In this paper we address the task of the comparison and the classification of
3D shape sequences of human. The non-linear dynamics of the human motion and
the changing of the surface parametrization over the time make this task very
challenging. To tackle this issue, we propose to embed the 3D shape sequences
in an infinite dimensional space, the space of varifolds, endowed with an inner
product that comes from a given positive definite kernel. More specifically,
our approach involves two steps: 1) the surfaces are represented as varifolds,
this representation induces metrics equivariant to rigid motions and invariant
to parametrization; 2) the sequences of 3D shapes are represented by Gram
matrices derived from their infinite dimensional Hankel matrices. The problem
of comparison of two 3D sequences of human is formulated as a comparison of two
Gram-Hankel matrices. Extensive experiments on CVSSP3D and Dyna datasets show
that our method is competitive with state-of-the-art in 3D human sequence
motion retrieval. Code for the experiments is available at
this https URL

本文提出了将 3D 形状序列嵌入到一个无限维度的 varifolds 空间，使用正定核获得内积，并通过 Gram-Hankel 矩阵比较来解决人类 3D 序列动作获取问题。

利用 Current 和 Varifolds 的人类 3D 形状序列比较和分类

3D Shape Sequence of Human Comparison and Classification using Current  and Varifolds

Stein variational gradient descent (SVGD) is a non-parametric inference
algorithm that evolves a set of particles to fit a given distribution of
interest. We analyze the non-asymptotic properties of SVGD, showing that there
exists a set of functions, which we call the Stein matching set, whose
expectations are exactly estimated by any set of particles that satisfies the
fixed point equation of SVGD. This set is the image of Stein operator applied
on the feature maps of the positive definite kernel used in SVGD. Our results
provide a theoretical framework for analyzing the properties of SVGD with
different kernels, shedding insight into optimal kernel choice. In particular,
we show that SVGD with linear kernels yields exact estimation of means and
variances on Gaussian distributions, while random Fourier features enable
probabilistic bounds for distributional approximation. Our results offer a
refreshing view of the classical inference problem as fitting Stein's identity
or solving the Stein equation, which may motivate more efficient algorithms.

本文提出一种基于 Stein 算子的非参数推断方法，将 Stein 变分梯度下降（SVGD）用于解决推断问题，挖掘出一类函数，即 Stein 匹配集合，从而提供了更好的内核选择方法，并可以将问题转化为拟合 Stein 等式或求解 Stein 方程。

斯坦变分梯度下降作为时刻匹配

Stein Variational Gradient Descent as Moment Matching

We propose new positive definite kernels for permutations. First we introduce
a weighted version of the Kendall kernel, which allows to weight unequally the
contributions of different item pairs in the permutations depending on their
ranks. Like the Kendall kernel, we show that the weighted version is invariant
to relabeling of items and can be computed efficiently in $O(n \ln(n))$
operations, where $n$ is the number of items in the permutation. Second, we
propose a supervised approach to learn the weights by jointly optimizing them
with the function estimated by a kernel machine. Third, while the Kendall
kernel considers pairwise comparison between items, we extend it by considering
higher-order comparisons among tuples of items and show that the supervised
approach of learning the weights can be systematically generalized to
higher-order permutation kernels.

本文提出了若干种排列的正定核函数，其中包括了 Kendall 核函数、加权 Kendall 核函数，探究了它们的优化方法和在高阶排列核函数上的推广。