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

Advanced optimization algorithms for sensor arrays and multi-antenna communications

Optimization problems arise frequently in sensor array and multi-channel signal processing applications. Often, optimization needs to be performed subject to a matrix constraint. In particular, unitary matrices play a crucial role in communications and sensor array signal processing. They are involved in almost all modern multi-antenna transceiver techniques, as well as sensor array applications in biomedicine, machine learning and vision, astronomy and radars. In this thesis, algorithms for optimization under unitary matrix constraint stemming from Riemannian geometry are developed. Steepest descent (SD) and conjugate gradient (CG) algorithms operating on the Lie group of unitary matrices are derived. They have the ability to find the optimal solution in a numerically efficient manner and satisfy the constraint accurately. Novel line search methods specially tailored for this type of optimization are also introduced. The proposed approaches exploit the geometrical properties of the constraint space in order to reduce the computational complexity. Array and multi-channel signal processing techniques are key technologies in wireless communication systems. High capacity and link reliability may be achieved by using multiple transmit and receive antennas. Combining multi-antenna techniques with multicarrier transmission leads to high the spectral efficiency and helps to cope with severe multipath propagation. The problem of channel equalization in MIMO-OFDM systems is also addressed in this thesis. A blind algorithm that optimizes of a combined criterion in order to be cancel both inter-symbol and co-channel interference is proposed. The algorithm local converge properties are established as well

Unsupervised Neural Learning On Lie Group

This paper aims at presenting general results about a new class of learning rules for linear as well non-linear neural layers, which allows the weight-matrix, describing the connectionstrengths between the inputs and the neurons, to learn in unsupervised frameworks under the constraints of orthonormality, namely, when the network parameters can be arranged in vectors of constant lengths and orthogonal to each other. This paper follows our preceding work, devoted to the first analysis of learning rules on Stiefel-- Grassman manifold and on a wide bibliographical investigation in order to show the close relationships among existing contributions, and Ref. 23, devoted to a wide numerical comparison of orthonormal neural signal processing techniques in the principal/independent component analysis field. The present paper answers to the necessity of a more general treatment of the learning theories with orthonormal constraints and of a more detailed investigation of specific examples, from which useful hints on the general applicability of the proposed theory emerg