Matrix optimization based Euclidean embedding with outliers

TL;DR

This paper introduces a matrix optimization approach for Euclidean embedding that effectively handles outliers, providing accurate embeddings and outlier detection with theoretical guarantees and strong empirical performance.

Contribution

The paper proposes a novel matrix optimization model for Euclidean embedding that jointly estimates embeddings and detects outliers without prior information.

Findings

Achieves high-accuracy embeddings with non-asymptotic risk bounds.

Successfully identifies outliers with high probability under mild conditions.

Demonstrates superior performance in large network experiments.

Abstract

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.