LDSScanner: Exploratory Analysis of Low-Dimensional Structures in High-Dimensional Datasets.

Abstract

Many approaches for analyzing a high-dimensional dataset assume that the dataset contains specific structures, e.g., clusters in linear subspaces or non-linear manifolds. This yields a trial-and-error process to verify the appropriate model and parameters. This paper contributes an exploratory interface that supports visual identification of low-dimensional structures in a high-dimensional dataset, and facilitates the optimized selection of data models and configurations. Our key idea is to abstract a set of global and local feature descriptors from the neighborhood graph-based representation of the latent low-dimensional structure, such as pairwise geodesic distance (GD) among points and pairwise local tangent space divergence (LTSD) among pointwise local tangent spaces (LTS). We propose a new LTSD-GD view, which is constructed by mapping LTSD and GD to the axis and axis using 1D multidimensional scaling, respectively. Unlike traditional dimensionality reduction methods that preserve various kinds of distances among points, the LTSD-GD view presents the distribution of pointwise LTS ( axis) and the variation of LTS in structures (the combination of axis and axis). We design and implement a suite of visual tools for navigating and reasoning about intrinsic structures of a high-dimensional dataset. Three case studies verify the effectiveness of our approach.