IEEE Trans Cybern. 2022 Aug;52(8):7291-7302. doi: 10.1109/TCYB.2021.3049684. Epub 2022 Jul 19.
Linear discriminant analysis (LDA) is a well-known technique for supervised dimensionality reduction and has been extensively applied in many real-world applications. LDA assumes that the samples are Gaussian distributed, and the local data distribution is consistent with the global distribution. However, real-world data seldom satisfy this assumption. To handle the data with complex distributions, some methods emphasize the local geometrical structure and perform discriminant analysis between neighbors. But the neighboring relationship tends to be affected by the noise in the input space. In this research, we propose a new supervised dimensionality reduction method, namely, locality adaptive discriminant analysis (LADA). In order to directly process the data with matrix representation, such as images, the 2-D LADA (2DLADA) is also developed. The proposed methods have the following salient properties: 1) they find the principle projection directions without imposing any assumption on the data distribution; 2) they explore the data relationship in the desired subspace, which contains less noise; and 3) they find the local data relationship automatically without the efforts for tuning parameters. The performance of dimensionality reduction shows the superiorities of the proposed methods over the state of the art.
线性判别分析（LDA）是一种著名的监督降维技术，已广泛应用于许多实际应用中。LDA 假设样本是高斯分布的，并且局部数据分布与全局分布一致。然而，现实世界的数据很少满足这个假设。为了处理具有复杂分布的数据，一些方法强调局部几何结构，并在邻居之间进行判别分析。但是，邻近关系往往容易受到输入空间中噪声的影响。在这项研究中，我们提出了一种新的监督降维方法，即局部自适应判别分析（LADA）。为了直接处理具有矩阵表示形式的数据，如图像，我们还开发了二维 LADA（2DLADA）。所提出的方法具有以下显著特性：1）它们在不假设数据分布的情况下找到主要投影方向；2）它们在所需子空间中探索数据关系，其中包含较少的噪声；3）它们自动找到局部数据关系，而无需调整参数。降维的性能显示了所提出的方法优于现有技术。
