Count data modeling and classification using finite mixtures of distributions.

Area of Science:

• Statistical modeling
• Machine learning
• Data mining

Background:

• Count data is prevalent in fields like computer vision and information retrieval.
• Existing generative models for count data clustering include multinomial, Dirichlet, and generalized Dirichlet mixtures.

Purpose of the Study:

• To propose a novel clustering approach for count data using a mixture model.
• To introduce the multinomial Beta-Liouville mixture model.
• To compare its performance against existing models.

Main Methods:

• Analysis and comparison of multinomial, multinomial Dirichlet, and multinomial generalized Dirichlet mixture models.
• Development of a novel mixture model combining Beta-Liouville and multinomial distributions.
• Optimization using deterministic annealing expectation-maximization and minimum description length.

Main Results:

• The proposed multinomial Beta-Liouville mixture model demonstrates high accuracy in count data clustering.
• The new model has fewer parameters than the multinomial generalized Dirichlet mixture.
• Empirical experiments in text, image texture, and shape modeling validate the model's effectiveness.

Conclusions:

• The multinomial Beta-Liouville mixture model is an accurate and flexible approach for count data clustering.
• This novel model offers advantages in terms of parameter efficiency and performance.
• The proposed method shows significant potential for applications in data mining and computer vision.