Graph Construction from Data by Non-Negative Kernel Regression
Published in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020
Data driven graph constructions are often used in machine learning applications. However, learning an optimal graph from data is still a challenging task. K-nearest neighbor and -neighborhood methods are among the most common graph construction methods, due to their computational simplicity, but the choice of parameters such as K and associated with these methods is often ad hoc and lacks a clear interpretation. The main novelty of this paper is to formulate graph construction as the problem of finding a sparse signal approximation in kernel space, and identifying key similarities between methods in signal approximation and existing graph learning methods. We propose non-negative kernel regression (NNK), an improved approach for graph construction with interesting geometric and theoretical properties. We demonstrate experimentally the efficiency of NNK graphs, their robustness to choice of sparsity K and show that they can outperform state of the art graph methods in semi supervised learning tasks.
@inproceedings{shekkizhar2020graph,
title={Graph Construction from Data by Non-Negative Kernel Regression},
author={Shekkizhar, Sarath and Ortega, Antonio},
booktitle={ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
pages={3892--3896},
year={2020},
organization={IEEE}
}