Optimization algorithms exploiting unitary constraints

By Jonathan H. Manton. IEEE Transactions on Signal Processing, 2002

487 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/e0c27420a72a505f6de9554c4042a93d79ec022b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computational Theory and Mathematics

In Signal Processing

Citations in the corpus

Multi-Task Multi-View Clustering (2016, methodology): “We propose a co-clustering based multi-task multi-view clustering framework, which consists of three components: withinview-task clustering, multi-view relationship learning and multi-task relationship learning (Fig.”
Projection-like Retractions on Matrix Manifolds (2012, background): “1] and [27]) by certain approximations that reduce the computational burden per step without hurting the convergence properties of the iteration.”
Learning algorithms utilizing quasi-geodesic flows on the Stiefel manifold (2005, methodology): “One is because some authors argue the projection method outperforms the geodesic method in certain cases [20].”
Understanding symmetries in deep networks (2015, background): “On the other hand, optimization over a manifold with symmetries or invariances has been a topic of much research and provides guidance to other simpler metric constructions [8, 9, 10, 11, 12, 13, 14].”
Linear dimensionality reduction: survey, insights, and generalizations (2014, background): “n classic and straightforward results from dierential geometry. More recently, Edelman et al. (1998) sparked signicant interest in optimization over matrix manifolds. Some relevant examples include Manton (2002, 2004); Fiori (2005); Nishimori and Akaho (2005); Abrudan et al. (2008); Ulfarsson and So”
Multi-Task Multi-View Clustering for Non-Negative Data (2015, methodology): “Because of the unitary constraints, we further solve the optimization problem by mapping the variables to the Stiefel manifold [Manton, 2002].”
Lp-Nested Symmetric Distributions (2010, background): “We already proved the first induction step by computing equation (19).”
On-Manifold Preintegration for Real-Time Visual--Inertial Odometry (2015, methodology): “Moreover, it provides a grounded and unifying generalization of the error state model, commonly used in aerospace literature for filtering [49] and recently adopted in robotics for optimization [23, 34].”
Trust-Region Methods on Riemannian Manifolds (2007, methodology): “However, as pointed out by Manton [ Man02 , Section IX], the exponential may not be the most appropriate or computationally ecien t way of performing the update.”
Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Group (2019, methodology): “When it comes to the unitary case, the algorithms used in practice are similar to those used in the real case, cf. , (Manton, 2002; Abrudan et al., 2008).”
On the best low multilinear rank approximation of higher-order tensors (2010, background): “However, depending on the manifold, this choice may be computationally inefficient [ 55 ].”
Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform (2020, methodology): “onally expensive on the Stiefel manifold. Some methods use an efﬁcient pseudo-geodesic retraction instead of the exponential mapping. For example, Absil & Malick (2012); Gawlik & Leok (2018); Manton (2002) use a projection-based method to map the gradient back to the Stiefel manifold that re”