High-dimensional unsupervised selection and estimation of a finite generalized Dirichlet mixture model based on...

Area of Science:

• Statistics
• Machine Learning
• Data Mining

Background:

• Determining the number of clusters in high-dimensional data is challenging without prior knowledge.
• Finite mixture models are common for data clustering, but selecting the correct number of components is critical.
• The generalized Dirichlet distribution offers flexibility in modeling data distributions compared to the standard Dirichlet distribution.

Purpose of the Study:

• To apply the minimum message length (MML) principle for determining the optimal number of clusters in high-dimensional data.
• To utilize the generalized Dirichlet distribution for flexible mixture modeling of complex data structures.
• To validate the proposed MML-based approach against existing criteria using synthetic and real-world datasets.

Main Methods:

• Employing finite mixture models based on the generalized Dirichlet distribution to represent high-dimensional data.
• Applying the minimum message length (MML) principle to select the number of clusters that best describes the data.
• Comparing the MML criterion with other established selection criteria for mixture models.

Main Results:

• The minimum message length (MML) principle effectively determines the optimal number of clusters for mixture models.
• The generalized Dirichlet distribution provides a flexible framework for approximating diverse data distributions.
• Validation on synthetic and real data, including web page classification and texture summarization, demonstrates the method's efficacy.

Conclusions:

• The MML principle offers a robust method for unsupervised cluster number determination in mixture modeling.
• The generalized Dirichlet distribution enhances the applicability of mixture models to a wider range of data types.
• The proposed approach shows promise for practical applications in data classification and information retrieval.