  Unsupervised learning-based anomaly detection in latent space has gained
importance since discriminating anomalies from normal data becomes difficult in
high-dimensional space. Both density estimation and distance-based methods to
detect anomalies in latent space have been explored in the past. These methods
prove that retaining valuable properties of input data in latent space helps in
the better reconstruction of test data. Moreover, real-world sensor data is
skewed and non-Gaussian in nature, making mean-based estimators unreliable for
skewed data. Again, anomaly detection methods based on reconstruction error
rely on Euclidean distance, which does not consider useful correlation
information in the feature space and also fails to accurately reconstruct the
data when it deviates from the training distribution. In this work, we address
the limitations of reconstruction error-based autoencoders and propose a
kernelized autoencoder that leverages a robust form of Mahalanobis distance
(MD) to measure latent dimension correlation to effectively detect both near
and far anomalies. This hybrid loss is aided by the principle of maximizing the
mutual information gain between the latent dimension and the high-dimensional
prior data space by maximizing the entropy of the latent space while preserving
useful correlation information of the original data in the low-dimensional
latent space. The multi-objective function has two goals -- it measures
correlation information in the latent feature space in the form of robust MD
distance and simultaneously tries to preserve useful correlation information
from the original data space in the latent space by maximizing mutual
information between the prior and latent space.
