Overview MDS (Multidimensional Scaling) finds a low-dimensional representation that preserves pairwise distances between points. It’s useful for visualizing similarity/dissimilarity data.
Constructor new MDS ( options ?: MDSOptions )
Configuration options for MDS Number of dimensions in the embedding space.
dissimilarity
'euclidean' | 'precomputed'
default: "'euclidean'"
Dissimilarity measure:
'euclidean': Compute Euclidean distances from input features'precomputed': Input is a pre-computed distance matrix Seed for random number generator for reproducible results.
Maximum iterations for eigenvalue computation.
Methods fit Compute the MDS embedding from data or distance matrix.
Input data of shape [nSamples, nFeatures] or distance matrix of shape [nSamples, nSamples] if dissimilarity=‘precomputed’
Returns: The fitted MDS instancefitTransform ( X : Matrix ): Matrix
Fit the model and return the embedding.
Input data of shape [nSamples, nFeatures] or distance matrix if dissimilarity=‘precomputed’
Returns: Embedded data of shape [nSamples, nComponents]Properties Embedded coordinates in low-dimensional space, shape [nSamples, nComponents]
Sum of squared distances differences (stress value)
Number of features seen during fit (or number of samples if precomputed)
Example import { MDS } from '@elucidate/elucidate' ; // Example 1: Using Euclidean distances const data = [ [ 1.0 , 2.0 ], [ 1.5 , 2.5 ], [ 3.0 , 4.0 ], [ 3.5 , 4.5 ], [ 5.0 , 6.0 ], ]; const mds = new MDS ({ nComponents: 2 , dissimilarity: 'euclidean' , randomState: 42 }); const embedding = mds . fitTransform ( data ); console . log ( 'Embedded coordinates:' , embedding ); console . log ( 'Stress:' , mds . stress_ ); // Example 2: Using pre-computed distance matrix const distanceMatrix = [ [ 0.0 , 1.0 , 5.0 , 6.0 , 10.0 ], [ 1.0 , 0.0 , 4.0 , 5.0 , 9.0 ], [ 5.0 , 4.0 , 0.0 , 1.0 , 5.0 ], [ 6.0 , 5.0 , 1.0 , 0.0 , 4.0 ], [ 10.0 , 9.0 , 5.0 , 4.0 , 0.0 ], ]; const mdsPrecomputed = new MDS ({ nComponents: 2 , dissimilarity: 'precomputed' }); const embeddingFromDist = mdsPrecomputed . fitTransform ( distanceMatrix ); console . log ( 'Embedding from distances:' , embeddingFromDist );
Notes
MDS uses classical scaling (eigendecomposition of double-centered distance matrix)
Works well when pairwise distances are meaningful
Pre-computed mode is useful for custom distance metrics
The embedding preserves inter-point distances as much as possible