Max-p

The max-p-region problem is a special case of constrained clustering where a finite number of geographical areas are aggregated into the maximum number of regions (max-p-regions), such that each region is geographically connected and the clusters could maximize internal homogeneity.
maxpGreedy()
A simulated annealing algorithm to solve the max-p-region problem
function maxpGreedy(
    WeightResult w,
    Array vals,
    Number iterations,
    Array min_bound_values, 
    Array min_bounds,
    Array max_bound_values, 
    Array max_bounds,
    String scale_method,
    String distance_type,
    Number seed)
​
Arguments
Name
Type
Description
weights
WeightsResult
The weights object WeightsResult
vals
Array
The list of numeric vectors of selected variable.
iterations
Number
The number of iterations of greedy algorithm. Defaults to 1.
min_bounds_values
Array
The list of numeric array of selected minimum bounding variables.
min_bounds
Array
The list of minimum value that the sum value of bounding variables in each cluster should be greater than.
max_bounds_values
Array
The list of numeric array of selected maximum bounding variables.
max_bounds
Array
The list of minimum value that the sum value of bounding variables in each cluster should be less than.
scale_method
String
The scaling methods {'raw', 'standardize', 'demean', 'mad', 'range_standardize', 'range_adjust'}. Defaults to 'standardize'.
distance_method
String
The distance methods {"euclidean", "manhattan"}. Defaults to 'euclidean'.
seed
Number
The seed for random number generator
Return
Type
Description
ClusteringResult
The Clustering object: {'total_ss', 'within_ss', 'between_ss', 'ratio', 'clusters'}
Examples
Node.js
React
const jsgeoda = require('jsgeoda');
const fs = require('fs');
​
// load data
const data = fs.readFileSync('./data/natregimes.geojson').buffer;
​
// create jsgeoda instance
const geoda = await jsgeoda.New();
​
// load geojson in jsgeoda
const nat = geoda.readGeoJSON(data);
​
// create a queen contiguity weights
const w = geoda.getQueenWeights(nat);
​
// get values
const hr60 = geoda.getColumn(nat, "HR60");
const ue60 = geoda.getColumn(nat, "UE60");
​
// set minimum bound
const po60 = geoda.getColumn(nat, "PO60");
​
// apply azp_greedy
const min_bound_vals = [po60];
const min_bounds = [17845200];
const azp = geoda.maxp_greedy(w, [hr60, ue60], 49, min_bound_vals,min_bounds);
​
import React, { Component } from "react";
import ReactDOM from "react-dom";
import DeckGL from "@deck.gl/react";
import { GeoJsonLayer } from "@deck.gl/layers";
import { StaticMap } from "react-map-gl";
import colorbrewer from "colorbrewer";
import jsgeoda from "jsgeoda";
​
// Set your mapbox access token here
const MAPBOX_TOKEN =
  "pk.eyJ1IjoibGl4dW45MTAiLCJhIjoiY2locXMxcWFqMDAwenQ0bTFhaTZmbnRwaiJ9.VRNeNnyb96Eo-CorkJmIqg";
​
// The geojson data
const DATA_URL = `https://webgeoda.github.io/data/natregimes.geojson`;
​
class App extends Component {
  constructor() {
    super();
    this.state = {
      mapId: "",
      layer: null,
      viewPort: {
        longitude: -100.4,
        latitude: 38.74,
        zoom: 2.5,
        maxZoom: 20
      }
    };
  }
​
  // load spatial data when mount this component
  loadSpatialData(geoda) {
    fetch(DATA_URL)
      .then((res) => res.arrayBuffer())
      .then((data) => {
        // load geojson in jsgeoda, an unique id (string) will be returned for further usage
        const nat = geoda.readGeoJSON(data);
        const w = geoda.getQueenWeights(nat);
        const hr60 = geoda.getColumn(nat, "HR60");
        const ue60 = geoda.getColumn(nat, "UE60");
        const po60 = geoda.getColumn(nat, "PO60");
        const redcap = geoda.skater(w, 10, [hr60, ue60], 17845200, po60);
        //const redcap = geoda.schc(w, 10, [hr60, ue60], 'ward', 17845200, po60);
        //const redcap = geoda.redcap(w, 10, [hr60, ue60], "fullorder-wardlinkage", 17845200, po60);
        //const azp = geoda.azpGreedy(w, 20, [hr60, ue60], 1, [], [po60],[17845200]);
        //const redcap = geoda.azpTabu(w, 20, [hr60, ue60], 10, 10, 1, [], [po60],[17845200]);
        //const redcap = geoda.azpSA(w, 20, [hr60, ue60], 0.85, 1, 1, [], [po60],[17845200]);
        //const redcap = geoda.maxpGreedy(w, [hr60, ue60],  1, [po60],[17845200]);
        const colors = colorbrewer["Paired"][10].map((c) =>
          c
            .toLowerCase()
            .match(/[0-9a-f]{2}/g)
            .map((x) => parseInt(x, 16))
        );
​
        // Viewport settings
        const view_port = geoda.get_viewport(
          nat,
          window.innerHeight,
          window.innerWidth
        );
​
        // Create GeoJsonLayer
        const layer = new GeoJsonLayer({
          id: "GeoJsonLayer",
          data: DATA_URL,
          filled: true,
          getFillColor: (f) => this.getFillColor(f, redcap.clusters, colors),
          stroked: true,
          pickable: true
        });
​
        // Trigger to draw map
        this.setState({
          mapId: nat,
          layer: layer,
          viewPort: view_port
        });
      });
  }
​
  componentDidMount() {
    // jsgeoda.New() function will create an instance from WASM
    jsgeoda.New().then((geoda) => {
      this.loadSpatialData(geoda);
    });
  }
​
  // Determine which color for which geometry
  getFillColor(f, clusters, colors) {
    const i = f.properties.POLY_ID - 1;
    const c = clusters[i] - 1;
    return colors[c];
  }
​
  render() {
    return (
      <div>
        <DeckGL
          initialViewState={this.state.viewPort}
          layers={[this.state.layer]}
          controller={true}
          getTooltip={({ object }) =>
            object && `${object.properties.NAME}: ${object.properties.HR60}`
          }
        >
          <StaticMap mapboxApiAccessToken={MAPBOX_TOKEN} />
        </DeckGL>
      </div>
    );
  }
}
​
ReactDOM.render(<App />, document.getElementById("root"));
​
​
Try it yourself in the playground (jsgeoda + deck.gl):
​
maxpSA()
A simulated annealing algorithm to solve the max-p-region problem
function maxpSA(
    WeightResult w,
    Array vals,
    Number cooling_rate,
    Number sa_maxit,
    Number iteration,
    Array min_bound_values, 
    Array min_bounds,
    Array max_bound_values, 
    Array max_bounds,
    String scale_method,
    String distance_type,
    Number seed)
​
Arguments
Name
Type
Description
weights
WeightsResult
The weights object WeightsResult
values
Array
The list of numeric vectors of selected variable.
cooling_rate
Number
The cooling rate of a simulated annealing algorithm. Defaults to 0.85
sa_maxit
Number
The number of iterations of simulated annealing. Defaults to 1
iterations
Number
The number of iterations of greedy algorithm. Defaults to 1.
min_bounds_values
Array
The list of numeric array of selected minimum bounding variables.
min_bounds
Array
The list of minimum value that the sum value of bounding variables in each cluster should be greater than.
max_bounds_values
Array
The list of numeric array of selected maximum bounding variables.
max_bounds
Array
The list of minimum value that the sum value of bounding variables in each cluster should be less than.
scale_method
String
The scaling methods {'raw', 'standardize', 'demean', 'mad', 'range_standardize', 'range_adjust'}. Defaults to 'standardize'.
distance_method
String
The distance methods {"euclidean", "manhattan"}. Defaults to 'euclidean'.
seed
Number
The seed for random number generator.
Return
Type
Description
ClusteringResult
The Clustering object: {'total_ss', 'within_ss', 'between_ss', 'ratio', 'clusters'}
maxpTabu()
A simulated annealing algorithm to solve the max-p-region problem
function maxpTabu (
    WeightResult w,
    Array vals,
    Number tabu_length,
    Number conv_tabu,
    Number iterations,
    Array min_bound_values, 
    Array min_bounds,
    Array max_bound_values, 
    Array max_bounds,
    String scale_method,
    String distance_type,
    Number seed)
​
Arguments
weights
WeightsResult
The weights object WeightsResult
values
Array
The list of numeric vectors of selected variable.
tabu_length
Number
The length of a tabu search heuristic of tabu algorithm. Defaults to 10.
conv_tabu
Number
The number of non-improving moves. Defaults to 10.
iterations
Number
The number of iterations of greedy algorithm. Defaults to 1.
min_bounds_values
Array
The list of numeric array of selected minimum bounding variables.
min_bounds
Array
The list of minimum value that the sum value of bounding variables in each cluster should be greater than.
max_bounds_values
Array
The list of numeric array of selected maximum bounding variables.
max_bounds
Array
The list of minimum value that the sum value of bounding variables in each cluster should be less than.
scale_method
String
The scaling methods {'raw', 'standardize', 'demean', 'mad', 'range_standardize', 'range_adjust'}. Defaults to 'standardize'.
distance_method
String
The distance methods {"euclidean", "manhattan"}. Defaults to 'euclidean'.
seed
Number
The seed for random number generator.
Return
Type
Description
ClusteringResult
The Clustering object: {'total_ss', 'within_ss', 'between_ss', 'ratio', 'clusters'}

Last modified 2yr ago

Name	Type	Description
`weights`	WeightsResult	The weights object `WeightsResult`
`vals`	Array	The list of numeric vectors of selected variable.
`iterations`	Number	The number of iterations of greedy algorithm. Defaults to 1.
`min_bounds_values`	Array	The list of numeric array of selected minimum bounding variables.
`min_bounds`	Array	The list of minimum value that the sum value of bounding variables in each cluster should be greater than.
`max_bounds_values`	Array	The list of numeric array of selected maximum bounding variables.
`max_bounds`	Array	The list of minimum value that the sum value of bounding variables in each cluster should be less than.
`scale_method`	String	The scaling methods {'raw', 'standardize', 'demean', 'mad', 'range_standardize', 'range_adjust'}. Defaults to 'standardize'.
`distance_method`	String	The distance methods {"euclidean", "manhattan"}. Defaults to 'euclidean'.
`seed`	Number	The seed for random number generator

Type	Description
ClusteringResult	The Clustering object: {'total_ss', 'within_ss', 'between_ss', 'ratio', 'clusters'}