42 reputation
5
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location Hamburg, Germany
age 27
visits member for 2 years, 5 months
seen Sep 12 at 18:05

Nov
1
awarded  Teacher
Aug
27
accepted Calculating the coefficients of one form of bi-variate polynomial from its another form
Aug
27
comment Calculating the coefficients of one form of bi-variate polynomial from its another form
Thanks. It really helped.
Aug
27
revised Calculating the coefficients of one form of bi-variate polynomial from its another form
Improved the question, after realizing its triviality from the comments.
Aug
27
asked Calculating the coefficients of one form of bi-variate polynomial from its another form
Aug
24
awarded  Supporter
Aug
16
comment Minimization on the Lie Group SO(3)
Thanks, it's really comprehensive! But, the last part has caused another question: The matrix exponential should behave like: $exp: so(n) \rightarrow SO(n)$ assuming $\hat{.}: \mathbb{R}^n \rightarrow so(n)$ but that doesn't seem to be the case with the result in: $$ \exp(\hat{\mathbf a}) = \begin{bmatrix}\mathbf{I}_{n\times n} &\mathbf a\\\mathbf{O}_{1\times n}&1 \end{bmatrix}~.$$
Aug
16
accepted Minimization on the Lie Group SO(3)
Aug
10
comment Minimization on the Lie Group SO(3)
But, in the case of Euclidean vector spaces: $$F = f(\mathbf x)^\top f(\mathbf x)$$ For Gauss-Newton: $$ \mathtt J :=\left.\frac{\partial f}{\partial \mathbf x} \right|_{\mathbf x =\mathbf x^{(m)}} $$ This is the part of the confusion that when adapting this formulation for Lie Groups, why do the author restrict to calculate the derivative in the tangent space around the identity $\mathbf p =\mathbf 0$.
Aug
9
comment Minimization on the Lie Group SO(3)
I hope it is clearer now.
Aug
9
revised Minimization on the Lie Group SO(3)
added 7 characters in body
Aug
9
comment Minimization on the Lie Group SO(3)
I have rephrased the question.
Aug
9
revised Minimization on the Lie Group SO(3)
added 3 characters in body
Aug
9
comment Jacobian matrix of the Rodrigues' formula (exponential map)
There is a doubt: To optimize an objective function $\mathcal O(\mathtt R^{(m)})$: $$\mathcal O(\mathtt R^{(m+1)}) \approx \mathcal O(\mathtt R^{(m)}) + \mathbb g^\top\delta + \delta^\top \mathtt H \delta$$ The gradient $\mathbb g$ and Hessian $\mathtt H$ are calculated at the point corresponding to $\mathtt R^{(m)}$ which is initially $\mathbf p = \mathbf 0$. My question is as soon as we update $\mathtt R^{(m)}$, it longer corresponds to $\mathbf p = \mathbf 0$. So, we need to calculate gradient and Hessian at different $\mathbf p$ i.e. $\mathbf p^{(m+1)} = \delta + \mathbf p^{(m)}$
Aug
9
answered Jacobian matrix of the Rodrigues' formula (exponential map)
Aug
9
asked Minimization on the Lie Group SO(3)
Jul
23
awarded  Scholar
Jul
23
accepted Mahalanobis Distance using Eigen-Values of the Covariance Matrix
Jul
23
comment Mahalanobis Distance using Eigen-Values of the Covariance Matrix
This is exactly my question. Rephrased: In the cases where $\mathbf{S}$ is singular, does the simplified expression functionally represent the Mahalanobis distance?
Jul
23
revised Mahalanobis Distance using Eigen-Values of the Covariance Matrix
deleted 1170 characters in body