Polynomial Regression on Riemannian Manifolds
Polynomial Regression on Riemannian Manifolds
Polynomial Regression on Riemannian Manifolds
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<str<strong>on</strong>g>Polynomial</str<strong>on</strong>g> <str<strong>on</strong>g>Regressi<strong>on</strong></str<strong>on</strong>g><br />
(∇ ˙γ ) k ˙γ = 0 becomes linearized system<br />
˙γ = v 1<br />
∇ ˙γ v i = v i+1 i = 1, . . . , k − 1<br />
∇ ˙γ v k = 0.<br />
Want to find initial c<strong>on</strong>diti<strong>on</strong>s for this ODE that minimize<br />
E(γ) =<br />
N∑<br />
g i (γ(t i ))<br />
i=1<br />
<str<strong>on</strong>g>Polynomial</str<strong>on</strong>g> <str<strong>on</strong>g>Regressi<strong>on</strong></str<strong>on</strong>g> <strong>on</strong> <strong>Riemannian</strong> <strong>Manifolds</strong> 8