Flexible Orthogonal Neighborhood Preserving Embedding

By Tianji Pang, Feiping Nie, Junwei Han. 2017

17 citations recorded by the source corpus.

In this paper, we propose a novel linear subspace learning algorithm called Flexible Orthogonal Neighborhood Preserving Embedding (FONPE), which is a linear approximation of Locally Linear Embedding (LLE) algorithm. Our novel objective function integrates two terms related to manifold smoothness and a flexible penalty defined on the projection fitness. Different from Neighborhood Preserving Embedding (NPE), we relax the hard constraint P X = Y by modeling the mismatch between P X and Y, which makes it better cope with the data sampled from a non-linear manifold. Besides, instead of enforcing an orthogonality between the projected points, i.e. (P X)(P X) = I, we enforce the mapping to be orthogonal, i.e. P P = I. By using this method, FONPE tends to preserve distances so that the overall geometry can be preserved. Unlike LLE, as FONPE has an explicit linear mapping between the input and the reduced spaces, it can handle novel testing data straightforwardly. Moreover, when P becomes an identity matrix, our model can be transformed into denoising LLE (DLLE). Compared with the standard LLE, we demonstrate that DLLE can handle data with noise better. Comprehensive experiments on several benchmark databases demonstrate the effectiveness of our algorithm.

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. Kevin Chen-Chuan Chang
2. Vincent Wenchen Zheng
3. Hongyun Cai
4. Evgeny Burnaev
5. Sergey Ivanov

In Computer Vision and Pattern Recognition

1. Hongyun Cai
2. Kevin Chen-Chuan Chang
3. Vincent Wenchen Zheng

Citations in the corpus

• A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications (2017, background): “(5) + O(community detection) + (community proximity constraint) ULGE [2] W ¼ ZD 1ZT , where Z ¼ argminzT i 1¼1;zi 0 Pm j¼1 kXi ujk 2 2zij þ g Pm j¼1 z 2 ij a ¼ argminkaTX Fpk2F þ akak 2 F whereFp is the top p eigenvectors ofW LLE [102] KNN,W ¼ argmin P i kXi P j WijXjk 2 y ¼ argmin P i kyi P j Wijyj”