DimBridge: Interactive Explanation of Visual Patterns in Dimensionality Reductions with Predicate Logic

TL;DR

DimBridge addresses the interpretability gap in dimensionality reduction by linking 2D projections to original high-dimensional data through first-order predicates. It introduces a Predicate Induction Engine with two algorithms—Recursive Predicate Induction and a differentiable Predicate Regression—to derive subspaces that explain user-selected visual patterns, enforced with smoothness across interactive draws. The system combines Projection, Predicate, and SPLOM views to allow interactive exploration, visualization of predicates, and contextual evaluation of patterns across domains such as generative models, motion capture, diabetes, and Mn1-xGexTe alloys. This approach yields compact, human-interpretable explanations of DR results, enhances pattern discovery, and supports domain experts in hypothesis testing and data-driven insights.

Abstract

Dimensionality reduction techniques are widely used for visualizing high-dimensional data. However, support for interpreting patterns of dimension reduction results in the context of the original data space is often insufficient. Consequently, users may struggle to extract insights from the projections. In this paper, we introduce DimBridge, a visual analytics tool that allows users to interact with visual patterns in a projection and retrieve corresponding data patterns. DimBridge supports several interactions, allowing users to perform various analyses, from contrasting multiple clusters to explaining complex latent structures. Leveraging first-order predicate logic, DimBridge identifies subspaces in the original dimensions relevant to a queried pattern and provides an interface for users to visualize and interact with them. We demonstrate how DimBridge can help users overcome the challenges associated with interpreting visual patterns in projections.

Figures (10)

• Figure 1: Illustration of differentiable proxy function (\ref{['eq:bump_function']}) centered at $\boldsymbol{\mu} = (0,0)$ with $\mathbf{a}=(1, 1/2)$ and $b=7$.
• Figure 2: We show how DimBridge allows one to better understand a potential cluster within the output space of a generative vision model. Upon performing a brush in the scatterplot (1), DimBridge finds a predicate comprised of 4 attributes (2) that, combined, help distinguish cheetahs from other animals (3), e.g. a big animal with spotted features. In comparison, highlighting brushed data points in randomly chosen four features (4) does not help in distinguishing key features of cheetahs from other animals.
• Figure 3: We show how DimBridge allows one to better contrast one region of the dimensionality reduction plot from another. Upon brushing two regions, DimBridge finds a predicate that explains the two regions from the rest of the data points. DimBridge finds that while both kittens (blue) and puppies (orange) are not big animals, kittens have whiskers, and puppies have bigger ears.
• Figure 4: DR plot of the Motion Capture dataset. Left: color by subject. Middle: color by bracing conditions. Right: color by time.
• Figure 5: DimBridge shows that the curve following the flow of time in the figure captures only one subject and condition, and the segment represents a period with increased angles on left and right ankles and slightly decreased angles on left and right knees.