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LLE ​

Locally Linear Embedding (LLE) seeks a lower-dimensional projection of the data which preserves distances within local neighborhoods.

How It Works ​

Locally Linear Embedding (LLE) represents each data point as a linear combination of its nearest neighbors. It then finds a low-dimensional embedding that preserves these local linear relationships.

Why or When to Use ​

Use LLE when the data lies on a non-linear manifold and you want to preserve local neighborhood distances (local geometry) while unfolding the manifold.

Example ​

How-to (Code) ​

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

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

// 1. Initialize the algorithm
const lle = new druid.LLE(data);

// 2. Compute the projection
const projection = lle.transform();

Larger Datasets ​

LLE builds a nearest-neighbor graph before solving for the embedding. By default it uses an exact index — a KD-Tree or BallTree, whichever suits the metric — which costs O(N²) on large inputs. Pass any KNN index as knn to swap that out for an approximate one:

javascript
const knn = new druid.HNSW(data, { metric: druid.euclidean, ef: 100 });
const lle = new druid.LLE(data, { neighbors: 10, knn });

The eigenproblem LLE solves tolerates a few incorrect edges, so an approximate graph is usually enough. HNSW, Annoy and NNDescent all work here.