Nonlinear Manifold Learning via Graph Curvature

With the rapid increase of the data, not only the scale of data is very large, but also the dimensionality of the initial data is very high. It is increasingly difficult to perform feature extraction on high-dimensional datasets, called curse of dimensionality. Traditional manifold learning algorithms propose to explore the underlying local or global geometric structure of the high-dimensional datasets for feature extraction. However, such algorithms can only mine a set of local linear structures of the datasets, and it is extremely limited to uncover the higher-order non-Euclidean geometric structure. In this paper, we propose a new nonlinear manifold learning algorithm to exploit the curvature information of the dataset, which can quantify the spatial similarity between data points more accurately and improve the accuracy of feature extraction. We perform a group of clustering experiments on several types of image datasets, and the related experimental results show that our algorithm outperforms the existing manifold learning algorithms.