Skeleton-based action recognition (SAR) in videos is an important but
challenging task in computer vision. The recent state-of-the-art models for SAR
are primarily based on graph convolutional neural networks (GCNs), which are
powerful in extracting the spatial information of skeleton data. However, it is
yet clear that such GCN-based models can effectively capture the temporal
dynamics of human action sequences. To this end, we propose the DevLSTM module,
which exploits the path development -- a principled and parsimonious
representation for sequential data by leveraging the Lie group structure. The
path development, originated from Rough path theory, can effectively capture
the order of events in high-dimensional stream data with massive dimension
reduction and consequently enhance the LSTM module substantially. Our proposed
G-DevLSTM module can be conveniently plugged into the temporal graph,
complementing existing advanced GCN-based models. Our empirical studies on the
NTU60, NTU120 and Chalearn2013 datasets demonstrate that our proposed hybrid
model significantly outperforms the current best-performing methods in SAR
tasks. The code is available at this https URL

提出了一个结合轨迹发展的 DevLSTM 模块，用于捕捉视频动作序列的时间动态，有效提取高维流数据中的事件顺序并显著提升 LSTM 模块性能，在 Skeleton-based action recognition (SAR) 领域取得了显著的优势。

GCN-DevLSTM: 基于骨骼的动作识别中的路径发展

GCN-DevLSTM: Path Development for Skeleton-Based Action Recognition

We present a new Riemannian metric, termed Log-Cholesky metric, on the
manifold of symmetric positive definite (SPD) matrices via Cholesky
decomposition. We first construct a Lie group structure and a bi-invariant
metric on Cholesky space, the collection of lower triangular matrices whose
diagonal elements are all positive. Such group structure and metric are then
pushed forward to the space of SPD matrices via the inverse of Cholesky
decomposition that is a bijective map between Cholesky space and SPD matrix
space. This new Riemannian metric and Lie group structure fully circumvent
swelling effect, in the sense that the determinant of the Fr\'echet average of
a set of SPD matrices under the presented metric, called Log-Cholesky average,
is between the minimum and the maximum of the determinants of the original SPD
matrices. Comparing to existing metrics such as the affine-invariant metric and
Log-Euclidean metric, the presented metric is simpler, more computationally
efficient and numerically stabler. In particular, parallel transport along
geodesics under Log-Cholesky metric is given in a closed and easy-to-compute
form.

通过 Cholesky 分解，我们在对称正定矩阵流形上引入了一种新的黎曼度量 —— 对数 Cholesky 度量，并建立了 Lie 群结构和双不变度量。与现有度量法相比，该方法更简单，更高效且更稳定。