ï»¿Imports System Imports System.Text Imports CenterSpace.NMath.Core Imports System.IO Namespace CenterSpace.NMath.Core.Examples.VisualBasic ' A .NET example in Visual Basic showing how to compute a consensus matrix averaging different NMF clusterings. ' ' A Nonnegative Matrix Factorization (NMF) is an approximate factorization ' of a positive matrix v into a product of two matrices w and h: ' v ~ wh ' This factorization can by used to group, or cluster, the columns of v ' (the columns of v are usually refered to as "samples"). NMF uses an ' iterative algorithm with random starting values for w and h. This, coupled ' with the fact that the factorization is not unique, means that if you cluster ' the columns of v using an NMF cluster several different times, you may get several ' different clusterings. The NMF consensus matrix is a way to average ' the possibly different clusterings, and is computed using the following process: ' ' Cluster the columns of v using NMF n times. Each NMF clustering will yield ' a "connectivity matrix". The connectivity matrix is a symmetric matrix ' whose i, jth entry is 1 if columns i and j of v were clustered together, ' and 0 if they were not. The "consensus matrix" is also a symmetric matrix ' whose i, jth entry is formed by taking the average of the i, jth entries of ' the n connectivity matrices. ' ' It is clear that each i, jth entry of the consensus matrix has a value between 0 ' (columns i and j were not clustered together on any of the n runs) and 1 (columns ' i and j were clustered together on all n runs). Thus the i, jth entry of a ' consensus matrix may be considered, in some sense, a "probability" that columns ' i and j belong to the same cluster. ' A consensus matrix C may also used to perform a hierarchical clustering of the ' columns of v by using as the distance function: ' ' distance between columns i and j = 1.0 - C[i,j] ' ' This is demonstrated in the example below. Module NMFConsensusMatrixExample Sub Main() ' Read in some data... Dim Data As DataFrame = DataFrame.Load("nmf_data.dat", True, True, ControlChars.Tab, True) ' Extract the data as a DoubleMatrix. Dim V As DoubleMatrix = Data.ToDoubleMatrix() ' Set the order of the NMF (this is the number of columns in w, where ' v ~ wh Dim K As Integer = 3 ' Set the number of runs or connectivity matrices to use to form the ' consensus matrix. Dim NumberOfRuns As Integer = 70 ' Construct a consensus matrix using the "divergence" update ' algorithm. Dim ConsensusMatrix As New NMFConsensusMatrix(Of NMFDivergenceUpdate)(V, Data.ColumnHeaders, K, NumberOfRuns) Console.WriteLine() ' Print out the number of runs in which the NMF algorithm actually converged to an answer, and the ' resulting consensus matrix. Console.WriteLine("{0} runs out of {1} converged.", ConsensusMatrix.NumberOfConvergedRuns, NumberOfRuns) Console.WriteLine() Console.WriteLine("Consensus Matrix:") Console.WriteLine(ConsensusMatrix.ToTabDelimited("G3")) ' Let's look at the first column and for each successive column print out the ' "probability" that they are clustered together (we'll use the column ' names from the data frame instead of column numbers). Dim Label As String = ConsensusMatrix.Labels(0) Console.WriteLine() Dim J As Integer For J = 1 To (ConsensusMatrix.Order - 1) Console.WriteLine("The ""probability"" that {0} is clustered with {1} is {2}", Label, ConsensusMatrix.Labels(J), ConsensusMatrix(0, J)) Next ' Perform a hierarchical cluster analysis using the consensus matrix ' to define the distance function as described in the class description ' above. ' The cluster analysis class wants to cluster the rows of a matrix. Since we ' are essentially clustering a bunch of column numbers, we'll provide a matrix ' with one column and n rows where n is the number of columns of v (and the ' order of of the consensus matrix). The column will contain the numbers 0 ' to n - 1 (basically, we're just clustering the numbers 0,...,n - 1). Dim ItemNumbers As New DoubleMatrix(ConsensusMatrix.Order, 1, 0, 1) ' The distance function object holds the consensus matrix C and returns the distance ' between i and j as 1.0 - C[i,j] Dim DistanceFunctionObject As New ConsensusMatrixDistance(ConsensusMatrix) Dim ClusterAnalysisDist As New Distance.Function(AddressOf DistanceFunctionObject.CaDistance) Dim CA As New ClusterAnalysis(ItemNumbers, ClusterAnalysisDist) ' Form three clusters using the cluster analysis cut tree function and print them out. Dim ClusterS As ClusterSet = CA.CutTree(3) Console.WriteLine() Dim ClusterNumber As Integer Dim I As Integer For ClusterNumber = 0 To (ClusterS.NumberOfClusters - 1) Dim Members() As Integer = ClusterS.Cluster(ClusterNumber) Console.Write("Cluster number {0} contains: ", ClusterNumber) For I = 0 To (Members.Length - 1) Console.Write("{0} ", ConsensusMatrix.Labels(Members(I))) Next Console.WriteLine() Next Console.WriteLine() Console.WriteLine("Press Enter Key") Console.Read() End Sub End Module Class ConsensusMatrixDistance Private ConsensusMatrix As ConnectivityMatrix Public Sub New(ByVal Conn As ConnectivityMatrix) ConsensusMatrix = Conn End Sub Public Function CaDistance(ByVal Data1 As DoubleVector, ByVal Data2 As DoubleVector) As Double Dim I As Integer = Data1(0) Dim J As Integer = Data2(0) Return 1.0 - ConsensusMatrix(I, J) End Function End Class End Namespace← All NMath Stats Code Examples