由于真实世界中的复杂数据经常能够被表示成李群结构,文章设计了一个以李群特征作为输入的深度网络架构,以此利用深度学习强大的特征表示能力来进行模式识别等任务.在构建李群深度神经网络的过程中,为了保证在优化时李群特征能够被限定在微分流形的结构上,提出了适用于李群特征的深度学习算法.算法在特征学习的过程中不仅能够保证不损失数据流形结构的信息,同时也限定了参数优化的假设空间.基于李群特征的深度学习算法在CIFAR-BW和MNIST数据集上,通过为静态图像设计辐条模型的李群特征,实验结果表明算法在较少次数的迭代下就能够收敛到较为理想的结果.“,”Since complex data in the real world can often be represented as Lie group structures, this paper designs a deep network ar-chitecture with Lie group features as input, so as to make use of the powerful feature representation ability of deep learning for pat-tern recognition and other tasks. In the process of constructing Lie group deep neural network, in order to ensure that Lie group fea-tures can be restricted to the structure of differential manifold during optimization, a deep learning algorithm suitable for Lie group features was introduced. In the process of feature learning, the algorithm can not only ensure that the information of data manifold structure is not lost, but also limit the assumption space of parameter optimization. The deep learning algorithm based on Lie group features is applied to CIFAR-BW and MNIST data sets, and the Lie group features of the spoke models are designed for static imag-es. The experimental results show that the proposed algorithm can converge to a more ideal result in fewer iterations.