Wang Jingyu, Xie Fangyuan, Nie Feiping, Li Xuelong
IEEE Trans Neural Netw Learn Syst. 2022 Nov;33(11):6844-6855. doi: 10.1109/TNNLS.2021.3083695. Epub 2022 Oct 27.
High-dimensional data are highly correlative and redundant, making it difficult to explore and analyze. Amount of unsupervised dimensionality reduction (DR) methods has been proposed, in which constructing a neighborhood graph is the primary step of DR methods. However, there exist two problems: 1) the construction of graph is usually separate from the selection of projection direction and 2) the original data are inevitably noisy. In this article, we propose an unsupervised adaptive embedding (UAE) method for DR to solve these challenges, which is a linear graph-embedding method. First, an adaptive allocation method of neighbors is proposed to construct the affinity graph. Second, the construction of affinity graph and calculation of projection matrix are integrated together. It considers the local relationship between samples and global characteristic of high-dimensional data, in which the cleaned data matrix is originally proposed to remove noise in subspace. The relationship between our method and local preserving projections (LPPs) is also explored. Finally, an alternative iteration optimization algorithm is derived to solve our model, the convergence and computational complexity of which are also analyzed. Comprehensive experiments on synthetic and benchmark datasets illustrate the superiority of our method.
高维数据具有高度的相关性和冗余性，难以进行探索和分析。人们已经提出了大量无监督降维（DR）方法，其中构建邻域图是DR方法的首要步骤。然而，存在两个问题：1）图的构建通常与投影方向的选择分开，以及2）原始数据不可避免地存在噪声。在本文中，我们提出了一种用于DR的无监督自适应嵌入（UAE）方法来解决这些挑战，这是一种线性图嵌入方法。首先，提出了一种邻居的自适应分配方法来构建亲和图。其次，将亲和图的构建和投影矩阵的计算整合在一起。它考虑了样本之间的局部关系和高维数据的全局特征，其中最初提出了清理后的数据矩阵以去除子空间中的噪声。还探讨了我们的方法与局部保持投影（LPP）之间的关系。最后，推导了一种交替迭代优化算法来求解我们的模型，并分析了其收敛性和计算复杂度。在合成数据集和基准数据集上的综合实验说明了我们方法的优越性。
