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Parametric Methods III: Using Mixture of Parametric Distributions

  • Assuming data generated by a normal distribution could be sometimes overly simplified
  • Example (figure below): The objects between the two clusters cannot be captured as outliers since they are close to the estimated mean
  • To overcome this problem, assume the normal data is generated by two normal distributions. For any object o in the data set, the probability that o is generated by the mixture of the two distributions is given by 

\[ Pr(o|\Theta_{1}, \Theta_{2})= f_{\Theta_{1}}(o)+ f_{\Theta_{2}}(o)\]

       where fθ1 and fθ2 are the probability density functions of θ1 and θ2

  • Then use EM algorithm to learn the parameters μ1, σ1, μ2, σ2 from data
  • An object o is an outlier if it does not belong to any cluster

Speaker notes:

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