Global Spatial Projections

This example demonstrates how dimensionality reduction can be used for geospatial analysis by using a specialized metric.

Most dimensionality reduction techniques use euclidean distance by default, which works fine for flat planes. However, when working with coordinates on the Earth's surface, the Curvature of the Earth becomes significant.

Using the Haversine Distance (Great-Circle Distance) ensures that the distance between two points is calculated correctly along the sphere.

Projecting world cities using the spherical Haversine metric and SMACOF.

Projecting...

Regions

Africa

Americas

Asia

Europe

Oceania

This projection uses the Haversine Distance to correctly calculate distances along the Earth's curved surface.

Hover over points in the scatterplot to see the city names!

Why use Haversine?

• Spherical Accuracy: Traditional Euclidean distance "tunnels" through the Earth, while Haversine follows the surface.
• Metric-Aware DR: DruidJS allows you to swap metrics easily. Here, we use SMACOF (Metric MDS) with metric: 'haversine'.
• Topological Clusters: Notice how cities cluster by continent (Oceania, Europe, Americas, etc.) naturally based on their real-world proximity.

City Dataset

We are projecting 100 major world cities based solely on their latitude and longitude coordinates.

How-to (Code)

To use the haversine metric, ensure your coordinates are in radians. You can then pass the haversine metric function to algorithms like UMAP or MDS.

import * as druid from "@saehrimnir/druidjs";

// Helper to convert degrees to radians
const toRad = (d) => (d * Math.PI) / 180;

// Cities [lat, lon] in radians
const data = [
  [toRad(35.68), toRad(139.69)], // Tokyo
  [toRad(40.71), toRad(-74.01)], // New York
  // ... more cities
];

// Initialize SMACOF with the haversine metric
const smacof = new druid.SMACOF(data, {
  metric: druid.haversine,
  d: 2,
});

// Run the iterative optimization
const projection = smacof.transform(500);