Versatile Ordering Network: An Attention-based Neural Network for Ordering Across Scales and Quality Metrics

TL;DR

The paper tackles the challenge of learning to order data items across arbitrary quality metrics in visualization. It introduces Versatile Ordering Network (VON), a set-to-sequence model trained with reinforcement learning and a greedy rollout, guided by any given quality metric. Key contributions include a transformer-based encoder, a novel repositioning module for cross-scale transfer, and extensive evaluations in both dynamic and static scenarios showing competitive performance with specialized solvers and strong generalization. The approach enables metric-agnostic ordering suitable for interactive visualization, with practical implications for adapting ordering strategies to diverse datasets and user-defined metrics.

Abstract

Ordering has been extensively studied in many visualization applications, such as axis and matrix reordering, for the simple reason that the order will greatly impact the perceived pattern of data. Many quality metrics concerning data pattern, perception, and aesthetics are proposed, and respective optimization algorithms are developed. However, the optimization problems related to ordering are often difficult to solve (e.g., TSP is NP-complete), and developing specialized optimization algorithms is costly. In this paper, we propose Versatile Ordering Network (VON), which automatically learns the strategy to order given a quality metric. VON uses the quality metric to evaluate its solutions, and leverages reinforcement learning with a greedy rollout baseline to improve itself. This keeps the metric transparent and allows VON to optimize over different metrics. Additionally, VON uses the attention mechanism to collect information across scales and reposition the data points with respect to the current context. This allows VONs to deal with data points following different distributions. We examine the effectiveness of VON under different usage scenarios and metrics. The results demonstrate that VON can produce comparable results to specialized solvers. The code is available at https://github.com/sysuvis/VON.

Figures (17)

• Figure 1: Challenges in learning to order across scales and quality metrics: C1. The images in (A), (B), and (C) may span different regions in space and exhibit different point set structures.C2. The quality metrics may enforce different problem structures, as indicated by the graphs on the right. TSP enforces a linear route structure, while stress considers a complete graph between points. The different scales of points and quality metrics may require different ordering strategies to be learned.
• Figure 1: The training loss over 200 epochs for ordering images in Fashion-MNIST dataset using TSP metric. All models are trained using 50mix.
• Figure 2: An overview of VON workflow. The upper diagram illustrates the overarching framework and training process of VON, and the lower shows example data and ordering applications in visualization.
• Figure 2: Exploring CIFAR-10 dataset using VON. The demo interface consists of: (I) a scatter plot for selecting images, (II) the collection of selected images ordered by VON, (III) a detailed view for exploring selected images along an axis, and (IV) a drop-down list for selecting quality metrics. The color of a dot indicates the category of the corresponding image. (a), (b), and (c) show the ordering results using Moran's I, TSP, and stress majorization, respectively.
• Figure 3: The conceptual framework of VON. The left part shows the information considered in determining the next data point. The right part shows the data flow and the conceptual network modules. Note that the conceptual modules can be realized with various implementations.