Dimension selection for feature selection and dimension reduction with principal and independent component analysis

Area of Science:

• Data Science
• Statistical Analysis
• Machine Learning

Background:

• High-dimensional data presents challenges in feature extraction and dimension reduction.
• Principal Component Analysis (PCA) and Independent Component Analysis (ICA) are common dimensionality reduction techniques.
• Selecting the optimal lower dimension is crucial for effective analysis.

Discussion:

• This work proposes a novel dimension selection criterion based on bias-adjusted skewness and kurtosis.
• The method leverages the strengths of PCA for initial reduction and ICA for identifying non-Gaussian components.
• Performance is evaluated on real-world datasets and through comprehensive simulation studies.

Key Insights:

• A new, bias-adjusted criterion for optimal dimension selection is presented.
• The proposed method demonstrates superior performance for non-Gaussian data.
• The technique effectively balances data reduction with information preservation.

Outlook:

• Further validation on diverse, complex datasets is warranted.
• Potential applications in fields requiring robust feature extraction from high-dimensional data.
• Exploration of extensions to other statistical modeling techniques.