In single-cell research, tracing and analyzing high-throughput single-cell differentiation trajectories is crucial for understanding complex biological processes. Key to this is the modeling and generation of hierarchical data that represents the intrinsic structure within datasets. Traditional methods face limitations in terms of computational cost, performance, generative capacity, and stability. Recent VAEs based approaches have made strides in addressing these challenges but still require specialized network modules for each tree branch, limiting their stability and ability to capture deep hierarchical relationships. To overcome these challenges, we introduce diffusion-based approach called HDTree. HDTree captures tree relationships within a hierarchical latent space using a unified hierarchical codebook and quantized diffusion processes to model tree node transitions. This method improves stability by eliminating branch-specific modules and enhancing generative capacity through gradual hierarchical changes simulated by the diffusion process. HDTree's effectiveness is demonstrated through comparisons on both general-purpose and single-cell datasets, where it outperforms existing methods in terms of accuracy and performance. These contributions provide a new tool for hierarchical lineage analysis, enabling more accurate and efficient modeling of cellular differentiation paths and offering insights for downstream biological tasks. The code of HDTree is available at anonymous link https://anonymous.4open.science/r/code_HDTree_review-A8DB.

This story will introduce yet another implementation of Decision Trees, which I wrote as part of my thesis. Firstly, I will try to motivate why I have decided to take my time to come up with an own implementation of Decision Trees; I will list some of its features but also will list the disadvantages of the current implementation. Secondly, I will guide you through the basic usage of HDTree using code snippets and explaining some details along the way. Lastly, there will be some hints on how to customize and extend the HDTree with your own chunks of ideas. However, this article will not guide you through all of the basics of Decision Trees. There are really plenty of resources out there [1][2][3][16].

Classifiers trained on data sets possessing an imbalanced class distribution are known to exhibit poor generalisation performance. This is known as the imbalanced learning problem. The problem becomes particularly acute when we consider incremental classifiers operating on imbalanced data streams, especially when the learning objective is rare class identification. As accuracy may provide a misleading impression of performance on imbalanced data, existing stream classifiers based on accuracy can suffer poor minority class performance on imbalanced streams, with the result being low minority class recall rates. In this paper we address this deficiency by proposing the use of the Hellinger distance measure, as a very fast decision tree split criterion. We demonstrate that by using Hellinger a statistically significant improvement in recall rates on imbalanced data streams can be achieved, with an acceptable increase in the false positive rate.