IEEE Trans Neural Netw Learn Syst. 2021 Nov;32(11):4956-4970. doi: 10.1109/TNNLS.2020.3026426. Epub 2021 Oct 27.
In this article, a manifold learning algorithm based on straight-like geodesics and local coordinates is proposed, called SGLC-ML for short. The contribution and innovation of SGLC-ML lie in that; first, SGLC-ML divides the manifold data into a number of straight-like geodesics, instead of a number of local areas like many manifold learning algorithms do. Figuratively speaking, SGLC-ML covers manifold data set with a sparse net woven with threads (straight-like geodesics), while other manifold learning algorithms with a tight roof made of titles (local areas). Second, SGLC-ML maps all straight-like geodesics into straight lines of a low-dimensional Euclidean space. All these straight lines start from the same point and extend along the same coordinate axis. These straight lines are exactly the local coordinates of straight-like geodesics as described in the mathematical definition of the manifold. With the help of local coordinates, dimensionality reduction can be divided into two relatively simple processes: calculation and alignment of local coordinates. However, many manifold learning algorithms seem to ignore the advantages of local coordinates. The experimental results between SGLC-ML and other state-of-the-art algorithms are presented to verify the good performance of SGLC-ML.
本文提出了一种基于直纹测地线和局部坐标的流形学习算法，简称 SGLC-ML。SGLC-ML 的贡献和创新在于：首先，SGLC-ML 将流形数据划分为许多直纹测地线，而不像许多流形学习算法那样将其划分为许多局部区域。形象地说，SGLC-ML 用稀疏的网线（直纹测地线）覆盖流形数据集，而其他流形学习算法则用密集的屋顶（局部区域）覆盖数据集。其次，SGLC-ML 将所有直纹测地线映射到低维欧几里得空间的直线上。所有这些直线都从同一点开始，并沿着同一坐标轴延伸。这些直线正是直纹测地线的局部坐标，正如流形的数学定义所描述的那样。借助局部坐标，可以将降维分为两个相对简单的过程：局部坐标的计算和对齐。然而，许多流形学习算法似乎忽略了局部坐标的优势。通过与其他最先进算法的实验结果进行对比，验证了 SGLC-ML 的良好性能。
