[Feature Request] Add other ordination methods

[kMutagene]

Is your feature request related to a problem? Please describe. Not really a problem. Currently the only implemented ordination method in FSharp.Stats is PCA. PCA is applied on data where a linear relationship is expected and the distance measure of choice is euclidean distance.

Describe the solution you'd like Addition/implementation of the following Multidimensional Scaling algorithms:

• [ ] Principal Coordinates Analysis (PCoA, Classical Multidimensional Scaling'):

  • assumption of linear relationship
  • is similar in spirit to PCA but it takes a dissimilarity as input.
  • Using euclidean distance as distance measure produces the same outcome as PCA, but you can use others (e.g. log-fold change, Jacard)

• [ ] Non-metric multidimensional scaling (nMDS):

  • no linear relationship assumed
  • superset of classical MDS that generalizes the optimization procedure to a variety of loss functions and input matrices of known distances with weights and so on. A useful loss function in this context is called stress, which is often minimized using a procedure called stress majorization
  • non-metric MDS finds both a non-parametric monotonic relationship between the dissimilarities in the item-item matrix and the distances between items, and the location of each item in the low-dimensional space.