Visual analysis of dimensionality reduction quality for parameterized projections

Abstract

In recent years, many dimensionality reduction (DR) algorithms have been proposed for visual analysis of multidimensional data. Given a set of n-dimensional observations, such algorithms create a 2D or 3D projection thereof that preserves relative distances or neighborhoods. The quality of resulting projections is strongly influenced by many choices, such as the DR techniques used and their various parameter settings. Users find it challenging to judge the effectiveness of a projection in maintaining features from the original space and to understand the effect of parameter settings on these results, as well as performing related tasks such as comparing two projections. We present a set of interactive visualizations that aim to help users with these tasks by revealing the quality of a projection and thus allowing inspection of parameter choices for DR algorithms, by observing the effects of these choices on the resulting projection. Our visualizations target questions regarding neighborhoods, such as finding false and missing neighbors and showing how such projection errors depend on algorithm or parameter choices. By using several space-filling techniques, our visualizations scale to large datasets. We apply our visualizations on several recent DR techniques and high-dimensional datasets, showing how they easily offer local detail on point and group neighborhood preservation while relieving users from having to understand technical details of projections.