Multidimensional Scaling (MDS) Quiz

Multi-Dimensional Scaling (MDS)

• There are two types of MDS: Classical MDS (metric scaling) and Non-metric MDS (modern MDS), with Non-metric MDS being the most commonly used.

Comparison with Clustering

• Both Clustering and MDS analyze distances (dissimilarities) and cases (individuals)/variables.
• Clustering has a weak or no model and many decisions seem arbitrary.
• MDS has an explicit model, displays distance-like data as a geometrical picture, and each object/case/variable is represented as a point in multidimensional space.

Types of MDS

• Classical MDS uses proximity matrix same as in clustering.
• Non-metric MDS is also known as modern MDS.

Key Concepts

• The goal is to reduce dimensions to obtain a useful simplification of the data (parsimonious model), but avoid over-simplification.
• Mathematically, MDS seeks to reduce the proximity matrix down to lower dimensions (e.g., 2D space).
• Stress is a measure of badness of fit, and the goal is to minimize stress to achieve a good MDS.
• Iterative procedure is used to reduce stress and achieve the best resemblance of proximity matrix.

Stress and Fit

• Lower stress values indicate a better fit.
• Stress is affected by the number of dimensions and variables; more dimensions can result in lower stress, while more variables can result in higher stress.

Interpreting Number of Dimensions

• Method 1: Scree plot can be used to determine the number of dimensions.
• Method 2: Graph can be used for subjective interpretation of dimensions.
• Dimensions may not always have meaning, but are defined by proximity (closeness is evidence of association).

Example of MDS

• MDS can be used to visualize relationships between different latent dimensions, such as cultural variations in expressions of men and women.
• The spatial mapping helps to visualize the relationships, where points close together are similar, and points far apart are dissimilar.