Factor analysis of mixed data for anomaly detection

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 focus on unsupervised detection and the continuous and categorical (mixed) variable case. We show that detecting anomalies in mixed data is enhanced through first embedding the data then assessing an anomaly scoring scheme. We propose a kurtosis-weighted Factor Analysis of Mixed Data for anomaly detection 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 is highly accurate for mixed data throughout these diverse scenarios.