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Sometimes the hardest part of an analysis is knowing what something is called.

What are some R packages, but more importantly, terminology I should be searching for to define contiguous city neighborhoods based on home price changes - basically a topographic map treating these price changes as elevations (and ignoring how real estate people have defined neighborhoods).

I'm not sure if this is called "natural neighborhood delination" or "spatially restricted clustering" or just "grouping analysis".

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Many different hierarchical (and/or agglomerative) clustering techniques would work. Here are a few example discussions, Spatial statistics tools : clustering analysis on raster data and What tools for regionalization/redistricting can you recommend? –  Andy W Feb 25 '13 at 20:32
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In the retail industry, these can sometimes be called "submarkets", or "mini-markets". A couple of examples of this in use include:

From an article on Multifamily Insight Blog:

A submarket is a geographic area defined by streets, natural barriers and the specific properties in which a property is in competition for customers

Or, from CoStar.com:

A submarket:

  • Represents the division of the primary market.
  • Outlines a specific geographic boundary that describes a core area that is competitive with other submarkets.
  • Constitutes a generally accepted primary competitive set of areas.
  • Represents similar property types (office, industrial, retail, etc.)
  • Does not overlap other submarkets and is a contiguous geographic area.
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Could you expand this a little to explain how "submarkets" would differ from "how real estate people have defined neighborhoods"? –  whuber Feb 25 '13 at 20:50
    
I was just trying to provide some "terminology [he could] be searching for to define contiguous city neighborhoods". –  RyanDalton Feb 25 '13 at 21:28
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