Nonlinear Dimensionality Reduction With Missing Data Using Parametric Multiple Imputations.

Area of Science:

• Machine Learning
• Data Science
• Computational Statistics

Background:

• Dimensionality reduction (DR) is crucial for representing high-dimensional (HD) data in low-dimensional (LD) spaces.
• Neighbor embedding DR methods excel but struggle with ubiquitous incomplete datasets.
• Existing imputation methods are suboptimal for nonlinear DR, failing to minimize expected cost functions.

Purpose of the Study:

• To develop a general methodology for nonlinear DR that directly handles missing data.
• To enable the application of any DR scheme optimizing a criterion on incomplete datasets.
• To obtain an LD embedding that minimizes the expected cost function on incomplete data.

Main Methods:

• Fitting an HD extension of Gaussian mixture models to incomplete data to model feature dependencies.
• Employing multiple imputation paradigms with the fitted model.
• Obtaining a single LD embedding that minimizes the expected cost function.

Main Results:

• The proposed framework successfully integrates missing data handling into nonlinear DR.
• The method yields superior LD embeddings compared to alternative approaches on incomplete datasets.
• Demonstrated effectiveness across extensive experimental evaluations.

Conclusions:

• The developed methodology provides a robust solution for nonlinear DR with missing data.
• This approach overcomes limitations of existing methods, enabling accurate LD representation.
• The framework offers a significant advancement for machine learning applications with real-world incomplete data.