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.