Multidimensional Scaling (MDS)

Algorithm overview

Multidimensional scaling using classical MDS algorithm.

Classical MDS converts a distance matrix into a centered similarity matrix and computes its dominant eigenvectors to recover coordinates that preserve the original pairwise dissimilarities.

MDS embeds points into lower dimensions while preserving pairwise distances as much as possible.

This algorithm is especially useful when:

• Distance geometry is more important than original feature axes.
• You need interpretable 2D/3D maps for exploratory analysis.
• You are comparing similarity relationships across entities.

JavaScript implementation

@kanaries/ml makes classical multidimensional scaling available in JavaScript for cases where you care more about preserving pairwise distances than about modeling the original feature axes directly. That is useful in browser-based visualization tools, similarity explorers, and Node.js analytics pipelines that already work from distance matrices.

Because MDS often feeds directly into charts and exploratory interfaces, keeping it inside the JS layer is especially practical for frontend-heavy products.

Quick start

from sklearn.manifold import MDS

X = [[0, 0, 1], [0, 1, 1], [1, 0, 0], [1, 1, 0]]

mds = MDS(n_components=2, random_state=0)
embedding = mds.fit_transform(X)

import { Manifold } from '@kanaries/ml';

const X = [[0, 0, 1], [0, 1, 1], [1, 0, 0], [1, 1, 0]];

const mds = new Manifold.MDS({ nComponents: 2 });
const embedding = mds.fitTransform(X);

Quick JavaScript example

import { Manifold } from '@kanaries/ml';

const X = [[0, 0, 1], [0, 1, 1], [1, 0, 0], [1, 1, 0]];

const mds = new Manifold.MDS({ nComponents: 2 });
const embedding = mds.fitTransform(X);

Detailed API reference

interface MDSOptions {
    nComponents?: number;
    dissimilarity?: 'euclidean' | 'precomputed';
}
constructor(options: MDSOptions = {})

Options

• nComponents (number, default 2): dimension of the embedded space.
• dissimilarity ('euclidean' | 'precomputed', default 'euclidean'): if 'precomputed', the input to fitTransform should be a distance matrix.

fitTransform(data: number[][]): number[][] computes the embedding and returns it.

getEmbedding(): number[][] returns the computed embedding.

Implementation workflow

1. Choose or compute a distance matrix aligned with your domain.
2. Fit MDS with target component count for visualization.
3. Validate stress/error and inspect neighborhood preservation quality.

JavaScript deployment notes

• Use MDS when your core input is a distance or dissimilarity structure rather than a traditional feature matrix.
• It is especially valuable for interactive visualization and exploratory analysis rather than high-throughput production inference.
• Watch dataset size because pairwise distance handling can become expensive quickly.