Matrix optimization based Euclidean embedding with outliers
This work is significant for researchers and practitioners in statistics and machine learning who need to perform Euclidean embedding on data potentially contaminated with outliers, improving the robustness of such analyses.
This paper addresses the problem of Euclidean embedding from noisy observations with outliers by proposing a matrix optimization-based model. The method jointly produces reliable embeddings and identifies outliers, achieving high accuracy and outlier identification with high probability under certain sample size conditions.
Euclidean embedding from noisy observations containing outlier errors 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 paper, 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 for large networks.