Graphs from Features: Tree-Based Graph Layout for Feature Analysis

Feature Analysis has become a very critical task in data analysis and visualization. Graph structures are very flexible in terms of representation and may encode important information on features but are challenging in regards to layout being adequate for analysis tasks. In this study, we propose and develop similarity-based graph layouts with the purpose of locating relevant patterns in sets of features, thus supporting feature analysis and selection. We apply a tree layout in the first step of the strategy, to accomplish node placement and overview based on feature similarity. By drawing the remainder of the graph edges on demand, further grouping and relationships among features are revealed. We evaluate those groups and relationships in terms of their effectiveness in exploring feature sets for data analysis. Correlation of features with a target categorical attribute and feature ranking are added to support the task. Multidimensional projections are employed to plot the dataset based on selected attributes to reveal the effectiveness of the feature set. Our results have shown that the tree-graph layout framework allows for a number of observations that are very important in user-centric feature selection, and not easy to observe by any other available tool. They provide a way of finding relevant and irrelevant features, spurious sets of noisy features, groups of similar features, and opposite features, all of which are essential tasks in different scenarios of data analysis. Case studies in application areas centered on documents, images and sound data demonstrate the ability of the framework to quickly reach a satisfactory compact representation from a larger feature set.

Force-Directed Graph Layouts by Edge Sampling

Recent work shows that sampling algorithms can be an effective tool for graph visualization. This paper extends prior work by applying edge sampling algorithms to speed up the spring force calculation in force-directed graph layout algorithms. An experiment on 72 graphs finds that some sampling algorithms achieve comparable quality as no sampling. This result is confirmed with visualizations of the graph layout results. However, runtime improvements are small, especially for graphs with 10,000 vertices or fewer, indicating that the runtime savings might not be worth the risk to layout quality. Therefore, this paper suggests that accurate spring forces may be more important to force-directed graph layout algorithms than accurate electric forces. A copy of this paper plus the code and data to reproduce the results are available at https://osf.io/4ja29/

A Random Sampling O(n) Force-calculation Algorithm for Graph Layouts

This paper proposes a linear-time repulsive-force-calculation algorithm with sub-linear auxiliary space requirements, achieving an asymptotic improvement over the Barnes-Hut and Fast Multipole Method force-calculation algorithms. The algorithm, named random vertex sampling (RVS), achieves its speed by updating a random sample of vertices at each iteration, each with a random sample of repulsive forces. This paper also proposes a combination algorithm that uses RVS to derive an initial layout and then applies Barnes-Hut to refine the layout. An evaluation of RVS and the combination algorithm compares their speed and quality on 109 graphs against a Barnes-Hut layout algorithm. The RVS algorithm performs up to 6.1 times faster on the tested graphs while maintaining comparable layout quality. The combination algorithm also performs faster than Barnes-Hut, but produces layouts that are more symmetric than using RVS alone. Data and code: https://osf.io/nb7m8/