Missing data imputation through GTM as a mixture of t-distributions

Area of Science:

• Machine Learning
• Statistical Modeling
• Data Mining

Background:

• Generative Topographic Mapping (GTM) is a probabilistic model, an alternative to Self-Organizing Maps.
• GTM can be viewed as a constrained mixture model, typically using Gaussian distributions.
• Student t-distributions offer robustness against outliers in mixture models, making them an attractive alternative to Gaussians.

Purpose of the Study:

• Redefine GTM using Student t-distributions to create the t-GTM.
• Modify the Expectation-Maximization algorithm for missing data imputation within the t-GTM framework.
• Evaluate the t-GTM's performance in outlier detection and missing data imputation.

Main Methods:

• Developed the t-GTM by incorporating Student t-distributions into the GTM framework.
• Adapted the Expectation-Maximization algorithm for parameter estimation and missing data imputation.
• Conducted experiments to compare t-GTM with the standard Gaussian GTM.

Main Results:

• The t-GTM effectively detects outliers and minimizes their influence on parameter estimation.
• t-GTM demonstrates superior performance in imputing missing values compared to the Gaussian GTM.
• Experimental results validate the robustness and accuracy of the t-GTM.

Conclusions:

• The t-GTM offers a robust extension of Generative Topographic Mapping.
• This model provides improved capabilities for handling outliers and imputing missing data.
• The t-GTM represents a significant advancement in mixture modeling for data analysis.