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Shape Preserver ​

This example illustrates the difference between algorithms that focus on Local Probabilities vs. Topological Preservation.

When visualizing complex, disjoint, or non-convex manifolds (like the "Two Moons" dataset), standard techniques like t-SNE can sometimes "shatter" the continuous structure as they try to flatten the points into 2D based on local similarity.

Calculating projections...

Comparison Details ​

  • t-SNE: Excels at revealing fine-grained clusters, but it doesn't strictly preserve the global or topological shape. In the Moons dataset, it often separates the points into clusters that lose the continuous "arc" shape.
  • TopoMap: A specialized algorithm that guarantees the preservation of 0-dimensional topology. It uses Minimum Spanning Trees (MST) to ensure that the skeletal structure of the manifold stays intact, resulting in a cleaner preservation of the continuous arcs.

Choosing the right algorithm depends on whether you care more about density/sub-clusters (use t-SNE/UMAP) or the underlying structure and continuity of your data (use TopoMap).

How-to (Code) ​

TopoMap provides a simple interface consistent with other DR algorithms in DruidJS. It is particularly effective for high-dimensional data that forms continuous shapes. You can find out more in the TopoMap API Reference.

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

const data = [
  /* ... multi-dimensional data ... */
];

// Initialize TopoMap
const topomap = new druid.TopoMap(data);

// Project into 2D
// Topomap is non-iterative, so it returns the result directly
const projection = topomap.transform();