Unravelling the variations of the society of England and Wales through diffusion mapping analysis of census 2011.

We propose a new approach to identify geographical clustering and inequality hotspots from decadal census data, with a particular emphasis on the method itself. Our method uses diffusion mapping to study the 181 408 output areas in England and Wales (EW), which enables us to decompose the census data's EW-specific feature structures. We further introduce a localization metric, inspired by statistical physics, to reveal the significance of minority groups in London. Our findings can be adapted to analogous datasets, illuminating spatial patterns and differentiating within datasets, especially when meaning factors for determining the datasets' structure are scarce and spatially heterogeneous. This approach enhances our ability to describe and explore patterns of social deprivation and segregation across the country, thereby contributing to the development of targeted policies. We also underscore the method's intrinsic objectivity, guaranteeing its ability to offer comprehensive and unbiased analysis, unswayed by preconceived hypotheses or subjective interpretations of data patterns.