Reconstructing the data inner structure and identifying abnormal points are two major tasks in many data analysis processes. A step beyond the decomposition of a data set as inliers and outliers, that then may be interpreted as anomalies, is to distinguish local from global outliers. This paper introduces a unified approach based on a revised version of an isolation forest that allows for both the reconstruction of dense regions of points, the identification of anomalies and the generation of contextual explanations about the abnormality of these points. To make the anomaly detection more informative and reliable, anomalies are compared to the reconstructed partition of the inliers so as to explain why they are considered abnormal and from which local generation mechanism they could originate from. Relying on a common data property, namely the isolation of anomalies from dense groups of regularities, eases the understanding of the data set structure and makes the provided explanations more informative than those provided by two independent mechanisms, one for clustering and one for detecting anomalies. Conducted experimentations show the relevance of the structural knowledge extracted from the proposed isolation forest and the effectiveness and robustness of the approach thanks to the unified isolation-based data model to analyse different facets of the data.