- 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
- 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).
- 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.
- 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.
- 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.