Many popular machine learning methods for classification, anomaly detection, clustering, and dimensionality reduction rely on distance functions. However, these methods' theoretical foundations and practical performance critically depend on well-defined and meaningful distance functions on the input space. While distances are well-defined in Euclidean spaces, extending them to popular structured data stored in formats such as JSON, XML, ProtoBuffer, or MessagePack remains challenging. To fill this gap, this work proposes the Hierarchically-Structured Tree Distance (HTD), a fully differentiable distance tailored to these heterogeneous data formats. HTD is flexible, parameterized by weights, and supports automatic recursive construction, enabling it to be used on various datasets and tasks. This effectiveness and generality is demonstrated on a wide range of tasks, such as classification, anomaly detection, fast retrieval (indexing), and clustering, and on diverse datasets. The experimental comparison shows that classical distance-based methods with the HTD often rival or outperform state-of-the-art neural network models with orders of magnitude more parameters. HTD thus opens the door to scalable, interpretable, and efficient modeling of hierarchically structured data.

Deep generative models are challenging the classical methods in the field of anomaly detection nowadays. Every newly published method provides evidence of outperforming its predecessors, sometimes with contradictory results. The objective of this article is twofold: to compare anomaly detection methods of various paradigms with a focus on deep generative models and identification of sources of variability that can yield different results. The methods were compared on popular tabular and image datasets. We identified that the main sources of variability are the experimental conditions: 1) the type of dataset (tabular or image) and the nature of anomalies (statistical or semantic) and 2) strategy of selection of hyperparameters, especially the number of available anomalies in the validation set. Methods perform differently in different contexts, i.e., under a different combination of experimental conditions together with computational time. This explains the variability of the previous results and highlights the importance of careful specification of the context in the publication of a new method. All our code and results are available for download.