Bastian Rieck and Heike Leitte
Exploring and comparing clusterings of multivariate data sets using persistent homology

Abstract: Clustering algorithms support exploratory data analysis by grouping inputs that share similar features. Especially the clustering of unlabelled data is said to be a fiendishly difficult problem, because users not only have to choose a suitable clustering algorithm but also a suitable number of clusters. The known issues of existing clustering validity measures comprise instabilities in the presence of noise and restrictive assumptions about cluster shapes. In addition, they cannot evaluate individual clusters locally. We present a new measure for assessing and comparing different clusterings both on a global and on a local level. Our measure is based on the topological method of persistent homology, which is stable and unbiased towards cluster shapes. Based on our measure, we also describe a new visualization that displays similarities between different clusterings (using a global graph view) and supports their comparison on the individual cluster level (using a local glyph view). We demonstrate how our visualization helps detect different—but equally valid—clusterings of data sets from multiple application domains.



Kappe, Christopher P and Schütz, Lucas and Gunther, Stefan and Hufnagel, Lars and Lemke, Steffen and Leitte, Heike
Reconstruction and Visualization of Coordinated 3D Cell Migration Based on Optical Flow

Abstract: Animal development is marked by the repeated reorganization of cells and cell populations, which ultimately determine form and shape of the growing organism. One of the central questions in developmental biology is to understand precisely how cells reorganize, as well as how and to what extent this reorganization is coordinated. While modern microscopes can record video data for every cell during animal development in 3D+t, analyzing these videos remains a major challenge: reconstruction of comprehensive cell tracks turned out to be very demanding especially with decreasing data quality and increasing cell densities. In this paper, we present an analysis pipeline for coordinated cellular motions in developing embryos based on the optical flow of a series of 3D images. We use numerical integration to reconstruct cellular long-term motions in the optical flow of the video, we take care of data validation, and we derive a LIC-based, dense flow visualization for the resulting pathlines. This approach allows us to handle low video quality such as noisy data or poorly separated cells, and it allows the biologists to get a comprehensive understanding of their data by capturing dynamic growth processes in stills. We validate our methods using three videos of growing fruit fly embryos.