Efficient Regularization-based Normalization for Interactive Multidimensional Data Analysis Without Scaling Artifacts

Molchanov, Vladimir; Rave, Hennes; Linsen, Lars

Abstract

Attribute values in multidimensional datasets often have different measurement units, making data normalization an essential preprocessing step for visualization algorithms such as multidimensional data projections. However, existing normalization techniques are often sensitive to noise, rely on specific data models, are computationally expensive, or have other limitations. The state-of-the-art method for computing optimal scalings of multidimensional data attributes is based on Lloyd relaxation in a linearly projected space. However, its high computational complexity hinders its applicability to datasets of moderate or large sizes. We overcome this limitation by efficiently regularizing the distribution of projected samples using integral images. Our method reduces scaling-induced artifacts, leading to more reliable multidimensional data analysis. In numerical experiments, we demonstrate that our approach, generally, outperforms state-of-the-art methods in computation time, scalability, accuracy, and stability.