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This report tends to concisely and incisively explain Multidimensional Scaling(MDS), a non-linear projection class of methods which can be used in dimensionality reduction, and thus data visualization of high-dimensional datasets.

The report is composed of four sections:

  1. What is MDS?
  2. How does MDS work? MDS in R
  3. Why MDS? MDS vs. PCA
  4. Conclusion
  5. References

If one prefers video lectures rather than verbal reports, one can have a look at this video …, which is prepared based on the current report by this author.

In a sequent report, I would explain a specific sort of MDS, called Multidimensional Unfolding, which is able to cope with asymmetric data.

1. What is MDS?

let’s start with an intuitive explanation with a familiar dataset.

Figure 1 is the geographical map of 11 cities in US, highlighet by blue markers.