Nie Feiping, Zhao Xiaowei, Wang Rong, Li Xuelong
IEEE Trans Pattern Anal Mach Intell. 2022 Dec;44(12):9315-9330. doi: 10.1109/TPAMI.2022.3162498. Epub 2022 Nov 7.
Linear discriminant analysis (LDA) has been proven to be effective in dimensionality reduction. However, the performance of LDA depends on the consistency assumption of the global structure and the local structure. Some work extended LDA along this line of research and proposed local formulations of LDA. Unfortunately, the learning scheme of these algorithms is suboptimal in that the intrinsic relationship between data points is pre-learned in the original space, which is usually affected by the noise and redundant features. Besides, the time cost is relatively high. To alleviate these drawbacks, we propose a Fast Locality Discriminant Analysis framework (FLDA), which has three advantages: (1) It can divide a non-Gaussian distribution class into many sub-blocks that obey Gaussian distributions by using the anchor-based strategy. (2) It captures the manifold structure of data by learning the fuzzy membership relationship between data points and the corresponding anchor points, which can reduce computation time. (3) The weights between data points and anchor points are adaptively updated in the subspace where the irrelevant information and the noise in high-dimensional space have been effectively suppressed. Extensive experiments on toy data sets, UCI benchmark data sets and imbalanced data sets demonstrate the efficiency and effectiveness of the proposed method.
线性判别分析（LDA）已被证明在降维方面是有效的。然而，LDA的性能取决于全局结构和局部结构的一致性假设。一些工作沿着这条研究路线扩展了LDA，并提出了LDA的局部公式。不幸的是，这些算法的学习方案并不理想，因为数据点之间的内在关系是在原始空间中预先学习的，而原始空间通常受到噪声和冗余特征的影响。此外，时间成本相对较高。为了缓解这些缺点，我们提出了一种快速局部判别分析框架（FLDA），它具有三个优点：（1）它可以通过使用基于锚点的策略将非高斯分布类划分为许多服从高斯分布的子块。（2）它通过学习数据点与相应锚点之间的模糊隶属关系来捕捉数据的流形结构，这可以减少计算时间。（3）数据点与锚点之间的权重在高维空间中无关信息和噪声已被有效抑制的子空间中自适应更新。在玩具数据集、UCI基准数据集和不平衡数据集上进行的大量实验证明了该方法的有效性和高效性。
