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Probabilistic Model-Based Clustering

  • Cluster analysis is to find hidden categories.
  • A hidden category (i.e., probabilistic cluster) is a distribution over the data space, which can be mathematically represented using a probability density function (or distribution function).
  • Ex. 2 categories for digital cameras sold
    • consumer line vs. professional line
    • density functions f1, f2 for C1, C2
    • obtained by probabilistic clustering
  • A mixture model assumes that a set of observed objects is a mixture of instances from multiple probabilistic clusters, and conceptually each observed object is generated independently
  • Our task : infer a set of k probabilistic clusters that is mostly likely to generate D using the above data generation process

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