Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA).

Area of Science:

• Statistics
• Machine Learning
• Data Analysis

Background:

• Sparse Principal Component Analysis (PCA) is crucial for high-dimensional data.
• Existing sparse PCA methods face computational challenges and parameter tuning issues.

Purpose of the Study:

• Introduce Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA), a novel sparse PCA technique.
• Evaluate EESPCA's performance against state-of-the-art methods in terms of speed, accuracy, and error.

Main Methods:

• EESPCA computes squared eigenvector loadings from matrix eigenvalues and sub-matrices.
• Two EESPCA versions are explored: fixed threshold and cross-validation threshold.
• Performance is benchmarked against established sparse PCA algorithms.

Main Results:

• Fixed threshold EESPCA offers an order-of-magnitude speed improvement.
• EESPCA accurately identifies true zero principal component loadings.
• The method maintains low out-of-sample reconstruction and PC estimation errors.

Conclusions:

• EESPCA is a computationally efficient and accurate sparse PCA technique.
• It is particularly relevant for high-dimensional data analysis and resampling methods.
• EESPCA provides a practical alternative to existing sparse PCA approaches.