Category: Publications

In this article we use the PageRank function along with persistent homology to obtain a scalable graph descriptor and utilize it to compare the similarities between graphs.

In this paper, we study the parallel analysis of the construction of Mapper. We give a provably correct parallel algorithm to execute Mapper on a multiple processors. Our algorithm relies on a divide and conquer strategy for the codomain cover which gets pulled back to the domain cover.

We propose a parallel augmented Reeb graph algorithm on triangulated meshes with and without a boundary. That is, in addition to our parallel algorithm for computing a Reeb graph, we describe a method for extracting the original manifold data from the Reeb graph structure.

We present a multi-stage user study focusing on 4 factors—distribution size of clusters, number of points, size ofpoints, and opacity of points—that influence cluster identification in scatterplots. From these parameters, we have constructed 2 models, a distance-based model, and a density-based model, using the merge tree data structure from Topological Data Analysis. Our analysis demonstrates that these factors play an important role in the number of clusters perceived, and it verifies that the distance-based and density-based models can reasonably estimate the number of clusters a user observes.

We present a comprehensive framework for evaluating line chart smoothing methods under a variety of visual analytics tasks. The framework is based on 8 measures of the line smoothing effectiveness tied to 8 low-level visual analytics tasks. We analyze 12 methods coming from 4 commonly used classes of line chart smoothing—rank filters, convolutional filters, frequency domain filters, and subsampling.

We present TopoLines, a method for smoothing line charts using techniques from Topological Data Analysis. The design goal of TopoLines is to maintain prominent peaks in the data while minimizing any residual error. We evaluate TopoLines for 2 visual analytics tasks by comparing to 5 popular line smoothing methods with data from 4 application domains.

In this paper, we leverage persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout by adding and removing contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout.