Supervised dimensionality reduction for big data.

Area of Science:

• Biomedical data science
• Machine learning
• Dimensionality reduction

Background:

• High-dimensional biomedical data (millions of features) are common.
• Small sample sizes relative to feature numbers necessitate dimensionality reduction for valid inferences.
• Existing methods lack interpretability, scalability, and statistical guarantees for high-dimensional data.

Purpose of the Study:

• To develop an interpretable, scalable supervised dimensionality reduction method for high-dimensional biomedical data.
• To improve data representations for subsequent classification tasks.
• To provide strong statistical theoretical guarantees for the proposed method.

Main Methods:

• Extension of principal component analysis (PCA) by incorporating class-conditional moment estimates.
• Introduction of Linear Optimal Low-rank Projection (LOLP) using class-conditional means.
• Validation using synthetic and real-world benchmark datasets, including brain imaging and genomics.

Main Results:

• LOLP and its generalizations significantly improve data representations for classification.
• The method demonstrates computational efficiency and scalability, handling datasets with over 150 million features.
• LOLP outperforms other scalable linear dimensionality reduction techniques in accuracy on large datasets.

Conclusions:

• LOLP offers an effective and efficient solution for dimensionality reduction in high-dimensional biomedical data.
• The method provides improved accuracy for subsequent classification tasks.
• It addresses the need for interpretable, scalable, and statistically sound methods in data-driven biomedical research.