Signed Laplacian Embedding for Supervised Dimension Reduction

By Chen Gong, Dacheng Tao, Jie Yang, Keren Fu. 2014

17 citations recorded by the source corpus.

Manifold learning is a powerful tool for solving nonlinear dimension reduction problems. By assuming that the high-dimensional data usually lie on a low-dimensional manifold, many algorithms have been proposed. However, most algorithms simply adopt the traditional graph Laplacian to encode the data locality, so the discriminative ability is limited and the embedding results are not always suitable for the subsequent classification. Instead, this paper deploys the signed graph Laplacian and proposes Signed Laplacian Embedding (SLE) for supervised dimension reduction. By exploring the label information, SLE comprehensively transfers the discrimination carried by the original data to the embedded low-dimensional space. Without perturbing the discrimination structure, SLE also retains the locality.Theoretically, we prove the immersion property by computing the rank of projection, and relate SLE to existing algorithms in the frame of patch alignment. Thorough empirical studies on synthetic and real datasets demonstrate the effectiveness of SLE.

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): “(2) whereWii 2Wij þWjj ¼ kXi Xjk2 SLE [86] KNN,Wij ¼ 1=lr;LðXiÞ ¼ LðXjÞ ¼ Cr 1;LðXiÞ 6¼ LðXjÞ Eq.”