自适应子空间图的局部比值和判别分析

随着科技快速发展，数据维度急剧增加，传统降维算法难以寻找数据最优子空间，严重影响分类器性能，提出了基于自适应子空间图的局部比值和判别分析算法。提出了考虑局部结构的比值和判别分析算法；通过交替迭代的优化方法，避免了现有比值和优化方法寻找到的次优解；在最优子空间学习近邻相似图而不是原始空间，避免其受到原始空间噪声点的影响；引入了香农熵约束，避免出现平凡解；最后将样本投影到最优的子空间。在合成数据集和人脸数据集上，被提出的算法与大量主流的判别分析算法进行分类任务实验。大量实验结果表明，被提出的算法能够学习到更好判别性能的投影子空间，具有更优的分类效果。

Local ratio sum discriminant analysis based on adaptive subspace graph

With the rapid development of science and technology and the sharp increase of data dimensions, it is difficult for traditional dimensionality reduction algorithms to find the optimal subspace of the data, which seriously affects the performance of the classifier. This paper proposes a local ratio sum discriminant analysis based on adaptive subspace graph. The ratio sum discriminant analysis considering the local structure is proposed; the alternative iterative optimization method is used to avoid the suboptimal solution found by the existing ratio sum optimization methods; the nearest neighbor similarity graph is learned in the optimal subspace instead of the original space, so as to avoid it. Influenced by the original spatial noise points; the Shannon entropy constraint is introduced to avoid trivial solutions; finally, the samples are projected to the optimal subspace. On synthetic datasets and face datasets, the proposed algorithm is tested with a large number of SOTA discriminant analysis algorithms for classification tasks. A large number of experimental results show that the proposed algorithm can learn a projection subspace with better discriminant performance and has better classification effect.