1. Overview:
   • Multidimensional Scaling is a statistical technique used to visualize the level of similarity or dissimilarity between individual cases in a dataset.
   • It translates “information about the pairwise distances among a set of objects or individuals” into a configuration of points mapped into an abstract Cartesian space.
   • MDS helps reveal hidden structures and relationships in data.
   • It provides a lower-dimensional representation of data while preserving pairwise distances
2. How It Works:
   • Given a distance matrix with distances between each pair of objects, MDS algorithm places each object into an N-dimensional space (lower-dimensional representation).
   • The goal is to preserve the between-object distances as closely as possible.
   • For N = 1, 2, and 3, the resulting points can be visualized on a scatter plot.
   • The output of MDS is a set of points (coordinates) in an N-dimensional space (usually 2D or 3D).
3. Types of MDS:
   • Classical Multidimensional Scaling (PCoA):
     • Takes an input matrix of dissimilarities between pairs of items.
     • Outputs a coordinate matrix that minimizes a loss function called “strain.”
     • Useful for brand similarity studies, product positioning, and market segmentation.
   • Non-Metric MDS:
     • Focuses on ordinal or rank-order data.
     • Preserves rank order rather than exact distances.
     • Useful when exact distances are not available.
4. Applications:
   • Market Research: Brand similarity, product positioning.
   • Psychology: Visualizing relationships, assessing importance of variables.
   • Data Visualization: Representing high-dimensional data in a lower-dimensional space.
5. Strengths and Weaknesses:
   • Advantages:
     • Reveals relationships and similarities.
     • Simplifies complex tables.
     • Useful for large datasets.
   • Disadvantages:
     • Subjective decision-making.
     • Doesn’t deal in real numbers.
     • Requires effort to create the table.