Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important patterns when the manifolds are distorted or masked by certain influential data attributes. This paper presents a feature learning framework, FEALM, designed to generate a set of optimized data projections for nonlinear DR in order to capture important patterns in the hidden manifolds. These projections produce maximally different nearest-neighbor graphs so that resultant DR outcomes are significantly different. To achieve such a capability, we design an optimization algorithm as well as introduce a new graph dissimilarity measure, named neighbor-shape dissimilarity. Additionally, we develop interactive visualizations to assist comparison of obtained DR results and interpretation of each DR result. We demonstrate FEALM's effectiveness through experiments and case studies using synthetic and real-world datasets.

翻译：降维（DR）在高维数据可视化分析中扮演着至关重要的角色。DR的主要目标之一是揭示隐藏在内在低维流形中的模式。然而，当流形受到某些重要数据属性的扭曲或掩盖时，DR往往会忽略关键模式。本文提出了一种名为FEALM的特征学习框架，旨在生成一组优化的数据投影，用于非线性降维，从而捕获隐藏流形中的重要模式。这些投影能够产生最大差异化的最近邻图，使得最终降维结果显著不同。为实现这一能力，我们设计了一种优化算法，并引入了一种新的图相异度度量——邻域形状相异度。此外，我们还开发了交互式可视化工具，以辅助比较降维结果并解释每个结果的含义。通过使用合成数据集和真实数据集的实验与案例研究，我们验证了FEALM的有效性。