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arXiv · 2212.00212

Simpler flag optimization

Zehua Lai·Lek-Heng Lim·Ke Ye
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Abstract

We study the geometry of flag manifolds under different embeddings into a product of Grassmannians. We show that differential geometric objects and operations -- tangent vector, metric, normal vector, exponential map, geodesic, parallel transport, gradient, Hessian, etc -- have closed-form analytic expressions that are computable with standard numerical linear algebra. Furthermore, we are able to derive a coordinate descent method in the flag manifold that performs well compared to other gradient descent methods.

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Zehua Lai, Lek-Heng Lim, Ke Ye. 2022-12-01. Simpler flag optimization. https://arxiv.org/abs/2212.00212

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