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Topology across scales on heterogeneous cell data

Fig 4

Persistence weighted death simplices (PWDS) visualisation.

A: Colouring and weighting of the persistence diagram. The colouring in the diagram distinguishes features based on their birth values, with red representing features formed by proximal points, blue for those formed by distal points, and a continuous gradation of colour for features in between. The intensity of the colour reflects the feature’s persistence (death minus birth), with darker shades indicating more prominent features. B: Visualisation of persistence weighted death simplices (PWDS) for five loops with increasing noise with thresholds and . Each triangle indicates the approximate location of a loop detected by persistent homology with alpha complexes, coloured as described above. The PWDS visualisation of the first loop shows only red triangles, indicating features formed by proximal points, with a prominent red triangle for the large loop and smaller red triangles for voids. As noise is added inside the loop, blue triangles appear for features formed by distal points, and the large loop becomes less prominent. With increasing noise, the red triangles shrink and lighten, and eventually, only light-red triangles remain, indicating the loss of structure at the larger scale.

doi: https://doi.org/10.1371/journal.pcbi.1013460.g004