[Paper Review] Casting Multiple Shadows: High-Dimensional Interactive Data Visualisation with Tours and Embeddings

Stuart Lee, Ursula Laa+1 more|arXiv (Cornell University)|Dec 11, 2020

Data Visualization and Analytics42 references4 citations

TL;DR

This paper proposes a novel interactive visualization framework, implemented in the R package *liminal*, that combines t-SNE embeddings with dynamic tours to improve interpretability of high-dimensional data. By linking tours—sequences of linear projections—with non-linear embeddings, the method enables users to detect distortions in t-SNE visualizations, verify cluster structure, and assess neighborhood preservation, significantly enhancing reliability in cluster orientation tasks for single-cell transcriptomics and simulation data.

ABSTRACT

Non-linear dimensionality reduction (NLDR) methods such as t-distributed stochastic neighbour embedding (t-SNE) are ubiquitous in the natural sciences, however, the appropriate use of these methods is difficult because of their complex parameterisations; analysts must make trade-offs in order to identify structure in the visualisation of an NLDR technique. We present visual diagnostics for the pragmatic usage of NLDR methods by combining them with a technique called the tour. A tour is a sequence of interpolated linear projections of multivariate data onto a lower dimensional space. The sequence is displayed as a dynamic visualisation, allowing a user to see the shadows the high-dimensional data casts in a lower dimensional view. By linking the tour to an NLDR view, we can preserve global structure and through user interactions like linked brushing observe where the NLDR view may be misleading. We display several case studies from both simulations and single cell transcriptomics, that shows our approach is useful for cluster orientation tasks.

Motivation & Objective

• To address the challenge of interpreting non-linear dimensionality reduction (NLDR) methods like t-SNE, which often obscure or distort global data structure due to complex parameterization.
• To improve the reliability of cluster identification in high-dimensional data by combining NLDR with dynamic linear projections (tours).
• To provide interactive diagnostics that help analysts assess whether t-SNE embeddings preserve meaningful topological and geometric relationships in the data.
• To reduce perceptual misinterpretations of spurious clusters by enabling real-time comparison between the tour and t-SNE views through linked brushing.

Proposed method

• The framework integrates t-SNE embeddings with a dynamic grand tour, which systematically projects high-dimensional data onto low-dimensional views through interpolated linear projections.
• Interactive linked brushing allows users to select regions in the t-SNE view and simultaneously highlight corresponding points in the tour view, enabling cross-verification of local and global structure.
• Neighborhood preservation is assessed by computing k-nearest neighbors (k-NN) graphs on a reference dataset and comparing them with those in the t-SNE and tour projections.
• The method uses opacity, color scales, or selection to encode distances or neighbor relationships, supporting one-to-many brushing for detecting mismatches between embeddings and original data geometry.
• The implementation leverages R packages like *ggplot2*, *cowplot*, and *FNN*/*RcppAnnoy* for efficient nearest-neighbor computation and interactive rendering.
• A 'sage tour' is proposed as a non-linear transformation to mitigate overplotting and crowding in the tour view, improving visibility of dense clusters.

Experimental results

Research questions

• RQ1 Can linking a tour with a t-SNE embedding help detect misleading visualizations caused by parameterization in non-linear dimensionality reduction?
• RQ2 How effectively can dynamic linear projections reveal global data structure that is obscured in t-SNE visualizations?
• RQ3 To what extent can linked brushing between tour and t-SNE views improve the validation of cluster structure and neighborhood preservation?
• RQ4 Can interactive diagnostics reduce the risk of misinterpreting spurious clusters in high-dimensional data, especially in the absence of ground truth?
• RQ5 How can scalable visualization techniques support interpretable analysis of large single-cell transcriptomics datasets?

Key findings

• The framework successfully detects distortions in t-SNE visualizations, such as the merging of distinct clusters in piecewise linear data structures like tree-like geometries.
• In simulation studies, the tour preserved the true shape and separation of clusters, while t-SNE often failed to do so, especially under suboptimal parameter settings.
• Linked brushing enabled analysts to identify regions in t-SNE where local neighborhoods were poorly preserved, revealing potential artifacts in the embedding.
• In single-cell transcriptomics, the combined tour-t-SNE view allowed for more reliable cluster orientation and validation of marker gene expression patterns.
• The use of k-NN graphs in both views revealed discrepancies between the embedding and original data, supporting the detection of non-preserved neighborhoods.
• The implementation in the *liminal* R package, including support for one-to-many brushing and fast neighbor computation, enables scalable and interactive exploration of high-dimensional data.