Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs. Specifically, we transform each instance of the time-varying graph into metric spaces, extract topological features using persistent homology, and compare those features over time. We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the data. To validate our approach, we conduct several case studies on real world data sets and show how our method can find cyclic patterns, deviations from those patterns, and one-time events in time-varying graphs. We also examine whether persistence-based similarity measure as a graph metric satisfies a set of well-established, desirable properties for graph metrics

PROPHECY—a database for high-resolution phenomics

The rapid recent evolution of the field phenomics—the genome-wide study of gene dispensability by quantitative analysis of phenotypes—has resulted in an increasing demand for new data analysis and visualization tools. Following the introduction of a novel approach for precise, genome-wide quantification of gene dispensability in Saccharomyces cerevisiae we here announce a public resource for mining, filtering and visualizing phenotypic data—the PROPHECY database. PROPHECY is designed to allow easy and flexible access to physiologically relevant quantitative data for the growth behaviour of mutant strains in the yeast deletion collection during conditions of environmental challenges. PROPHECY is publicly accessible at http://prophecy.lundberg.gu.se