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

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);

React

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'}