  Anomaly detection aims to identify observations that deviate from the typical
pattern of data. Anomalous observations may correspond to financial fraud,
health risks, or incorrectly measured data in practice. We show detecting
anomalies in high-dimensional mixed data is enhanced through first embedding
the data then assessing an anomaly scoring scheme. We focus on unsupervised
detection and the continuous and categorical (mixed) variable case. We propose
a kurtosis-weighted Factor Analysis of Mixed Data for anomaly detection,
FAMDAD, to obtain a continuous embedding for anomaly scoring. We illustrate
that anomalies are highly separable in the first and last few ordered
dimensions of this space, and test various anomaly scoring experiments within
this subspace. Results are illustrated for both simulated and real datasets,
and the proposed approach (FAMDAD) is highly accurate for high-dimensional
mixed data throughout these diverse scenarios.
