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I am performing a Near analysis by group (https://blogs.esri.com/esri/arcgis/2010/09/16/nearbygroup/) on points:

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Points following each others linearly represent structures. They have same attribute. I would like to do a Near analysis by group, but instead of analyzing groups of same attribute, I want to analyze points with different attributes.

I cannot find any way to do this except maybe changing the core python code of the toolbox?

My goal is to statistically get the averaged distance at which structures meet closely each other the most often. This distance will be used as bandwidth (search radius) for a kernel density analysis on ArcGIS. I try to optimize this bandwidth.

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Make a copy of your point feature class. The script below will add two new fields to one of them for Distance and Nearest_FID. Code is commented. Change paths to suit your needs.

import arcpy

# return unique values from field
# courtesy of arcpy cafe at https://arcpy.wordpress.com/2012/02/01/create-a-list-of-unique-field-values/
def unique_values(table, field):
    with arcpy.da.SearchCursor(table, [field]) as cursor:
        return sorted({row[0] for row in cursor})

# workspace where the two point files reside
arcpy.env.workspace = r"C:\Users\*****\Documents\ArcGIS\Default.gdb"

# reference to each point set
pointset_1 = "pointset_1"
pointset_2 = "pointset_2"

# add fields to one of them
arcpy.AddField_management(pointset_1, "Distance", "DOUBLE")
arcpy.AddField_management(pointset_1, "Nearest_FID", "LONG")

# create list of unique group values
group_names = unique_values(pointset_1, "NAME")

# for each group
for group in group_names:
    query_1 = "NAME = '" + group + "'"
    query_2 = "NAME <> '" + group + "'"
    temp_lyr_1 = "lyr1_" + group
    temp_lyr_2 = "lyr2_" + group

    # select the group from pointset_1
    arcpy.MakeFeatureLayer_management(pointset_1, temp_lyr_1)
    arcpy.SelectLayerByAttribute_management(temp_lyr_1, "NEW_SELECTION", query_1)

    # get all the values for OBJECTID in this group
    fc_id_list = unique_values(temp_lyr_1, "OBJECTID")

    # select all in pointset_2 that is not in the group
    arcpy.MakeFeatureLayer_management(pointset_2, temp_lyr_2)
    arcpy.SelectLayerByAttribute_management(temp_lyr_2, "NEW_SELECTION", query_2)

    # for each feature in the group (pointset_1)
    for fc_id in fc_id_list:
        query_1 = "NAME = '" + group + "' AND OBJECTID = " + str(fc_id)
        temp_lyr_3 = "lyr_" + str(fc_id)

        # select only that feature
        arcpy.MakeFeatureLayer_management(temp_lyr_1, temp_lyr_3)
        arcpy.SelectLayerByAttribute_management(temp_lyr_3, "NEW_SELECTION", query_1)

        # perform near analysis for that feature to the other groups in pointset_2
        arcpy.Near_analysis(temp_lyr_3, temp_lyr_2)

        # according to ArcGIS docs this will automatically set non selected each time to -1
        # so we grab the data and insert it into our created fields.
        with arcpy.da.SearchCursor(temp_lyr_3, ["NEAR_DIST", "Distance", "NEAR_FID"]) as cursor:
            for row in cursor:
                arcpy.CalculateField_management(temp_lyr_3, "Distance", row[0], "PYTHON_9.3")
                arcpy.CalculateField_management(temp_lyr_3, "Nearest_FID", row[2], "PYTHON_9.3")

# you can write more to remove unwanted fields NEAR_DIST, NEAR_FID etc

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