# 2.2 Distance-Based Weights Distance-based weights are constructed using distance measures between all pairs of observations. The neighbor relation can be determined by a given ***distance band*****,** so every other observation that falls within the distance band is considered as neighbors of one observation. Another way to determine neighbor relation is to find ***K nearest neighbors*** (***KNN***) for each observation. For more information, please read: **CONTENTS** 1. min\_distthreshold() 2. distance\_weights() 3. knn\_weights() ### 1. min\_distthreshold() In order to avoid isolates (islands) that would result from too stringent a critical distance, the distance must be chosen such that each location has at least one neighbor. Such a distance conforms to a *max-min* criterion, i.e., it is the largest of the nearest neighbor distances. **Synopsis** Short version ```sql float min_distthreshold(integer gid, geometry the_geom) ``` Full version ```sql float min_distthreshold(integer gid, geometry the_geom, boolean is_arc, boolean is_mile) ``` **Arguments** | Input Arguments | Type | Description | | --------------- | -------- | ------------------------------------------------------------------------------ | | gid | integer | the feature id of geometry: e.g. gid, fid, ogc\_*fid,* cartodb*\_*id | | the\_geom | geometry | the geometry (only points and polygons are supported) | | is\_arc | boolean | if compute arc distance between two observations. Default: FALSE. | | is\_mile | boolean | if convert distance unit from mile to kilometer(KM). Default: TRUE. | **Return** | **Value** | Description | | --------- | ------------------------------------------------------------------------------- | | float | the minimum distance that makes sure each observation has at least one neighbor | **Examples** ```sql SELECT min_distthreshold(gid, the_geom) FROM natregimes; min_distthreshold ------------------- 1.46578 (1 row) ``` ### 2. distance\_weights() With the distance band, one can create a distance-based spatial weights using WINDOW function distance\_weights() **Synopsis** Short version: ```sql float distance_weights(integer gid, geometry the_geom, float dist_band) ``` Full Version: ```sql float distance_weights(integer gid, geometry the_geom, float dist_band, float power, boolean is_inverse, boolean is_arc, boolean is_mile) ``` **Arguments:** | Input Arguments | Type | Description | | --------------- | -------- | ------------------------------------------------------------------------------------------------------------ | | gid | integer | the feature id of geometry: e.g. gid, fid, ogc*fid,* cartodb*\_*id | | the\_geom | geometry | the geometry (only points and polygons are supported) | | dist\_band | float | the distance band/threshold that makes sure each observation has at least one neighbor | | power | float | the power/exponent corresponds to the number of times the base (dist\_band) is used as a factor. Default: 1. | | is\_inverse | boolean | if apply inverse on distance value. Default: False. | | is\_arc | boolean | if compute arc distance between two observations. Default: FALSE. | | is\_mile | boolean | if convert distance unit from mile to kilometer(KM). Default: TRUE. | **Return** | **Value** | Description | | --------- | ------------------------------------------------------------------------------------------- | | bytea | the weights structure for each observation in binary format, which is defined in table 2.1. | **Examples** ```sql SELECT distance_weights(gid, the_geom, 1.46578) OVER() FROM natregimes; distance_weights -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ \x770700001400600800001608000014080000130800005f08000017080000c3070000c5070000c70700007107000074070000750700001e0700002a0700002107000020070000b9060000be060000c407000062060000e8e6a83f95d1b13f7049833f76be5f3f622eae3f10b88f3ff95bdf3e1218953f2716533fb6f0893fa2cc093ff686333f3787dd3e9c8b943f74c 8303f7074533f3d608c3f9fe47c3fec4c313faf3bad3f \x7a0000000e007b0000006d000000cc000000b300000098000000970000008d000000b20000005c0000004e00000025000000670000006800000039000000b9d4af3f5f5dad3f0ba3aa3f80a43a3ffeb2d93eb76d613fa2ed8d3fa3828e3fdba3753f36f80c3f4354b63f5839993fe7b6403fbeb4983f \xeb0000001200260100003f01000066010000ce000000490100002501000024010000010100000401000002010000ea000000c9000000cb00000096000000b0000000af0000009500000094000000678c663fa55ab03ff45eac3f5639613fe17ea53f227f6a3f6d34943f8fcf523fa3487e3f49c6b73eeb61513f3336683ff2cdb03ece2b9e3fb1c47c3f3a57393f771 6ab3f99bf883f ... ``` ### 3. knn\_weights() **Synopsis** Short version: ```sql float knn_weights(integer gid, geometry the_geom, integer k) ``` Full Version: ```sql float knn_weights(integer gid, geometry the_geom, integer k, float power, boolean is_inverse, boolean is_arc, boolean is_mile) ``` **Arguments:** | Input Arguments | Type | Description | | --------------- | -------- | ------------------------------------------------------------------------------------------------------------ | | gid | integer | the feature id of geometry: e.g. gid, fid, ogc*fid,* cartodb*\_*id | | geom | geometry | the geometry (only points and polygons are supported) | | k | integer | the k nearest neighbors | | power | float | the power/exponent corresponds to the number of times the base (dist\_band) is used as a factor. Default: 1. | | is\_inverse | boolean | if apply inverse on distance value. Default: False. | | is\_arc | boolean | if compute arc distance between two observations. Default: FALSE. | | is\_mile | boolean | if convert distance unit from mile to kilometer(KM). Default: TRUE. | **Return** | **Value** | Description | | --------- | ------------------------------------------------------------------------------------------- | | bytea | the weights structure for each observation in binary format, which is defined in table 2.1. | **Examples** ```sql SELECT knn_weights(gid, the_geom, 5) OVER() FROM natregimes; knn_weights ------------------------------------------------------------------------------------------------ \x770700000500c40700007407000021070000c30700001e070000ec4c313fa2cc093f74c8303ff95bdf3e3787dd3e \x7a000000050097000000b3000000680000004e00000098000000b76d613f80a43a3fe7b6403f36f80c3ffeb2d93e \xeb000000050001010000ea000000af000000cb000000020100008fcf523feb61513f3a57393ff2cdb03e49c6b73e ... ``` --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. 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