Multidimensional Scaling (MDS)

Multidimensional scaling (MDS) is a dimensionality reduction technique that places observations in a low-dimensional space so that distances between points approximate their original pairwise dissimilarities.

다차원척도법(MDS)은 점들 사이의 거리가 원래의 쌍별 비유사도를 근사하도록 관측값을 저차원 공간에 배치하는 차원축소 기법이다.

How do I visualize similarities between items or cases on a two-dimensional map?

항목이나 사례 간 유사성을 2차원 지도로 어떻게 시각화하나요?

Multidimensional scaling turns a matrix of pairwise distances or dissimilarities into a low-dimensional map where similar cases appear close together. It fits perceptual mapping and exploratory visualization, with metric MDS preserving distances and nonmetric MDS preserving their rank order.

When to use Multidimensional Scaling (MDS)

• Pairwise dissimilarities among cases, brands or stimuli
• Building a two-dimensional perceptual map
• Exploring structure in data computed with a non-Euclidean distance

When to use something else

• Interpretable linear components of variance are needed; use principal component analysis
• Preserving local neighborhoods in large high-dimensional data; use t-SNE or UMAP

Assumptions and requirements

• Meaningful dissimilarity measure
• Number of dimensions chosen in advance
• Metric MDS assumes interval-level distances; nonmetric MDS uses only rank order

What the analysis reports

• Coordinates for each observation
• Stress value
• Shepard diagram
• Two-dimensional configuration plot

How to report it

A two-dimensional nonmetric MDS solution was obtained with a stress value of [value].

Related methods

• Principal Component Analysis
• t-SNE
• Correspondence Analysis

Run Multidimensional Scaling (MDS) on Quorant