KKMDS

Kamada-Kawai multidimensional scaling: StressMDS fixed at weights: -2, so each pair is weighted by the inverse square of its target distance.

How It Works

That objective is the Kamada-Kawai energy from graph drawing, known in the MDS literature as elastic scaling. Minimization is Jacobi-preconditioned gradient descent with a backtracking line search, started from classical MDS on the same distances — the original paper's Newton-Raphson is replaced by a warm start plus preconditioning, which avoids the O(N³) Hessian solves and most of the initialization sensitivity Kamada-Kawai is known for.

Why or When to Use

Its classic use is laying out a graph from its shortest-path distances: pass those as a "precomputed" matrix. MINFOTree does exactly that with its spanning tree.

On ordinary feature data it behaves as the most locally-focused member of the stress family. Reach for StressMDS directly if you want a different weighting; this class exists so the Kamada-Kawai name resolves to the right objective without having to remember which exponent it is.

Example

How-to (Code)

javascript

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

// On feature data
const projection = new druid.KKMDS(data).transform();

// On a graph, from its shortest-path distance matrix
const layout = new druid.KKMDS(graphDistances, { metric: "precomputed" }).transform();

Parameters

Identical to StressMDS, except that weights is fixed at -2 and cannot be overridden.

KKMDS ​

How It Works ​

Why or When to Use ​

Example ​