  Autoencoders are widely used in outlier detection due to their superiority in
handling high-dimensional and nonlinear datasets. The reconstruction of any
dataset by the autoencoder can be considered as a complex regression process.
In regression analysis, outliers can usually be divided into high leverage
points and influential points. Although the autoencoder has shown good results
for the identification of influential points, there are still some problems
when detect high leverage points. Through theoretical derivation, we found that
most outliers are detected in the direction corresponding to the
worst-recovered principal component, but in the direction of the well-recovered
principal components, the anomalies are often ignored. We propose a new loss
function which solve the above deficiencies in outlier detection. The core idea
of our scheme is that in order to better detect high leverage points, we should
suppress the complete reconstruction of the dataset to convert high leverage
points into influential points, and it is also necessary to ensure that the
differences between the eigenvalues of the covariance matrix of the original
dataset and their corresponding reconstructed results in the direction of each
principal component are equal. Besides, we explain the rationality of our
scheme through rigorous theoretical derivation. Finally, our experiments on
multiple datasets confirm that our scheme significantly improves the accuracy
of outlier detection.
