A Model-Based Approach to Simultaneous Clustering and Dimensional Reduction of Ordinal Data

Area of Science:

• Statistics
• Machine Learning
• Data Mining

Background:

• Clustering literature for continuous data is extensive, but limited for categorical data.
• Noise variables can obscure clustering structures in categorical datasets.
• Existing methods often struggle with simultaneous clustering and dimensionality reduction for ordered categorical data.

Purpose of the Study:

• To propose a novel model for simultaneous clustering and dimensionality reduction of ordered categorical data.
• To develop a method that identifies discriminative dimensions while discarding noise dimensions.
• To address the limitations of existing clustering techniques for categorical data with noise.

Main Methods:

• Utilizes an underlying response variable approach, modeling observed variables as discretized latent continuous variables.
• Employs a Gaussian mixture model for latent variables.
• Introduces a novel EM-like algorithm maximizing a composite log-likelihood on low-dimensional margins to overcome estimation challenges.

Main Results:

• The proposed model effectively performs simultaneous clustering and dimensionality reduction on ordered categorical data.
• The method successfully detects and utilizes discriminative dimensions while mitigating the impact of noise variables.
• Applications on real and simulated data demonstrate the model's effectiveness and robustness.

Conclusions:

• The developed model offers a significant advancement in clustering ordered categorical data, particularly in the presence of noise.
• The approach provides a robust framework for dimensionality reduction and feature selection within clustering tasks.
• This work enhances the capability of analyzing complex categorical datasets by effectively handling noisy dimensions.