Matrix optimization based Euclidean embedding with outliers

Euclidean embedding from noisy observations that contain outliers is an important and challenging problem in statistics and machine learning. Many existing methods would struggle with outliers due to a lack of detection ability. In this talk, we propose a matrix optimization based embedding model that can produce reliable embeddings and identify the outliers jointly. We show that the estimators obtained by the proposed method satisfy a non-asymptotic risk bound, implying that the model provides a high accuracy estimator with high probability when the order of the sample size is roughly the degree of freedom up to a logarithmic factor. Moreover, we show that under some mild conditions, the proposed model also can identify the outliers without any prior information with high probability. Finally, numerical experiments demonstrate that the matrix optimization-based model can produce configurations of high quality and successfully identify outliers even on large networks.

Dr. Chao Ding is an associate professor in Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He got his PhD from the Department of Mathematics in National University of Singapore. His researches aim to develop new generation of methods for studying matrix optimization and its applications.  He is currently an Associate Editor of Asia-Pacific Journal of Operational Research.