diff --git a/doc/16_getis_ord_gstar.md b/doc/16_getis_ord_gstar.md new file mode 100644 index 0000000..1b12ac9 --- /dev/null +++ b/doc/16_getis_ord_gstar.md @@ -0,0 +1,40 @@ +## Getis-Ord's G\* + +Getis-Ord's G\* is a geo-statistical measurement of the intensity of clustering of high or low values. The clustering of high values can be referred to as "hotspots" because these are areas of high activity or large (relative to the global mean) measurement values. Coldspots are clustered areas with low activity or small measurement values. + +### CDB_GetisOrdsG(subquery text, column_name text) + +#### Arguments + +| Name | Type | Description | +|------|------|-------------| +| subquery | text | A query of the data you want to pass to the function. It must include `column_name`, a geometry column (usually `the_geom`) and an id column (usually `cartodb_id`) | +| column_name | text | This is the column of interest for performing this analysis on. This column should be a numeric type. | +| w_type (optional) | text | Type of weight to use when finding neighbors. Currently available options are 'knn' (default) and 'queen'. Read more about weight types in [PySAL's weights documentation.](https://pysal.readthedocs.io/en/v1.11.0/users/tutorials/weights.html) | +| num_ngbrs (optional) | integer | Default: 5. If `knn` is chosen, this will set the number of neighbors. If `knn` is not chosen, any entered value will be ignored. Use `NULL` if not choosing `knn`. | +| permutations (optional) | integer | The number of permutations for calculating p-values. Default: 999 | +| geom_col (optional) | text | The column where the geometry information is stored. The format must be PostGIS Geometry type (SRID 4326). Default: `the_geom`. | +| id_col (optional) | text | The column that has the unique row identifier. | + +### Returns + +Returns a table with the following columns. + +| Name | Type | Description | +|------|------|-------------| +| z_score | numeric | z-score, a measure of the intensity of clustering of high values (hotspots) or low values (coldspots). Positive values represent 'hotspots', while negative values represent 'coldspots'. | +| p_value | numeric | p-value, a measure of the significance of the intensity of clustering | +| p_z_sim | numeric | p-value based on standard normal approximation from permutations | +| rowid | integer | The original `id_col` that can be used to associate the outputs with the original geometry and inputs | + +#### Example Usage + +The following query returns the original table augmented with the values calculated from the Getis-Ord's G\* analysis. + +```sql +SELECT i.*, m.z_score, m.p_value + FROM cdb_crankshaft.CDB_GetisOrdsG('SELECT * FROM incident_reports_clustered', + 'num_incidents') As m + JOIN incident_reports_clustered As i + ON i.cartodb_id = m.rowid; +``` diff --git a/src/pg/sql/16_getis.sql b/src/pg/sql/16_getis.sql new file mode 100644 index 0000000..578f15a --- /dev/null +++ b/src/pg/sql/16_getis.sql @@ -0,0 +1,18 @@ +-- Getis-Ord's G +-- Hotspot/Coldspot Analysis tool +CREATE OR REPLACE FUNCTION + CDB_GetisOrdsG( + subquery TEXT, + column_name TEXT, + w_type TEXT DEFAULT 'knn', + num_ngbrs INT DEFAULT 5, + permutations INT DEFAULT 999, + geom_col TEXT DEFAULT 'the_geom', + id_col TEXT DEFAULT 'cartodb_id') +RETURNS TABLE (z_score NUMERIC, p_value NUMERIC, p_z_sim NUMERIC, rowid BIGINT) +AS $$ + from crankshaft.clustering import getis_ord + return getis_ord(subquery, column_name, w_type, num_ngbrs, permutations, geom_col, id_col) +$$ LANGUAGE plpythonu; + +-- TODO: make a version that accepts the values as arrays diff --git a/src/pg/test/expected/16_getis_test.out b/src/pg/test/expected/16_getis_test.out new file mode 100644 index 0000000..416844b --- /dev/null +++ b/src/pg/test/expected/16_getis_test.out @@ -0,0 +1,21 @@ +\pset format unaligned +\set ECHO all +\i test/fixtures/getis_data.sql +SET client_min_messages TO WARNING; +\set ECHO none +_cdb_random_seeds + +(1 row) +rowid|z_score|p_value +9|-0.7862|0.0500 +22|-0.3955|0.0330 +33|2.7045|0.0050 +35|1.9524|0.0130 +36|-1.2056|0.0170 +37|3.4785|0.0020 +38|-1.4622|0.0020 +40|5.7098|0.0030 +46|3.4704|0.0120 +47|-0.9994|0.0320 +48|-1.3650|0.0340 +(11 rows) diff --git a/src/pg/test/fixtures/getis_data.sql b/src/pg/test/fixtures/getis_data.sql new file mode 100644 index 0000000..3b47013 --- /dev/null +++ b/src/pg/test/fixtures/getis_data.sql @@ -0,0 +1,98 @@ +SET client_min_messages TO WARNING; +\set ECHO none + +-- +-- Getis-Ord's G* test dataset, subsetted from PySAL examples: +-- https://github.com/pysal/pysal/tree/952ea04029165048a774d9a1846cf86ad000c096/pysal/examples/stl +-- + + +CREATE TABLE getis_data ( + cartodb_id integer, + the_geom geometry(Geometry,4326), + hr8893 numeric +); + +COPY getis_data (cartodb_id, the_geom, hr8893) FROM stdin; +22 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8.45153700000000008 +\. + + +CREATE INDEX getis_data_gix ON getis_data USING GIST(the_geom); diff --git a/src/pg/test/sql/16_getis_test.sql b/src/pg/test/sql/16_getis_test.sql new file mode 100644 index 0000000..90fb34d --- /dev/null +++ b/src/pg/test/sql/16_getis_test.sql @@ -0,0 +1,15 @@ +\pset format unaligned +\set ECHO all +\i test/fixtures/getis_data.sql + +-- set random seed +SELECT cdb_crankshaft._cdb_random_seeds(1234); + +-- test against PySAL example dataset 'stl_hom' +SELECT rowid, round(z_score, 4) As z_score, round(p_value, 4) As p_value +FROM cdb_crankshaft.CDB_GetisOrdsG( + 'select * from getis_data', + 'hr8893', 'queen', NULL, 999, + 'the_geom', 'cartodb_id') As t(z_score, p_value, p_z_sim, rowid) +WHERE round(p_value, 4) <= 0.05 +ORDER BY rowid ASC; diff --git a/src/py/crankshaft/crankshaft/clustering/__init__.py b/src/py/crankshaft/crankshaft/clustering/__init__.py index ed34fe0..d9682fa 100644 --- a/src/py/crankshaft/crankshaft/clustering/__init__.py +++ b/src/py/crankshaft/crankshaft/clustering/__init__.py @@ -1,3 +1,4 @@ """Import all functions from for clustering""" from moran import * from kmeans import * +from getis import * diff --git a/src/py/crankshaft/crankshaft/clustering/getis.py b/src/py/crankshaft/crankshaft/clustering/getis.py new file mode 100644 index 0000000..a593e64 --- /dev/null +++ b/src/py/crankshaft/crankshaft/clustering/getis.py @@ -0,0 +1,52 @@ +""" +Getis-Ord's G geostatistics (hotspot/coldspot analysis) +""" + +import pysal as ps +import plpy +from collections import OrderedDict + +# crankshaft module +import crankshaft.pysal_utils as pu + +# High level interface --------------------------------------- + + +def getis_ord(subquery, attr, + w_type, num_ngbrs, permutations, geom_col, id_col): + """ + Getis-Ord's G* + Implementation building neighbors with a PostGIS database and PySAL's + Getis-Ord's G* hotspot/coldspot module. + Andy Eschbacher + """ + + # geometries with attributes that are null are ignored + # resulting in a collection of not as near neighbors if kNN is chosen + + qvals = OrderedDict([("id_col", id_col), + ("attr1", attr), + ("geom_col", geom_col), + ("subquery", subquery), + ("num_ngbrs", num_ngbrs)]) + + query = pu.construct_neighbor_query(w_type, qvals) + + try: + result = plpy.execute(query) + # if there are no neighbors, exit + if len(result) == 0: + return pu.empty_zipped_array(4) + except plpy.SPIError, err: + plpy.error('Query failed: %s' % err) + + attr_vals = pu.get_attributes(result) + + # build PySAL weight object + weight = pu.get_weight(result, w_type, num_ngbrs) + + # calculate Getis-Ord's G* z- and p-values + getis = ps.esda.getisord.G_Local(attr_vals, weight, + star=True, permutations=permutations) + + return zip(getis.z_sim, getis.p_sim, getis.p_z_sim, weight.id_order) diff --git a/src/py/crankshaft/test/fixtures/getis.json b/src/py/crankshaft/test/fixtures/getis.json new file mode 100644 index 0000000..02566fc --- /dev/null +++ b/src/py/crankshaft/test/fixtures/getis.json @@ -0,0 +1 @@ +[[0.004793783909323601, 0.17999999999999999, 0.49808756424021061], [-1.0701189472090842, 0.079000000000000001, 0.14228288580832316], [-0.67867750971877305, 0.42099999999999999, 0.24867110969448558], [-0.67407386707620487, 0.246, 0.25013217644612995], [-0.79495689068870035, 0.33200000000000002, 0.21331928959090596], [-0.49279481022182703, 0.058999999999999997, 0.31107878905057329], [-0.38075627530057132, 0.28399999999999997, 0.35169205342069643], [-0.86710921611314895, 0.23699999999999999, 0.19294108571294855], [-0.78618647240956485, 0.050000000000000003, 0.2158791250244505], [-0.76108527223116984, 0.064000000000000001, 0.22330306830813684], [-0.13340753531942209, 0.247, 0.44693554317763651], [-0.57584545722033043, 0.48999999999999999, 0.28235982246156488], [-0.78882694661192831, 0.433, 0.2151065788731219], [-0.38769767950046219, 0.375, 0.34911988661484239], [-0.56057819488052207, 0.41399999999999998, 0.28754255985169652], [-0.41354017495644935, 0.45500000000000002, 0.339605447117173], [-0.23993577722243081, 0.49099999999999999, 0.40519002230969337], [-0.1389080156677496, 0.40400000000000003, 0.44476141839645233], [-0.25485737510500855, 0.376, 0.39941662953554224], [-0.71218610582902353, 0.17399999999999999, 0.23817476979886087], [-0.54533105995872144, 0.13700000000000001, 0.2927629228714812], [-0.39547917847510977, 0.033000000000000002, 0.34624464252424236], [-0.43052658996257548, 0.35399999999999998, 0.33340631435564982], [-0.37296719193774736, 0.40300000000000002, 0.35458643102865428], [-0.66482612169465694, 0.31900000000000001, 0.25308085650392698], [-0.13772133540823422, 0.34699999999999998, 0.44523032843016275], [-0.6765304487868502, 0.20999999999999999, 0.24935196033890672], [-0.64518763494323472, 0.32200000000000001, 0.25940279912025543], [-0.5078622084312413, 0.41099999999999998, 0.30577498972600159], [-0.12652006733772059, 0.42899999999999999, 0.44966013262301163], [-0.32691133022814595, 0.498, 0.37186747562269029], [0.25533848511500978, 0.42399999999999999, 0.39923083899077472], [2.7045138116476508, 0.0050000000000000001, 0.0034202212972238577], [-0.1551614486076057, 0.44400000000000001, 0.43834701985429037], [1.9524487722567723, 0.012999999999999999, 0.025442473674991528], [-1.2055816465306763, 0.017000000000000001, 0.11398941970467646], [3.478472976017831, 0.002, 0.00025213964072468009], [-1.4621715757903719, 0.002, 0.071847099325659136], [-0.84010307600180256, 0.085000000000000006, 0.20042529779230778], [5.7097646237318243, 0.0030000000000000001, 5.6566262784940591e-09], [1.5082367956567375, 0.065000000000000002, 0.065746966514827365], [-0.58337270103430816, 0.44, 0.27982121546450034], [-0.083271860457022437, 0.45100000000000001, 0.46681768733385554], [-0.46872337815000953, 0.34599999999999997, 0.31963368715684204], [0.18490279849545319, 0.23799999999999999, 0.42665263797981101], [3.470424529947997, 0.012, 0.00025981817437825683], [-0.99942612137154796, 0.032000000000000001, 0.15879415560388499], [-1.3650387953594485, 0.034000000000000002, 0.08612042845912049], [1.8617160516432014, 0.081000000000000003, 0.03132156240215267], [1.1321188945775384, 0.11600000000000001, 0.12879222611766061], [0.064116686050580601, 0.27300000000000002, 0.4744386578180424], [-0.42032194540259099, 0.29999999999999999, 0.33712514016213468], [-0.79581215423980922, 0.123, 0.21307061309098785], [-0.42792753720906046, 0.45600000000000002, 0.33435193892883741], [-1.0629378527428395, 0.051999999999999998, 0.14390506780140866], [-0.54164761752225477, 0.33700000000000002, 0.29403064095211839], [1.0934778886820793, 0.13700000000000001, 0.13709201601893539], [-0.094068785378413719, 0.38200000000000001, 0.46252725802998929], [0.13482026574801856, 0.36799999999999999, 0.44637699118865737], [-0.13976995315653129, 0.34699999999999998, 0.44442087706276601], [-0.051047663924746682, 0.32000000000000001, 0.47964376985626245], [-0.21468297736730158, 0.41699999999999998, 0.41500724761906527], [-0.20873154637330626, 0.38800000000000001, 0.41732890604390893], [-0.32427876152583485, 0.49199999999999999, 0.37286349875557478], [-0.65254842943280977, 0.374, 0.25702372075306734], [-0.48611858196118796, 0.23300000000000001, 0.31344154643990074], [-0.14482354344529477, 0.32600000000000001, 0.44242509660469886], [-0.51052030974200002, 0.439, 0.30484349480873729], [0.56814382285283538, 0.14999999999999999, 0.28496865660103166], [0.58680919931668207, 0.161, 0.27866592887231878], [0.013390357044409013, 0.25800000000000001, 0.49465818005865647], [-0.19050728887961568, 0.41399999999999998, 0.4244558160399462], [-0.60531777422216049, 0.35199999999999998, 0.2724839368239631], [1.0899331115425805, 0.127, 0.13787130480311838], [0.17015055382651084, 0.36899999999999999, 0.43244586845546418], [-0.21738337124409801, 0.40600000000000003, 0.41395479459421991], [1.0329303331079593, 0.079000000000000001, 0.15081825117169467], [1.0218317101096221, 0.104, 0.15343027913308094]] diff --git a/src/py/crankshaft/test/fixtures/neighbors_getis.json b/src/py/crankshaft/test/fixtures/neighbors_getis.json new file mode 100644 index 0000000..be367ff --- /dev/null +++ b/src/py/crankshaft/test/fixtures/neighbors_getis.json @@ -0,0 +1 @@ +[{"neighbors": [3, 6, 7], "id": 1, "value": 1.624458}, {"neighbors": [10, 5, 8], "id": 2, "value": 2.2554919999999998}, {"neighbors": [1, 4, 7], "id": 3, "value": 1.4678899999999999}, {"neighbors": [9, 3, 5, 7], "id": 4, "value": 2.4842559999999998}, {"neighbors": [9, 2, 4, 10], "id": 5, "value": 0.0}, {"neighbors": [1, 11, 12, 7, 16], "id": 6, "value": 9.0486730000000009}, {"neighbors": [1, 3, 4, 6, 9, 11, 18, 19], "id": 7, "value": 6.0294889999999999}, {"neighbors": [2, 15, 10], "id": 8, "value": 1.8003849999999999}, {"neighbors": [4, 5, 7, 10, 13, 19, 20], "id": 9, "value": 4.581251}, {"neighbors": [2, 5, 8, 9, 13, 15, 17, 20, 21], "id": 10, "value": 3.7906070000000001}, {"neighbors": [18, 6, 7, 16], "id": 11, "value": 1.4474359999999999}, {"neighbors": [16, 6, 14], "id": 12, "value": 1.1919660000000001}, {"neighbors": [9, 10, 20], "id": 13, "value": 0.0}, {"neighbors": [12, 22, 16], "id": 14, "value": 1.608017}, {"neighbors": [17, 10, 23, 8], "id": 15, "value": 1.9498120000000001}, {"neighbors": [6, 11, 12, 14, 18, 22, 27, 28], "id": 16, "value": 0.74509000000000003}, {"neighbors": [10, 15, 21, 23, 26, 30], "id": 17, "value": 4.1733180000000001}, {"neighbors": [33, 7, 11, 16, 19, 27, 32], "id": 18, "value": 3.7832520000000001}, {"neighbors": [33, 7, 9, 18, 20, 24], "id": 19, "value": 2.0851359999999999}, {"neighbors": [9, 10, 13, 19, 21, 24], "id": 20, "value": 2.1763020000000002}, {"neighbors": [35, 10, 17, 20, 24, 26], "id": 21, "value": 6.3093469999999998}, {"neighbors": [28, 29, 14, 16], "id": 22, "value": 10.855743}, {"neighbors": [17, 25, 31, 30, 15], "id": 23, "value": 4.211354}, {"neighbors": [33, 19, 20, 21, 35], "id": 24, "value": 0.80481000000000003}, {"neighbors": [42, 31, 23], "id": 25, "value": 3.2153309999999999}, {"neighbors": [17, 34, 35, 21, 30], "id": 26, "value": 2.8336640000000002}, {"neighbors": [36, 39, 41, 16, 18, 28, 32], "id": 27, "value": 1.5920399999999999}, {"neighbors": [27, 36, 29, 22, 16], "id": 28, "value": 1.5711580000000001}, {"neighbors": [36, 28, 22, 38], "id": 29, "value": 3.1275900000000001}, {"neighbors": [34, 43, 17, 23, 26, 31], "id": 30, "value": 4.4168960000000004}, {"neighbors": [42, 43, 44, 23, 25, 30], "id": 31, "value": 3.0174859999999999}, {"neighbors": [33, 18, 27, 41], "id": 32, "value": 9.9242450000000009}, {"neighbors": [35, 37, 40, 41, 46, 18, 19, 24, 32], "id": 33, "value": 7.9739570000000004}, {"neighbors": [26, 35, 43, 45, 30], "id": 34, "value": 5.0054639999999999}, {"neighbors": [33, 34, 37, 40, 45, 21, 24, 26], "id": 35, "value": 2.4638909999999998}, {"neighbors": [38, 39, 47, 27, 28, 29], "id": 36, "value": 0.0}, {"neighbors": [33, 35, 40, 45, 46, 49, 51], "id": 37, "value": 7.377974}, {"neighbors": [36, 29, 47, 48], "id": 38, "value": 1.0038750000000001}, {"neighbors": [36, 41, 47, 50, 52, 27], "id": 39, "value": 3.1900469999999999}, {"neighbors": [33, 35, 37, 46], "id": 40, "value": 45.905405999999999}, {"neighbors": [33, 39, 46, 50, 27, 32], "id": 41, "value": 2.447597}, {"neighbors": [25, 44, 53, 31], "id": 42, "value": 1.2949580000000001}, {"neighbors": [34, 44, 45, 54, 59, 61, 30, 31], "id": 43, "value": 5.9330980000000002}, {"neighbors": [42, 43, 53, 54, 31], "id": 44, "value": 4.1339969999999999}, {"neighbors": [34, 35, 37, 43, 51, 59, 60], "id": 45, "value": 4.298311}, {"neighbors": [33, 37, 40, 41, 49, 50, 57], "id": 46, "value": 27.483827000000002}, {"neighbors": [36, 38, 39, 48, 52, 55, 56], "id": 47, "value": 0.96979099999999996}, {"neighbors": [55, 38, 47], "id": 48, "value": 0.0}, {"neighbors": [57, 51, 37, 46, 63], "id": 49, "value": 2.934466}, {"neighbors": [39, 41, 46, 52, 57, 58], "id": 50, "value": 4.4564269999999997}, {"neighbors": [37, 45, 49, 60, 63, 64], "id": 51, "value": 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54, 72], "id": 65, "value": 1.618018}, {"neighbors": [67, 68, 73, 76, 57, 58, 62], "id": 66, "value": 4.9108010000000002}, {"neighbors": [66, 71, 73, 75, 76, 57, 63, 64], "id": 67, "value": 1.991457}, {"neighbors": [73, 66, 62], "id": 68, "value": 3.1461920000000001}, {"neighbors": [70, 72, 74, 77, 59, 61], "id": 69, "value": 7.2666500000000003}, {"neighbors": [69, 71, 74, 78, 59, 60, 64], "id": 70, "value": 3.1109040000000001}, {"neighbors": [67, 75, 70, 78, 64], "id": 71, "value": 2.9802710000000001}, {"neighbors": [65, 69, 61, 77], "id": 72, "value": 3.8667669999999998}, {"neighbors": [76, 66, 67, 68], "id": 73, "value": 1.8684080000000001}, {"neighbors": [77, 69, 70, 78], "id": 74, "value": 12.577033999999999}, {"neighbors": [67, 76, 78, 71], "id": 75, "value": 7.8035990000000002}, {"neighbors": [73, 66, 67, 75], "id": 76, "value": 3.4714900000000002}, {"neighbors": [74, 69, 72], "id": 77, "value": 4.334822}, {"neighbors": [74, 75, 70, 71], "id": 78, "value": 8.4515370000000001}] diff --git a/src/py/crankshaft/test/test_clustering_getis.py b/src/py/crankshaft/test/test_clustering_getis.py new file mode 100644 index 0000000..835a121 --- /dev/null +++ b/src/py/crankshaft/test/test_clustering_getis.py @@ -0,0 +1,74 @@ +import unittest +import numpy as np + + +# from mock_plpy import MockPlPy +# plpy = MockPlPy() +# +# import sys +# sys.modules['plpy'] = plpy +from helper import plpy, fixture_file + +import crankshaft.clustering as cc +import crankshaft.pysal_utils as pu +from crankshaft import random_seeds +import json + +# Fixture files produced as follows +# +# import pysal as ps +# import numpy as np +# import random +# +# # setup variables +# f = ps.open(ps.examples.get_path("stl_hom.dbf")) +# y = np.array(f.by_col['HR8893']) +# w_queen = ps.queen_from_shapefile(ps.examples.get_path("stl_hom.shp")) +# +# out_queen = [{"id": index + 1, +# "neighbors": [x+1 for x in w_queen.neighbors[index]], +# "value": val} for index, val in enumerate(y)] +# +# with open('neighbors_queen_getis.json', 'w') as f: +# f.write(str(out_queen)) +# +# random.seed(1234) +# np.random.seed(1234) +# lgstar_queen = ps.esda.getisord.G_Local(y, w_queen, star=True, +# permutations=999) +# +# with open('getis_queen.json', 'w') as f: +# f.write(str(zip(lgstar_queen.z_sim, +# lgstar_queen.p_sim, lgstar_queen.p_z_sim))) + + +class GetisTest(unittest.TestCase): + """Testing class for Getis-Ord's G* funtion + This test replicates the work done in PySAL documentation: + https://pysal.readthedocs.io/en/v1.11.0/users/tutorials/autocorrelation.html#local-g-and-g + """ + + def setUp(self): + plpy._reset() + + # load raw data for analysis + self.neighbors_data = json.loads( + open(fixture_file('neighbors_getis.json')).read()) + + # load pre-computed/known values + self.getis_data = json.loads( + open(fixture_file('getis.json')).read()) + + def test_getis_ord(self): + """Test Getis-Ord's G*""" + data = [{'id': d['id'], + 'attr1': d['value'], + 'neighbors': d['neighbors']} for d in self.neighbors_data] + plpy._define_result('select', data) + random_seeds.set_random_seeds(1234) + result = cc.getis_ord('subquery', 'value', + 'queen', None, 999, 'the_geom', 'cartodb_id') + result = [(row[0], row[1]) for row in result] + expected = np.array(self.getis_data)[:, 0:2] + for ([res_z, res_p], [exp_z, exp_p]) in zip(result, expected): + self.assertAlmostEqual(res_z, exp_z, delta=1e-2)