[Insight-users] User inputs Mean and Variance for K-means

[Karthik Krishnan]

Hi Eric,

A variant of K-means that allows you to specify a mean and variance 
could be accomplished by fitting a Gaussian Mixture Model to your data.

GMM's are a soft / probablistic alternative to k-means. As the name 
implies it fits a set of gaussians to your data. As with k-means, you 
would start with k initial means for the gaussians and k initial 
variances (actually covariances for ND data, to be general).  So you can 
see, it lets you plug a known mean and variance. Unlike k-means clusters 
can overlap (you can discretize them later by choosing a threshold). 
Also, unlike k-means its less affected by noise or outliers in your 
data, since samples far away from the mean are weighted by the gaussian...

In ITK, there are a couple of ways you can go about fitting a GMM to 
your data :

1. See Examples/Statistics/ExpectationMaximizationMixtureModelEstimator.cxx
    This uses the EM method to estimate GMM's that fit your data. You 
can specify an initial set of gaussian distributions. Its an iterative 
process. In the E-step you would find the weights from each gaussian for 
a MeasurementVector. And in the M-step you would use those weights to 
update the gaussian. So the gaussian would shrink/grow/shift to fit your 
data.

2. If you already have an initial classification, you could use the 
classes Code/Algorithms/ImageKmeansModelEstimator or 
Examples/Statistics/BayesianClassifer.cxx

HTH
-karthik




Eric John wrote:

> Hello all,
>  
> Is anyone familiar with a Kmeans or similiar method for classifying in 
> ITK that allows the user specify a known mean and variance for each 
> label in an image? Or how to modify an Itk example to do so. Thanks!
>  
> Eric
>
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