LieCConv: An Image Classification Algorithm Based on Lie Group Convolutional Neural Network

In Lie group convolutional neural networks (LG-CNNs), the calculation and storage of Lie group distances have quadratic space complexity. In order to improve the memory utilization efficiency of LG-CNNs, a novel Lie group convolutional neural network called LieCConv is proposed. LieCConv utilizes an innovative sampling algorithm and a linear space complexity calculation and storage approach for Lie group distances, substantially enhancing network memory efficiency. Firstly, LieCConv employs a novel sampling algorithm called array-neighborhood sampling (ANS) in the downsampling stage. ANS only requires neighborhood information to obtain an excellent sample set with a low threshold of use. The sample set generated by ANS reflects the distribution of the original set. Then, LieCConv adopts a batch calculation and storage scheme for Lie group distances, which effectively declines the space complexity of calculating and storing Lie group distances from quadratic complexity to linear complexity, reducing the memory consumption during training. Finally, the contrast between ANS and farthest point sampling was presented, demonstrating that ANS better captures the distribution characteristics of the original dataset. The memory usage of LieCConv and LieConv was compared, revealing that LieCConv reduces the memory usage for calculating and storing Lie group distances to less than 500 MB. And the performance of LieCConv was evaluated on RotMNIST, RotFashionMNIST and TT100K, validating that LieCConv is universal and effective.