Description Usage Arguments Details Value Author(s) References See Also Examples
Finds \mathrm{argmin}_{(p,V)\in M\times (T_pM) ^ n}∑_{i=1} ^ {N} ρ(d(\mathrm{Exp}(p,Vx_i),y_i)) through a gradient descent algorithm.
1 2 3 4 5 6 7 8 9 10 |
manifold |
Type of manifold ( |
x |
A vector, matrix, or data frame of independent variables; for matrices and data frames, the rows and columns represent the subjects and independent variables, respectively. |
y |
A matrix or data frame whose columns represent points on the manifold. |
estimator |
M-type estimator ( |
c |
Multiplier of σ, the square root of the variance, used in
the cutoff parameter for the |
p_tol |
Termination condition for the distance between consecutive
updates of |
V_tol |
Termination condition for the distance between columns of
consecutive updates of |
max_iter |
Maximum number of gradient descent steps before ending the algorithm. |
Each column of x
should be centered to have an average of 0 for the
quickest and most accurate results. If all of the elements of a column of
x
are equal, the resulting vector will consist of NA
s. In the
case of the 'sphere'
, an error will be raised if all points are on a
pair of antipodes.
A named list containing
p |
a vector representing the estimate of the initial point on the manifold |
V |
a matrix representing the estimate of the initial velocities for each independent variable; the columns represent the independent variables. |
iteration |
number of gradient descent steps taken. |
Ha-Young Shin
Fletcher, P. T. (2013). Geodesic regression and the theory of least squares on Riemannian manifolds. International Journal of Computer Vision, 105, 171-185.
Kim, H. J., Adluru, N., Collins, M. D., Chung, M. K., Bendin, B. B., Johnson, S. C., Davidson, R. J. and Singh, V. (2014). Multivariate general linear models (MGLM) on Riemannian manifolds with applications to statistical analysis of diffusion weighted images. 2014 IEEE Conference on Computer Vision and Pattern Recognition, 2705-2712.
Shin, H.-Y. and Oh H.-S. (2020). Robust Geodesic Regression. <arXiv:2007.04518>
1 2 3 4 5 6 7 8 9 10 11 | # an example of multiple regression with two independent variables, with 64
# data points
x <- matrix(runif(2 * 64), ncol = 2)
x <- t(t(x) - colMeans(x))
y <- matrix(0L, nrow = 4, ncol = 64)
for (i in 1:64) {
y[, i] <- exp_map('sphere', c(1, 0, 0, 0), c(0, runif(1), runif(1),
runif(1)))
}
geo_reg('sphere', x, y, 'tukey', c = are_nr('tukey', 2, 6))
|
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