volume covering ellipsoids

作者：E. Harris · 发表于：ANZIAM Journal · 年份：2024 · DOI：10.21914/anziamj.v64.17956

We present a new initialisation of an adaptive batch strategy to compute the ε-approximate minimum volume covering ellipsoid (MVCE) for a set of n points. We focus on moderately sized datasets (up to dimension d = 100 and n = 1 000 000). The adaptive batch strategy works in an optimisation-deletion-adaptation cycle: we solve the MVCE problem using a smaller number of points, we delete points from consideration that are guaranteed to not lie on the boundary of the MVCE, and then carefully select a new batch of points. We propose a new initialisation, which involves selecting the points corresponding to some highest leverage scores. We show using numerical examples that this new initialisation tends to improve computation time as well as reduce the total number of cycles, as compared with initialising with a random selection of points. References C. L. Atwood. Sequences converging to D-optimal designs of experiments. Ann. Statist. 1.2 (1973), pp. 342–352. doi: 10.1214/aos/1176342371 Y.-J. Chen, M.-Y. Ju, and K.-S. Hwang. A virtual torque-based approach to kinematic control of redundant manipulators. IEEE Trans. Indust. Elec. 64.2 (2017), pp. 1728–1736. doi: 10.1109/TIE.2016.2548439 F. L. Chernousko. Ellipsoidal state estimation for dynamical systems. Nonlin. Anal. 63.5-7 (2005), pp. 872–879. doi: 10.1016/j.na.2005.01.009 D. Eberly. 3D game engine design: A practical approach to real-time computer graphics. CRC Press, 2007. doi: 10.1201/b18212 M. Frank and P. Wolfe. An algorith...