The Subspace Voyager: Exploring High-Dimensional Data along a Continuum of Salient 3D Subspaces

Visual Neural Decomposition to Explain Multivariate Data Sets

Investigating relationships between variables in multi-dimensional data sets is a common task for data analysts and engineers. More specifically, it is often valuable to understand which ranges of which input variables lead to particular values of a given target variable. Unfortunately, with an increasing number of independent variables, this process may become cumbersome and time-consuming due to the many possible combinations that have to be explored. In this paper, we propose a novel approach to visualize correlations between input variables and a target output variable that scales to hundreds of variables. We developed a visual model based on neural networks that can be explored in a guided way to help analysts find and understand such correlations. First, we train a neural network to predict the target from the input variables. Then, we visualize the inner workings of the resulting model to help understand relations within the data set. We further introduce a new regularization term for the backpropagation algorithm that encourages the neural network to learn representations that are easier to interpret visually. We apply our method to artificial and real-world data sets to show its utility.

Visual Analysis of Class Separations With Locally Linear Segments

High-dimensional labeled data widely exists in many real-world applications such as classification and clustering. One main task in analyzing such datasets is to explore class separations and class boundaries derived from machine learning models. Dimension reduction techniques are commonly applied to support analysts in exploring the underlying decision boundary structures by depicting a low-dimensional representation of the data distributions from multiple classes. However, such projection-based analyses are limited due to their lack of ability to show separations in complex non-linear decision boundary structures and can suffer from heavy distortion and low interpretability. To overcome these issues of separability and interpretability, we propose a visual analysis approach that utilizes the power of explainability from linear projections to support analysts when exploring non-linear separation structures. Our approach is to extract a set of locally linear segments that approximate the original non-linear separations. Unlike traditional projection-based analysis where the data instances are mapped to a single scatterplot, our approach supports the exploration of complex class separations through multiple local projection results. We conduct case studies on two labeled datasets to demonstrate the effectiveness of our approach.

Drag and Track: A Direct Manipulation Interface for Contextualizing Data Instances within a Continuous Parameter Space

We present a direct manipulation technique that allows material scientists to interactively highlight relevant parameterized simulation instances located in dimensionally reduced spaces, enabling a user-defined understanding of a continuous parameter space. Our goals are two-fold: first, to build a user-directed intuition of dimensionally reduced data, and second, to provide a mechanism for creatively exploring parameter relationships in parameterized simulation sets, called ensembles. We start by visualizing ensemble data instances in dimensionally reduced scatter plots. To understand these abstract views, we employ user-defined virtual data instances that, through direct manipulation, search an ensemble for similar instances. Users can create multiple of these direct manipulation queries to visually annotate the spaces with sets of highlighted ensemble data instances. User-defined goals are therefore translated into custom illustrations that are projected onto the dimensionally reduced spaces. Combined forward and inverse searches of the parameter space follow naturally allowing for continuous parameter space prediction and visual query comparison in the context of an ensemble. The potential for this visualization technique is confirmed via expert user feedback for a shock physics application and synthetic model analysis.