Development of learning subspace-based methods for pattern recognition

在2022财年，我们致力于解决传统深度神经网络框架独立处理图像集的问题，而不考虑图像集中图像的底层特征分布和方差。为了克服这一限制，我们设计了一种新的子空间学习方法，称为格拉斯曼学习互子空间方法（G-LMSM），这是一种可以集成到深度神经网络中的NN层。G-LMSM将图像集映射到低维输入子空间表示中，然后使用其正则角度的相似性度量（一种可解释且计算效率高的度量）与字典子空间进行匹配。G-LMSM的关键思想是将字典子空间学习为格拉斯曼流形上的点，格拉斯曼流形是一个光滑的非线性流形，可以捕获子空间的几何结构。这种学习是用黎曼随机梯度下降优化的，它是稳定的，高效的，理论上有充分的基础。所提出的方法在三个不同的任务上进行了评估：手形识别，人脸识别和面部情绪识别。我们的实验结果表明，G-LMSM在所有三项任务上的表现都优于最先进的方法，证明了它有潜力提高图像集对象识别的深度框架的性能。

In fiscal year 2022, we worked to address the problem that traditional deep neural network frameworks process image sets independently, without considering the underlying feature distribution and the variance of the images in the set. To overcome this limitation, we devised a new subspace learning method called Grassmannian learning mutual subspace method (G-LMSM), which is an NN layer that can be integrated into deep neural networks.G-LMSM maps the image set into a low-dimensional input subspace representation, which is then matched with dictionary subspaces using a similarity metric of their canonical angles, an interpretable and computationally efficient metric. The key idea of G-LMSM is to learn dictionary subspaces as points on the Grassmann manifold, which is a smooth, non-linear manifold that captures the geometric structure of subspaces. This learning is optimized with Riemannian stochastic gradient descent, which is stable, efficient, and theoretically well-grounded.The proposed method was evaluated on three different tasks: hand shape recognition, face identification, and facial emotion recognition. Our experimental results showed that G-LMSM outperformed state-of-the-art methods on all three tasks, demonstrating its potential to improve the performance of deep frameworks for object recognition from image sets.