# VB NMF Ordered Connectivity Matrix Example

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```Imports System.Text

Imports CenterSpace.NMath.Core

Imports System.IO

Public Class NMFOrderedConnectivityMatrixExample

A .NET example in Visual Basic showing how to create an ordered connectivity matrix to display the results of
NMF clustering.

An ordered connectivity matrix is created by taking a connectivity matrix
and reordering the rows and columns so that the most affiliated elements
appear as clustered values along the diagonal. The reordering is determined
as follows:

First a hierarchical cluster analysis is performed on the elements
represented in the connectivity matrix. For the purpose of clustering
the elements represented in the connectivity matrix are labeled 0, 1,
2,...,n-1, where n is the number of the elements.

Given two integers, i and j, the provided distance function should return
the distance between the ith and jth elements. If no distance function is
provided the default distance function returns the value 1.0 - aij for
the distance between the ith and jth elements, where aij is the i, jth
element of the connectivity matrix A.

After the hierarchical clustering process, the leaf nodes of the
dendrogram produced from the results are traversed in order to produce a
permutation vector. This permutation vector is used to reorder the rows
and columns of the input connectivity matrix, causing the most affiliated
elements to appear as clusters of higher values along the diagonal.

The connectivity matrix used in this example is an NMFConsensusMatrix which
is the result of using a Nonnegative Matrix Factorization (NMF) to cluster a set
of samples.  The display in the example is a "heat map" with tightly clustered
elements colored in darker "hotter" colors (red, orange, yellow) which "cooler"
colors (green and blue) being used for the more loosely affiliated elements.

Private HeatMap As Bitmap
Colors to use in the bitmap.

Private Colors As New List(Of Color)()
The heat map.

Sub Painting(ByVal sender As System.Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles MyBase.Paint
If (HeatMap Is Nothing) Then
Initialize()
End If
Dim BmpUpperLeftRow As Integer = 10
Dim BmpUpperLeftCol As Integer = 10
e.Graphics.DrawImage(HeatMap, BmpUpperLeftCol, BmpUpperLeftRow)
End Sub

Private Sub Initialize()

Height = 650
Width = 630

Colors to use in the heat map. The colors range from
reds and oranges, for highly affiliated elements, to
greens and blues for loosely affiliated elements.

First read in some data to cluster. In this example columns in the
the data frame represent samples to which we will apply a Nonnegative
Matrix Factorization (NMF) to get a connectivity matrix in the form of a
NMFConsensusMatrix.
Dim Data As DataFrame = DataFrame.Load("nmf_data.dat", True, True, ControlChars.Tab, True)

Order of the NMF.
Dim K As Integer = 3

Number of factorizations to use in constructing the consensus matrix.
Dim NumberOfRuns As Integer = 25

Construct the consensus matrix using a Gradient Descent, Constrained Least
Squares iterative algorithm.
Dim ConsensusMatrix As New NMFConsensusMatrix(Of NMFGdClsUpdate)(Data, K, NumberOfRuns)

Construct the ordered connectivity matrix from the consensus matrix.
Dim OrderedConsensusMatrix As New OrderedConnectivityMatrix(ConsensusMatrix)

Construct and display the heat map by displaying the number in the ordered consensus matrix
a pixels whose colors are "hotter" (red, orange) for higher values (highly affiliated), and
cooler (green, yellow) for smaller values (less affiliated). Note that all the numbers in the
consensus matrix are between 0 and 1.
Dim BlockSize As Integer = 600 / OrderedConsensusMatrix.Order
Dim S As Integer = (BlockSize + 1) * OrderedConsensusMatrix.Order
HeatMap = New Bitmap(S, S)
Dim RowOffset As Integer = 0
Dim ColumnOffset = 0
Dim I As Integer
Dim J As Integer
Dim C As Color
Dim BI As Integer
Dim BJ As Integer
For I = 0 To (OrderedConsensusMatrix.Order - 1)
For J = 0 To (OrderedConsensusMatrix.Order - 1)
C = GetColor(OrderedConsensusMatrix(I, J))
For BI = RowOffset To (RowOffset + BlockSize - 1)
For BJ = ColumnOffset To (ColumnOffset + BlockSize - 1)
HeatMap.SetPixel(BI, BJ, C)
Next
Next
ColumnOffset += BlockSize
Next
ColumnOffset = 0
RowOffset += BlockSize
Next

End Sub

Private Function GetColor(ByVal P As Double) As Color

If (P = 1.0) Then
Return Colors(0)
End If
If (P >= 0.9) Then
Return Colors(1)
End If
If (P >= 0.8) Then
Return Colors(2)
End If
If (P >= 0.7) Then
Return Colors(3)
End If
If (P >= 0.6) Then
Return Colors(4)
End If
If (P >= 0.5) Then
Return Colors(5)
End If
If (P >= 0.4) Then
Return Colors(6)
End If
If (P >= 0.3) Then
Return Colors(7)
End If
If (P >= 0.2) Then
Return Colors(8)
End If
If (P >= 0.1) Then
Return Colors(9)
End If
Return Color.MidnightBlue

End Function

End Class

```
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