Trustworthy Interactive Visual Exploration of Multidimensional Data Using Projections

来自测量、观察和模拟的多维数据是新知识的重要来源。然而，海量的数据需要降维和投影方法等技术来实现对多维数据集的更有效的探索和分析。数据属性的范围可能不同，通常取决于任意的测量单位。因此，在应用任何降维方法之前，数据预处理，特别是数据归一化是必要的。现有的数据归一化技术通常假设某些数据特征，例如，服从标准统计模型，或者随着数据大小的增加而不能很好地缩放。原始数据属性的不正确归一化可能导致较低维域中的人为误导性数据结构(簇、离群值、形状、密度层次)。我们提出了一个研究项目，旨在开发高效、可扩展和普遍适用的方法来规范化多维数据。新的归一化技术将与线性和非线性投影方法相结合。然后，由用户在投影域中观察到的数据结构可靠地表示原始数据的固有特征。当对时变和集成数据集进行预处理时，归一化系数的优化、分析和可解释性是所提出的技术的一部分。

Multidimensional data stemming from measurements, observations, and simulations are a significant source of new knowledge. The huge amount of data however, requires techniques such as dimensionality reduction and projection methods to enable more efficient exploration and analysis of multidimensional datasets. Data attributes may range on different scales, often depending on arbitrary measurement units. Therefore, data preprocessing and, in particular, data normalization is necessary prior to applying any dimensionality reduction method. Existing data normalization techniques usually assume certain data characteristics, e.g., obeying standard statistical models, or poorly scale as the data size increases. Improper normalization of raw data attributes may result in artificial misleading data structures (clusters, outliers, shapes, density hierarchies) in the lower-dimensional domain. We propose a research project aimed at developing efficient, scalable and generally applicable approaches for normalizing multidimensional data. New normalization techniques will be coupled with linear and non-linear projection methods. Then, data structures observed by the users in the projection domain reliably represent intrinsic features of the raw data. Optimization, analysis and interpretability of normalization coefficients when preprocessing time-varying and ensemble datasets are parts of the proposed techniques.