  Anomalies are those deviating from the norm. Unsupervised anomaly detection
often translates to identifying low density regions. Major problems arise when
data is high-dimensional and mixed of discrete and continuous attributes. We
propose MIXMAD, which stands for MIXed data Multilevel Anomaly Detection, an
ensemble method that estimates the sparse regions across multiple levels of
abstraction of mixed data. The hypothesis is for domains where multiple data
abstractions exist, a data point may be anomalous with respect to the raw
representation or more abstract representations. To this end, our method
sequentially constructs an ensemble of Deep Belief Nets (DBNs) with varying
depths. Each DBN is an energy-based detector at a predefined abstraction level.
At the bottom level of each DBN, there is a Mixed-variate Restricted Boltzmann
Machine that models the density of mixed data. Predictions across the ensemble
are finally combined via rank aggregation. The proposed MIXMAD is evaluated on
high-dimensional realworld datasets of different characteristics. The results
demonstrate that for anomaly detection, (a) multilevel abstraction of
high-dimensional and mixed data is a sensible strategy, and (b) empirically,
MIXMAD is superior to popular unsupervised detection methods for both
homogeneous and mixed data.
