Data Analysis Mathematics Linear Algebra Statistics
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QuickStart Samples

# Principal Component Analysis (PCA) QuickStart Sample (Visual Basic)

Illustrates how to perform a Principal Components Analysis using classes in the Extreme.Statistics.Multivariate namespace in Visual Basic.

```Option Infer On

Imports Extreme.Mathematics
Imports Extreme.Mathematics.LinearAlgebra.IO
Imports Extreme.Statistics
Imports Extreme.Statistics.Multivariate

Namespace Extreme.Numerics.QuickStart.VB

' Demonstrates how to use classes that implement
' Principal Component Analysis (PCA).
Module PCAnalysis

Sub Main()

' This QuickStart Sample demonstrates how to perform
' a principal component analysis on a set of data.
'
' The classes used in this sample reside in the
' Extreme.Statistics.Multivariate namespace..

' First, our dataset, 'depress.txt', which is from
'     Computer-Aided Multivariate Analysis, 4th Edition
'     by A. A. Afifi, V. Clark and S. May, chapter 16
'     See http:'www.ats.ucla.edu/stat/Stata/examples/cama4/default.htm

' The data is in delimited text format. Use a matrix reader to load it into a matrix.

' The data we want is in columns 8 through 27:
m = m.GetSubmatrix(0, m.RowCount - 1, 8, 27)

'
' Principal component analysis
'

' We can construct PCA objects in many ways. Since we have the data in a matrix,
' we use the constructor that takes a matrix as input.
Dim pca As New PrincipalComponentAnalysis(m)
' and immediately perform the analysis:
pca.Compute()

' We can get the contributions of each component:
Console.WriteLine(" #    Eigenvalue Difference Contribution Contrib. %")
For i As Integer = 0 To 4
' We get the ith component from the model...
Dim component As PrincipalComponent = pca.Components(i)
' and write out its properties
Console.WriteLine("{0,2}{1,12:F4}{1,11:F4}{2,14:F3}%{3,10:F3}%", _
i, component.Eigenvalue, component.EigenvalueDifference, _
100 * component.ProportionOfVariance, _
100 * component.CumulativeProportionOfVariance)
Next

' To get the proportions for all components, use the
' properties of the PCA object:
Dim proportions = pca.VarianceProportions

' To get the number of components that explain a given proportion
' of the variation, use the GetVarianceThreshold method:
Dim count As Integer = pca.GetVarianceThreshold(0.9)
Console.WriteLine("Components needed to explain 90% of variation: {0}", count)
Console.WriteLine()

' The value property gives the components themselves:
Console.WriteLine("Components:")
Console.WriteLine("Var.      1       2       3       4       5")
Dim pcs As PrincipalComponentCollection = pca.Components
For i As Integer = 0 To pcs.Count - 1

Console.WriteLine("{0,4}{1,8:F4}{2,8:F4}{3,8:F4}{4,8:F4}{5,8:F4}", _
i, pcs(0).Value(i), pcs(1).Value(i), pcs(2).Value(i), pcs(3).Value(i), pcs(4).Value(i))
Next
Console.WriteLine()

' The scores are the coefficients of the observations expressed as a combination
' of principal components.
Dim scores = pca.ScoreMatrix

' To get the predicted observations based on a specified number of components,
' use the GetPredictions method.
Dim prediction = pca.GetPredictions(count)
Console.WriteLine("Predictions imports {0} components:", count)
Console.WriteLine("   Pr. 1  Act. 1   Pr. 2  Act. 2   Pr. 3  Act. 3   Pr. 4  Act. 4", count)
For i As Integer = 0 To 9
Console.WriteLine("{0,8:F4}{1,8:F4}{2,8:F4}{3,8:F4}{4,8:F4}{5,8:F4}{6,8:F4}{7,8:F4}",
prediction(i, 0), m(i, 0),
prediction(i, 1), m(i, 1),
prediction(i, 2), m(i, 2),
prediction(i, 3), m(i, 3))
Next

Console.Write("Press any key to exit.")