namespace CenterSpace.NMath.Examples.FSharp open System open CenterSpace.NMath.Core /// <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← All NMath Code Examples