Deep Learning on Lie Groups for Skeleton-based Action Recognition

In recent years, skeleton-based action recognition has become a popular 3D classification problem. State-of-the-art methods typically first represent each motion sequence as a high-dimensional trajectory on a Lie group with an additional dynamic time warping, and then shallowly learn favorable Lie group features. In this paper we incorporate the Lie group structure into a deep network architecture to learn more appropriate Lie group features for 3D action recognition. Within the network structure, we design rotation mapping layers to transform the input Lie group features into desirable ones, which are aligned better in the temporal domain. To reduce the high feature dimensionality, the architecture is equipped with rotation pooling layers for the elements on the Lie group. Furthermore, we propose a logarithm mapping layer to map the resulting manifold data into a tangent space that facilitates the application of regular output layers for the final classification. Evaluations of the proposed network for standard 3D human action recognition datasets clearly demonstrate its superiority over existing shallow Lie group feature learning methods as well as most conventional deep learning methods.Comment: Accepted to CVPR 201

Log signatures in machine learning

Rough path theory, originated as a branch of stochastic analysis, is an emerging tool for analysing complex sequential data in machine learning with increasing attention. This is owing to the core mathematical object of rough path theory, i.e., the signature/log-signature of a path, which has analytical and algebraic properties. This thesis aims to develop a principled and effective model for time series data based on the log-signature method and the recurrent neural network (RNN). The proposed (generalized) Logsig-RNN model can be regarded as a generalization of the RNN model, which boosts the model performance of the RNN by reducing the time dimension and summarising the local structures of sequential data via the log-signature feature. This hybrid model serves as a generic neural network for a wide range of time series applications. In this thesis, we construct the mathematical formulation for the (generalized) Logsig-RNN model, analyse its complexity and establish the universality. We validate the effectiveness of the proposed method for time series analysis in both supervised learning and generative tasks. In particular, for the skeleton human action recognition tasks, we demonstrates that by replacing the RNN module by the Logsig-RNN in state-of-the-art (SOTA) networks improves the accuracy, efficiency and robustness. In addition, our generator based on the Logsig-RNN model exhibits better performance in generating realistic-looking time series data than classical RNN generators and other baseline methods from the literature. Apart from that, another contribution of our work is to construct a novel Sig-WGAN framework to address the efficiency issue and instability training of traditional generative adversarial networks for time series generation

Pairing games and markets

Pairing Games or Markets studied here are the non-two-sided NTU generalization of assignment games. We show that the Equilibrium Set is nonempty, that it is the set of stable allocations or the set of semistable allocations, and that it has has several notable structural properties. We also introduce the solution concept of pseudostable allocations and show that they are in the Demand Bargaining Set. We give a dynamic Market Procedure that reaches the Equilibrium Set in a bounded number of steps. We use elementary tools of graph theory and a representation theorem obtained here

LIO-GVM: an Accurate, Tightly-Coupled Lidar-Inertial Odometry with Gaussian Voxel Map

This letter presents an accurate and robust Lidar Inertial Odometry framework. We fuse LiDAR scans with IMU data using a tightly-coupled iterative error state Kalman filter for robust and fast localization. To achieve robust correspondence matching, we represent the points as a set of Gaussian distributions and evaluate the divergence in variance for outlier rejection. Based on the fitted distributions, a new residual metric is proposed for the filter-based Lidar inertial odometry, which demonstrates an improvement from merely quantifying distance to incorporating variance disparity, further enriching the comprehensiveness and accuracy of the residual metric. Due to the strategic design of the residual metric, we propose a simple yet effective voxel-solely mapping scheme, which only necessities the maintenance of one centroid and one covariance matrix for each voxel. Experiments on different datasets demonstrate the robustness and accuracy of our framework for various data inputs and environments. To the benefit of the robotics society, we open source the code at https://github.com/Ji1Xingyu/lio_gvm