LTSA
Local Tangent Space Alignment (LTSA) characterizes the local geometry of the data manifold using the tangent spaces at each data point, and then aligns these local tangent spaces to construct the global coordinate.
How It Works
Local Tangent Space Alignment (LTSA) computes the tangent space at each data point using its nearest neighbors. It then aligns these local tangent spaces to construct a global low-dimensional coordinate system.
Why or When to Use
Use LTSA for unfolding highly nonlinear and complex manifolds where the tangent space provides a good local approximation.
Example
How-to (Code)
import * as druid from "@saehrimnir/druidjs";
const data = [
/* ... multi-dimensional data ... */
];
// 1. Initialize the algorithm
const ltsa = new druid.LTSA(data);
// 2. Compute the projection
const projection = ltsa.transform();Larger Datasets
LTSA collects a local neighborhood around every point before aligning their tangent spaces. 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:
const knn = new druid.HNSW(data, { metric: druid.euclidean, ef: 100 });
const ltsa = new druid.LTSA(data, { neighbors: 10, knn });