Linear Discriminant Analysis (LDA) is commonly used for dimensionality reduction in pattern recognition and statistics. It is a supervised method that aims to find the most discriminant space of reduced dimension that can be further used for classification. In this work, we present a Grassmann Iterative LDA method (GILDA) that is based on Proxy Matrix Optimization (PMO). PMO makes use of automatic differentiation and stochastic gradient descent (SGD) on the Grassmann manifold to arrive at the optimal projection matrix. Our results show that GILDAoutperforms the prevailing manifold optimization method.

翻译：线性差异分析(LDA)通常用于减少图案识别和统计的维度,是一种监督方法,旨在找到可进一步用于分类的最小尺寸最相异的空间,在这项工作中,我们介绍了一种草地人迭代LDA方法,这种方法以代理矩阵优化为基础,PMO在格拉斯曼方块上采用自动区分和随机梯度梯度下沉(SGD),以达到最佳的预测矩阵。我们的结果显示,GILDAOUT符合流行的多元优化方法。