On linear dimension reduction based on diagonalization of scatter matrices for bioinformatics downstream analyses.

Area of Science:

• Bioinformatics
• Computational Biology
• Statistical Learning

Background:

• Dimension reduction is crucial for high-dimensional data analysis.
• Classical methods like PCA, ICA, and SIR are often formulated using scatter matrices.
• Existing theoretical guarantees typically require sample size to exceed the number of variables, limiting applicability in bioinformatics.

Purpose of the Study:

• To investigate the applicability of dimension reduction tools for small-n-large-p datasets.
• To explore the use of scatter matrix functionals for identifying relevant subspaces.
• To assess the effectiveness of these methods in bioinformatics contexts.

Main Methods:

• Review of classical supervised and unsupervised dimension reduction techniques.
• Formulation of methods using scatter matrix functionals as measures of multivariate dispersion.
• Application and illustration using a prostate cancer microarray dataset.

Main Results:

• Dimension reduction tools can be adapted for small-n-large-p data.
• Scatter matrices highlight different data features and reveal structures when compared.
• The study successfully illustrates subspace identification on a real-world bioinformatics dataset.

Conclusions:

• Dimension reduction methods, particularly those based on scatter matrices, are valuable for analyzing high-dimensional biological data.
• These techniques can effectively identify relevant subspaces even when the sample size is small relative to the number of variables.
• The findings support the use of these methods in bioinformatics for uncovering biological insights.