MDS Flashcards
(9 cards)
What is the main purpose of Multidimensional Scaling (MDS)?
To take a distance matrix and embed points in a Euclidean space so that the pairwise distances are preserved as closely as possible.
Why might we use MDS instead of traditional dimensionality reduction?
MDS is used when original features are unavailable, subjective, historical, or when it’s better to let users define similarity intuitively (e.g., surveys, ancient artifacts).
What does Kruskal’s STRESS1 measure?
It measures how well the distances in the low-dimensional embedding match the original distances; lower values indicate better fit.
STRESS1 > 0.1 is considered poor, < 0.05 is considered good.
What is the ‘elbow rule’ in MDS?
A method to select the optimal number of dimensions by plotting STRESS against dimensions and finding the point where improvements start diminishing.
Can flips and rotations change MDS results?
No, distances remain the same under flips, rotations, or reflections, so embeddings may look different but still be valid.
Describe the process of embedding with MDS.
Start with a distance matrix, choose metric or non-metric MDS, optimize to minimize STRESS, and interpret the embedding.
What are the tradeoffs in MDS?
Increasing dimensions reduces STRESS (improves fit) but makes interpretation harder. There’s a balance between accuracy and interpretability.
How do small distance matrices help understand MDS?
They allow manual embedding and geometric reasoning (e.g., forming triangles with known side lengths).
What does non-metric MDS preserve?
The rank order of distances rather than their exact values.
