We address the problem of detecting anomalies as samples that do not conform to structured patterns represented by low-dimensional manifolds. To this end, we conceive a general anomaly detection framework called Preference Isolation Forest (PIF), that combines the benefits of adaptive isolation-based methods with the flexibility of preference embedding. The key intuition is to embed the data into a high-dimensional preference space by fitting low-dimensional manifolds, and to identify anomalies as isolated points. We propose three isolation approaches to identify anomalies: (i)) Voronoi-iForest, the most general solution, (ii)) RuzHash-iForest, that avoids explicit computation of distances via Local Sensitive Hashing, and (iii)) Sliding-PIF, that leverages a locality prior to improve efficiency and effectiveness.