PowerBin: fast adaptive data binning with Centroidal Power Diagrams

Journal article

Adaptive binning is a crucial step in the analysis of large astronomical data sets, such as those from integral-field spectroscopy, to ensure a sufficient signal-to-noise ratio () for reliable model fitting. However, the widely used Voronoi-binning method and its variants suffer from two key limitations: they scale poorly with data size, often as , creating a computational bottleneck for modern surveys, and they can produce undesirable non-convex or disconnected bins. I introduce PowerBin, a new algorithm that overcomes these issues. I frame the binning problem within the theory of optimal transport, for which the solution is a Centroidal Power Diagram (CPD), guaranteeing convex bins. Instead of formal CPD solvers, which are unstable with real data, I develop a fast and robust heuristic based on a physical analogy of packed soap bubbles. This method reliably enforces capacity constraints even for non-additive measures like with correlated noise. I also present a new bin-accretion algorithm with complexity, removing the previous bottleneck. The combined PowerBin algorithm scales as , making it about two orders of magnitude faster than previous methods on million-pixel data sets. I demonstrate its performance on a range of simulated and real data, showing it produces high-quality, convex tessellations with excellent uniformity. The public python implementation provides a fast, robust, and scalable tool for the analysis of modern astronomical data.

Authors: Cappellari, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Oxford University Press
• Journal: Monthly Notices of the Royal Astronomical Society
• Volume: 544
• Issue: 2
• Pages: 1432-1446
• Article number: staf1726
• Publication date: 2025-10-16
• Acceptance date: 2025-10-06
• DOI: 10.1093/mnras/staf1726
• EISSN: 1365-2966
• ISSN: 0035-8711
• Language: English
• Keywords: techniques: image processing; software: data analysis; methods: numerical; galaxies: kinematics and dynamics; methods: data analysis; techniques: imaging spectroscopy