F# Principal Component Example

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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)

      printfn "%s" (df.ToString())
      printfn ""

      // 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.
      printfn "Number of Observations = %A" pca.NumberOfObservations
      printfn "Number of Variables = %A" pca.NumberOfVariables
      printfn "Column Means = %s" (pca.Means.ToString())
      printfn "Column Norms = %s" (pca.Norms.ToString())
      printfn "Data was centered? = %A" pca.IsCentered
      printfn "Data was scaled? = %A" pca.IsScaled
      printfn ""

      // The Loadings property gets the loading matrix. Each column is a principal component.
      printfn "Loadings = %s" (pca.Loadings.ToString())
      printfn ""

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

      // 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.
      printfn "Variance Proportions = %s" (pca.VarianceProportions.ToString())
      printfn ""
      printfn "Cumulative Variance Proportions = %s" (pca.CumulativeVarianceProportions.ToString())
      printfn ""

      // 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.
      printfn "PCs that account for 99%% of the variance = %s" (pca.Threshold(0.99).ToString())
      printfn ""

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

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

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