Learning Strictly Orthogonal p-Order Nonnegative Laplacian Embedding via Smoothed Iterative Reweighted Method
Haoxuan Yang, Kai Liu, Hua Wang, Feiping Nie
IJCAI - 2019
Laplacian Embedding (LE) is a powerful method to reveal the intrinsic geometry of high-dimensional data by using graphs. Imposing the orthogonal and nonnegative constraints onto the LE objective has proved to be effective to avoid degenerate and negative solutions, which, though, are challenging to achieve simultaneously because they are nonlinear and nonconvex. In addition, recent studies have shown that using the p-th order of the L2-norm distances in LE can find the best solution for clustering and promote the robustness of the embedding model against outliers, although this makes the optimization objective nonsmooth and difficult to efficiently solve in general. In this work, we study LE that uses the p-th order of the L2-norm distances and satisfies both orthogonal and nonnegative constraints. We introduce a novel smoothed iterative reweighted method to tackle this challenging optimization problem and rigorously analyze its convergence. We demonstrate the effectiveness and potential of our proposed method by extensive empirical studies on both synthetic and real data sets.
Links
- View publications from Kai Liu
- View publications from Hua Wang
- View publications presented in IJCAI
- View publications in the project, An Intelligence-Driven Patient Care Approach to Reduce Medical Errors
- View publications in the project, Mining Brain Imaging Genomics Data for Improved Cognitive Health
- View publications researching Embeddings
- View publications applied to Computer Vision
Cite this paper
MLA
Yang, Haoxuan, et al. "Learning strictly orthogonal p-order nonnegative laplacian embedding via smoothed iterative reweighted method." Proceedings of the 28th International Joint Conference on Artificial Intelligence. AAAI Press, 2019.
BibTeX
@inproceedings{yang2019learning,
title={Learning strictly orthogonal p-order nonnegative laplacian embedding via smoothed iterative reweighted method},
author={Yang, Haoxuan and Liu, Kai and Wang, Hua and Nie, Feiping},
booktitle={Proceedings of the 28th International Joint Conference on Artificial Intelligence},
pages={4040--4046},
year={2019},
organization={AAAI Press}
}