  Anomaly and outlier detection in datasets is a long-standing problem in
machine learning. In some cases, anomaly detection is easy, such as when data
are drawn from well-characterized distributions such as the Gaussian. However,
when data occupy high-dimensional spaces, anomaly detection becomes more
difficult. We present CLAM (Clustered Learning of Approximate Manifolds), a
fast hierarchical clustering technique that learns a manifold in a Banach space
defined by a distance metric. CLAM induces a graph from the cluster tree, based
on overlapping clusters determined by several geometric and topological
features. On these graphs, we implement CHAODA (Clustered Hierarchical Anomaly
and Outlier Detection Algorithms), exploring various properties of the graphs
and their constituent clusters to compute scores of anomalousness. On 24
publicly available datasets, we compare the performance of CHAODA (by measure
of ROC AUC) to a variety of state-of-the-art unsupervised anomaly-detection
algorithms. Six of the datasets are used for training. CHAODA outperforms other
approaches on 14 of the remaining 18 datasets.
