Local and Global Regressive Mapping for Manifold Learning with Out-of-Sample Extrapolation

By Yi Yang, Feiping Nie, Shiming Xiang, Yueting Zhuang, Wenhua Wang. 2010

60 citations recorded by the source corpus.

Over the past few years, a large family of manifold learning algorithms have been proposed, and applied to various applications. While designing new manifold learning algorithms has attracted much research attention, fewer research efforts have been focused on out-of-sample extrapolation of learned manifold. In this paper, we propose a novel algorithm of manifold learning. The proposed algorithm, namely Local and Global Regressive Mapping (LGRM), employs local regression models to grasp the manifold structure. We additionally impose a global regression term as regularization to learn a model for out-of-sample data extrapolation. Based on the algorithm, we propose a new manifold learning framework. Our framework can be applied to any manifold learning algorithms to simultaneously learn the low dimensional embedding of the training data and a model which provides explicit mapping of the out-of-sample data to the learned manifold. Experiments demonstrate that the proposed framework uncover the manifold structure precisely and can be freely applied to unseen data.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Shirui Pan
2. Feng Xia
3. Ke Sun
4. Liangtian Wan
5. Abdul Aziz
6. Huan Liu
7. Shuo Yu
8. Jiliang Tang

In Computer Vision and Pattern Recognition

1. Ke Sun
2. Feng Xia
3. Shirui Pan
4. Huan Liu
5. Jiliang Tang
6. Zheng Zhao
7. Feiping Nie
8. Dacheng Tao

Citations in the corpus

• Graph Learning: A Survey (2021, methodology): “The graph structure can be captured by using a local regression model and a global regression process based on Local and Global Regressive Mapping (LGRM) [76].”