title: Toward the optimization of normalized graph Laplacian.
abstract: Normalized graph Laplacian has been widely used in many practical machine learning algorithms, e.g., spectral clustering and semisupervised learning. However, all of them use the Euclidean distance to construct the graph Laplacian, which does not necessarily reflect the inherent distribution of the data. In this brief, we propose a method to directly optimize the normalized graph Laplacian by using pairwise constraints. The learned graph is consistent with equivalence and nonequivalence pairwise relationships, and thus it can better represent similarity between samples. Meanwhile, our approach, unlike metric learning, automatically determines the scale factor during the optimization. The learned normalized Laplacian matrix can be directly applied in spectral clustering and semisupervised learning algorithms. Comprehensive experiments demonstrate the effectiveness of the proposed approach.
authors.affiliation: Nanyang Technological University, 639798, Singapore. zixu1986@gmail.com
authors.forename: Bo
authors.initials: B
authors.lastname: Xie
authors.forename: Meng
authors.initials: M
authors.lastname: Wang
authors.forename: Dacheng
authors.initials: D
authors.lastname: Tao
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D002965:Classification; D016000:Cluster Analysis; D003198:Computer Simulation; D003661:Decision Support Techniques; D006801:Humans; D010363:Pattern Recognition, Automated