MDS: Multidimensional scaling
2024-03-07
Plan
What is MDS and why do we use it?
Demonstration
Comparison with PCA
What is MDS?
A tool to convert a distance or dissimilarity matrix into a set of points in a plane
Can be based on distances (using one of many metrics) or ranks of dissimilarities, when it is called non-metric MDS (NMDS)
NMDS suitable if you can rank objects as being closer or farther away, but the scale of the quantification is skewed or not important
Cites on a map
MDS analysis
Use latitude and longitude of cities to compute distance between each pair
Use MDS on distance matrix to reconstruct relative positions
Cites on a map
MDS analysis
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Use latitude and longitude of cities to compute distance between each pair
- How do we compute that distance? Euclidean? Great circle?
Use MDS on distance matrix to reconstruct relative positions
Cites on a map
How and when to use MDS?
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When you can compute the similarity of pairs of objects (or distance between pairs).
How similar are the species in two communities?
How similar are two countries based on economic development?
Columns are objects (sample locations, countries)
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Be sure the observations (rows) are all measured in the same units
- Abundance
- Proportions
- Scaling or transformation may be required
How is MDS different from PCA?
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Both make plots of points on abstract axes
- Possibly with arrows showing direction of change of other variables
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Otherwise, completely different methods!
PCA is a rotation and projection of data to select linear combinations of original variables that highlight variation
MDS converts pairwise distance or dissimilarity matrix into relative positions
Further reading
- Code for plots shown here are in the course notes
- An additional example based on Morse code is in the notes
- Data and analysis shows combinations of dots and dashes that are likely to be misinterpreted by recipient
Task
- Practice PCA and MDS methods