Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature and Torsion estimation of 3D functional data: A geometric
  approach to build the mean shape under the Frenet Serret framework   The analysis of curves has been routinely dealt with using tools from
functional data analysis. However its extension to multi-dimensional curves
poses a new challenge due to its inherent geometric features that are difficult
to capture with the classical approaches that rely on linear approximations. We
develop an alternative characterization of a mean that reflects shape variation
of the curves. Based on a geometric representation of the curves through the
Frenet-Serret ordinary differential equations, we introduce a new definition of
mean curvature and mean torsion, as well as mean shape through the notion of
mean vector field. This new formulation of the mean for multi-dimensional
curves allows us to integrate the parameters for the shape features into the
unified functional data modelling framework. We formulate the estimation
problem of the functional parameters in a penalized regression and develop an
efficient algorithm. We demonstrate our approach with both simulated data and
real data examples.

18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga