论文标题
多维缩放，Sammon映射和ISOMAP：教程和调查
Multidimensional Scaling, Sammon Mapping, and Isomap: Tutorial and Survey
论文作者
论文摘要
多维缩放（MDS）是第一个基本多种学习方法之一。它可以分为几种方法，即经典MD，内核经典MD，公制MDS和非金属MDS。 Sammon映射和ISOMAP可以分别视为公制MD和内核经典MD的特殊情况。在本教程和调查论文中，我们详细回顾了MDS，Sammon映射和ISOMAP的理论。我们解释了所有提到的MDS类别。然后，解释了Sammon映射，ISOMAP和内核ISOMAP。引入了使用本本特征和内核映射的MDS和ISOMAP的样本外嵌入。然后，引入了nystrom近似及其在地标MD和地标的ISOMAP中的使用，以用于大数据嵌入。我们还提供了一些模拟来说明这些方法的嵌入。
Multidimensional Scaling (MDS) is one of the first fundamental manifold learning methods. It can be categorized into several methods, i.e., classical MDS, kernel classical MDS, metric MDS, and non-metric MDS. Sammon mapping and Isomap can be considered as special cases of metric MDS and kernel classical MDS, respectively. In this tutorial and survey paper, we review the theory of MDS, Sammon mapping, and Isomap in detail. We explain all the mentioned categories of MDS. Then, Sammon mapping, Isomap, and kernel Isomap are explained. Out-of-sample embedding for MDS and Isomap using eigenfunctions and kernel mapping are introduced. Then, Nystrom approximation and its use in landmark MDS and landmark Isomap are introduced for big data embedding. We also provide some simulations for illustrating the embedding by these methods.
