Multidimensional Bin-Width Optimization for Histogram and Its Application to Four-Dimensional Neutron Inelastic Scattering Data

We propose a method for optimizing bin widths for multidimensional We propose a method for optimizing bin widths for multidimensional histograms. In recent years, a large amount of four-dimensional event data has been obtainable in neutron inelastic scattering experiments conducted by chopper spectrometers[1]. As preprocessing, researchers make histograms from obtained event data. At present, the researchers only empirically select bin widths and slice conditions to get a two-dimensional histogram, while checking the histogram in a visual approach[2]. We propose a method which can automatically make a multi-dimensional histogram from event data. Our method was derived from the one-dimensional bin width optimization method[3]. In this paper, we use artificial data to investigate the behavior of our method. We applied the proposed method to both sliced two-dimensional event data and the whole four-dimensional event data. Comparing their results, we have found that the optimized bin-width strongly depends on the dimensionality of the data. Moreover, the optimum bin widths are affected by the number of events and the magnitude of the white background noise.
[1]M. Russina and F. Mezei, 2009
[2]Y. Inamura et al., 2013
[3]H. Shimazaki and S. Shinomoto, 2007