Cluster a correlation matrix

This code demonstrates how you can cluster data using the correlation matrix.

// Create a correlation matrix from fake data, in this case with 2 embedded patterns and
// relative noise of 0.25.  
FakeCorrelationMatrix(2,0.25)

// Cluster the correlation matrix with 2 expected patterns.  
// Picks starting cluster guesses randomly and for high values of noise it might give a poor
// result.   The /SEED=(ticks) flag makes it give random initial guesses on each run.  
CorrelationClustering(2,Fake_Corr_Matrix)

// Display the data with cluster assignment, the original correlation matrix, and the clustered correlation matrix.  
Graph0(); Graph1(); Graph2()

// Create fake data and a correlation matrix from it.  
Function FakeCorrelationMatrix(num_patterns,relative_noise)
    Variable num_patterns // The number of patterns in the fake data.  
    Variable relative_noise // The standard deviation of the noise relative to the signal.  
    Variable length=50 // Each pattern should have this length.  
    Variable num_signals=30 // The number of cells/channels/signals in the fake data.  
    Make /o/n=(length,num_patterns) Base_Patterns=gnoise(1) // Make  a bunch of canonical patterns.  
    Make /o/n=(length,num_signals) Data // The matrix of fake data.  
    Make /o/n=(length,num_signals) Waterfall_Colors=q // Colors for the waterfall plot.  
    Make /o/n=(num_signals) Pattern_Values=floor(abs(enoise(num_patterns))) // The true pattern identities, chosen as an integer 0 to num_patterns-1.  
    Variable i
    for(i=0;i<num_signals;i+=1)
        Data[][i]=Base_Patterns[p][Pattern_Values[i]] // Each row will be a different pattern.  
        Data+=gnoise(relative_noise) // Add noise to everything.  
    endfor
    MatrixOp /O Fake_Corr_Matrix=syncCorrelation(Data) // Compute the covariance matrix.  
    MatrixOp /O Variances=varcols(Data)
    Fake_Corr_Matrix/=sqrt(Variances[p]*Variances[q]) // Convert to degree of correlation.  
    KillWaves /Z Base_Patterns,Variances // Cleanup.  
End

// Cluster a correlation matrix by swapping rows (and columns).  
Function CorrelationClustering(num_patterns,Corr_Matrix)
    Variable num_patterns // Number of patterns that you expect to find.  
    Wave Corr_Matrix // The correlation (or covariance) matrix.  
    KMeans /INIT=1 /NCLS=(num_patterns) /OUT=2 /SEED=(ticks) Corr_Matrix // K-Means clustering.  
    Duplicate /o Corr_Matrix Clustered_Matrix // Prepared the clustered correlation matrix.  
    Duplicate /o W_KMMembers Sorting_Index; Sorting_Index=p
    Sort W_KMMembers,Sorting_Index // Create a sorting index to use to swap out rows (and columns).  
    Clustered_Matrix=Corr_Matrix[Sorting_Index[p]][Sorting_Index[q]] // Shuffle rows (and columns).  
    Wave /Z Waterfall_Colors
    if(WaveExists(Waterfall_Colors))
        Wave W_KMMembers // The pattern number that each signal most represents (the K-Means clustering result).  
        Waterfall_Colors=W_KMMembers[q] // Color the waterfall plot according to the clustering result.  
    endif
    KillWaves /Z M_KMClasses,W_KMMembers // Cleanup.  
End

Window Graph0() : Graph
    PauseUpdate; Silent 1       // building window...
    Display /W=(509.25,50,924,358.25) as "Raw Correlation Matrix"
    AppendImage/T Fake_Corr_Matrix
    ModifyImage Fake_Corr_Matrix ctab= {-1,*,RedWhiteBlue,0}
    ModifyGraph margin(left)=14,margin(bottom)=14,margin(top)=14,margin(right)=14
    ModifyGraph mirror=2
    ModifyGraph nticks=4
    ModifyGraph minor=1
    ModifyGraph fSize=9
    ModifyGraph standoff=0
    ModifyGraph tkLblRot(left)=90
    ModifyGraph btLen=3
    ModifyGraph tlOffset=-2
    SetAxis/A/R left
EndMacro

Window Graph1() : Graph
    PauseUpdate; Silent 1       // building window...
    Display /W=(2.25,386.75,438.75,743.75) as "Clustered Correlation Matrix"
    AppendImage/T Clustered_Matrix
    ModifyImage Clustered_Matrix ctab= {-1,1,RedWhiteBlue,0}
    ModifyGraph margin(left)=14,margin(bottom)=14,margin(top)=14,margin(right)=14
    ModifyGraph mirror=2
    ModifyGraph nticks=3
    ModifyGraph minor=1
    ModifyGraph fSize=9
    ModifyGraph standoff=0
    ModifyGraph tkLblRot(left)=90
    ModifyGraph btLen=3
    ModifyGraph tlOffset=-2
    SetAxis/A/R left
EndMacro

Window Graph2() : Graph
    PauseUpdate; Silent 1       // building window...
    NewWaterfall /W=(-0.75,47,510.75,362.75)Data as "Data"
    ModifyWaterfall angle=45, axlen= 0.6, hidden= 0
    ModifyGraph negRGB=(0,0,65535)
    ModifyGraph zColor(Data)={Waterfall_Colors,*,*,Rainbow}
EndMacro

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