There is a long cartographic tradition of describing cities through a focus on the characteristics of their residents. A review of the history of this type of urban social analysis highlights some persistent challenges. In this paper existing geodemographic approaches are extended through coupling the Kohonen Self-Organizing Map algorithm (SOM), a data-mining technique, with geographic information systems (GIS). This approach allows the construction of linked maps of social (attribute) and geographic space. This novel type of geodemographic classification allows ad hoc hierarchical groupings and exploration of the relationship between social similarity and geographic proximity. It allows one to filter complex demographic datasets and is capable of highlighting general social patterns while retaining the fundamental social fingerprints of a city. A dataset describing 79 attributes of the 2217 census tracts in New York City is analyzed to illustrate the technique. Pairs of social and geographic maps are formally compared using simple pattern metrics. Our analysis of New York City calls into question some assumptions about the functional form of spatial relationships that underlie many modeling and statistical techniques.