Dimensionality reduction (DR) techniques help analysts understand patterns in high-dimensional spaces. These techniques, often represented by scatter plots, are employed in diverse science domains and facilitate similarity analysis among clusters and data samples. For datasets containing many granularities or when analysis follows the information visualization mantra, hierarchical DR techniques are the most suitable approach since they present major structures beforehand and details on demand. However, current hierarchical DR techniques are not fully capable of addressing literature problems because they do not preserve the projection mental map across hierarchical levels or are not suitable for most data types. This work presents HUMAP, a novel hierarchical dimensionality reduction technique designed to be flexible in preserving local and global structures and the mental map throughout hierarchical exploration. We provide empirical evidence of our technique's superiority compared with current hierarchical approaches and show two case studies to demonstrate its strengths.

翻译：降维技术帮助分析人员理解高维空间中的模式。这些技术通常以散点图形式呈现，广泛应用于多个科学领域，便于分析聚类和数据样本间的相似性。对于包含多粒度层次的数据集，或当分析遵循信息可视化箴言时，分层降维技术最为适用，因其能预先呈现主要结构，并按需提供细节。然而，现有分层降维技术在解决文献中的问题时能力不足，原因在于它们要么无法在层次间保持投影的心理意象，要么不适用于大多数数据类型。本文提出了一种新颖的分层降维技术HUMAP，其设计灵活，能在层次化探索过程中同时保持局部与全局结构以及心理意象。我们通过实证证据证明了该技术相较于现有分层方法的优越性，并展示了两项案例研究以突出其优势。