Development of learning subspace-based methods for pattern recognition

在2022财年，我们致力于解决传统的深度神经网络框架独立处理图像集的问题，而不考虑图像集中的潜在特征分布和方差。为了克服这一局限性，我们设计了一种新的子空间学习方法--Grassman学习互动子空间方法(G-LMSM)，它是一个可以集成到深层神经网络中的NN层，将图像集映射到低维输入子空间表示，然后使用它们的典型角的相似性度量与字典子空间进行匹配，该度量是一种可解释且计算高效的度量。G-LMSM的核心思想是将字典子空间学习为Grassmann流形上的点，Grassmann流形是一种光滑的非线性流形，它捕获子空间的几何结构。该方法采用Riemannian随机梯度下降法进行优化，具有稳定、高效和理论基础良好的特点，并在手形识别、人脸识别和表情识别三个不同的任务上进行了评估。我们的实验结果表明，G-LMSM在所有三个任务上都优于最先进的方法，表明它有潜力提高图像集中目标识别的深层框架的性能。

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.