Artifacts in biomedical signal recordings, such as gene expression, sonar image and electroencephalogram, have a great influence on the related research because the artifacts with large value usually break the neighbor structure in the datasets. However, the conventional graph embedding (GE) used for dimension reduction such as linear discriminant analysis, principle component analysis and locality preserving projections is essentially defined in the L2 norm space and is prone to the presence of artifacts, resulting in biased sub-structural features. In this work, we defined graph embedding in the L1 norm space and used the maximization strategy to solve this model with the aim of restricting the influence of outliers on the dimension reduction of signals. The quantitative evaluation with different outlier conditions demonstrates that an L1 norm-based GE structure can estimate hyperplanes, which are more stable than those of conventional GE-based methods. The applications to a variety of datasets also show that the proposed L1 GE is more robust to outlier influence with higher classification accuracy estimated. The proposed L1 GE may be helpful for capturing reliable mapping information from the datasets that have been contaminated with outliers.