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Generalized Negative Binomial Processes and the Representation of Cluster Structures
The paper introduces the concept of a cluster structure to define a joint
distribution of the sample size and its exchangeable random partitions. The
cluster structure allows the probability distribution of the random partitions
of a subset of the sample to be dependent on the sample size, a feature not
presented in a partition structure. A generalized negative binomial process
count-mixture model is proposed to generate a cluster structure, where in the
prior the number of clusters is finite and Poisson distributed and the cluster
sizes follow a truncated negative binomial distribution. The number and sizes
of clusters can be controlled to exhibit distinct asymptotic behaviors. Unique
model properties are illustrated with example clustering results using a
generalized Polya urn sampling scheme. The paper provides new methods to
generate exchangeable random partitions and to control both the cluster-number
and cluster-size distributions.Comment: 30 pages, 8 figure
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