F# Principal Component Example

namespace CenterSpace.NMath.Stats.Examples.FSharp

open System

open CenterSpace.NMath.Core
open CenterSpace.NMath.Stats



  /// <summary>
  /// A .NET example in C# showing how to perform a principal component analysis on a data set.
  /// </summary>
  module PrincipalComponentExample =

      // Read in data from a file. These data give air pollution and related values
      // for 41 U.S. cities.
      //   SO2: Sulfur dioxide content of air in micrograms per cubic meter 
      //   Temp: Average annual temperature in degrees Fahrenheit 
      //   Man: Number of manufacturing enterprises employing 20 or more workers 
      //   Pop: Population size in thousands from the 1970 census 
      //   Wind: Average annual wind speed in miles per hour 
      //   Rain: Average annual precipitation in inches 
      //   RainDays: Average number of days with precipitation per year 
      // Source: http://lib.stat.cmu.edu/DASL/Datafiles/AirPollution.html

      let df = DataFrame.Load("..\\..\\PrincipalComponentExample.dat", true, true, "\t", true)

      Console.WriteLine()
      Console.WriteLine(df.ToString() + "\n")

      // Class DoublePCA performs a double-precision principal component
      // analysis on a given data set. The data may optionally be centered and
      // scaled before analysis takes place. By default, variables are centered
      // but not scaled.
      let pca = new DoublePCA(df)

      // Once your data is analyzed, you can can retrieve information about the data.
      // If centering was specified, the column means are substracted from
      // the column values before analysis takes place. If scaling was specified,
      // column values are scaled to have unit variance before analysis by dividing
      // by the column norm.
      Console.WriteLine("Number of Observations = " + pca.NumberOfObservations.ToString())
      Console.WriteLine("Number of Variables = " + pca.NumberOfVariables.ToString())
      Console.WriteLine()
      Console.WriteLine("Column Means = " + pca.Means.ToString())
      Console.WriteLine()
      Console.WriteLine("Column Norms = " + pca.Norms.ToString())
      Console.WriteLine()
      Console.WriteLine("Data was centered? = " + pca.IsCentered.ToString())
      Console.WriteLine("Data was scaled? = " + pca.IsScaled.ToString())
      Console.WriteLine()

      // The Loadings property gets the loading matrix. Each column is a principal component.
      Console.WriteLine("Loadings = " + pca.Loadings.ToString())
      Console.WriteLine()

      // You can retrieve a particular principal component using the indexer.
      Console.WriteLine("First principal component = " + pca.[0].ToString())
      Console.WriteLine()
      Console.WriteLine("Second principal component = " + pca.[1].ToString())
      Console.WriteLine()

      // The first principal component accounts for as much of the variability in the
      // data as possible, and each succeeding component accounts for as much of the
      // remaining variability as possible.
      Console.WriteLine("Variance Proportions = " + pca.VarianceProportions.ToString())
      Console.WriteLine()
      Console.WriteLine("Cumulative Variance Proportions = " + pca.CumulativeVarianceProportions.ToString())
      Console.WriteLine()

      // You can also get the number of principal components required to account for
      // a given proportion of the total variance. In this case, a plane fit to the
      // original 7-dimensional space accounts for 99% of the variance.
      Console.WriteLine("PCs that account for 99% of the variance = " + pca.Threshold(0.99).ToString())
      Console.WriteLine()

      // The Score matrix is the data formed by transforming the original data into
      // the space of the principal components.
      Console.WriteLine("Scores = " + pca.Scores.ToString())

      Console.WriteLine()
      Console.WriteLine("Press Enter Key")
      Console.Read() |> ignore