[Paper Review] Exploring Dimensionality Reductions with Forward and Backward Projections

Marco Cavallo, Çağatay Demiralp|arXiv (Cornell University)|Jul 13, 2017

Data Visualization and Analytics37 references3 citations

TL;DR

This paper introduces forward and backward projection interactions, along with prolines and feasibility maps, to enable dynamic, bidirectional exploration of dimensionality-reduced data in scatter plots. Integrated into the Praxis tool, these techniques allow users to manipulate data points interactively and observe changes in projections and vice versa, significantly improving hypothesis generation and interpretability in exploratory data analysis with PCA and autoencoders.

ABSTRACT

Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms generally lack clear relation to the initial data dimensions. Therefore, interpreting and reasoning about dimensionality reductions can be difficult. In this work, we introduce two interaction techniques, extit{forward projection} and extit{backward projection}, for reasoning dynamically about scatter plots of dimensionally reduced data. We also contribute two related visualization techniques, extit{prolines} and extit{feasibility map} to facilitate and enrich the effective use of the proposed interactions, which we integrate in a new tool called extit{Praxis}. To evaluate our techniques, we first analyze their time and accuracy performance across varying sample and dimension sizes. We then conduct a user study in which twelve data scientists use extit{Praxis} so as to assess the usefulness of the techniques in performing exploratory data analysis tasks. Results suggest that our visual interactions are intuitive and effective for exploring dimensionality reductions and generating hypotheses about the underlying data.

Motivation & Objective

• Address the challenge of interpreting dimensionality reduction (DR) results, where reduced dimensions lack clear mappings to original features.
• Overcome the limitations of static visualizations by enabling dynamic, interactive exploration of DR scatter plots.
• Improve user understanding and hypothesis generation in exploratory data analysis through bidirectional data-visualization coupling.
• Develop and evaluate novel visualization techniques—prolines and feasibility maps—that support effective interaction with DR results.
• Create a scalable, intuitive tool (Praxis) that supports what-if analysis in DR-based visualizations for both linear (PCA) and nonlinear (autoencoder) methods.

Proposed method

• Introduce forward projection: users modify high-dimensional feature values of a data point and observe the resulting change in its 2D projection.
• Introduce backward projection: users manipulate a point’s 2D position in the scatter plot and observe the inferred change in its high-dimensional feature values.
• Develop prolines as visual aids that show the direction and magnitude of feature changes in forward projection, highlighting influential dimensions.
• Design feasibility maps to visualize the range of possible high-dimensional values consistent with a given 2D projection, supporting uncertainty awareness.
• Implement the Praxis tool integrating forward and backward projections, prolines, and feasibility maps for interactive DR exploration.
• Leverage the visual embedding model to formalize bidirectional interactions, ensuring that changes in data and visualization are proportionally reflected in both directions.

Experimental results

Research questions

• RQ1 How can forward and backward projection interactions improve user understanding and hypothesis generation in dimensionality-reduced data visualizations?
• RQ2 To what extent do prolines and feasibility maps enhance the interpretability and usability of dimensionality reduction visualizations?
• RQ3 How do the computational performance and accuracy of forward and backward projections scale with varying data sample sizes and feature dimensions?
• RQ4 Can the proposed interactions be effectively applied to both linear (PCA) and nonlinear (autoencoder) dimensionality reduction techniques?
• RQ5 How do users perceive the intuitiveness and effectiveness of bidirectional interactions in exploratory data analysis tasks?

Key findings

• The forward and backward projection interactions are intuitive and effective for dynamic, hypothesis-driven exploration of dimensionality-reduced data.
• The computational performance of forward and backward projections scales efficiently across varying sample and dimension sizes, supporting real-time interaction.
• The user study with twelve data scientists confirms that the proposed interactions enhance exploratory data analysis by enabling effective what-if analysis.
• Prolines and feasibility maps significantly improve interpretability by visually highlighting key features and feasible data regions.
• The integration of bidirectional interactions in Praxis supports a more transparent and interactive experience, reducing the black-box perception of DR methods.
• The techniques are effective across both linear (PCA) and nonlinear (autoencoder) dimensionality reduction, demonstrating broad applicability.