Model selection for Gaussian kernel PCA denoising.

Area of Science:

• Computational statistics
• Machine learning
• Data analysis

Background:

• Principal Component Analysis (PCA) is a dimensionality reduction technique.
• Kernel PCA (KPCA) extends PCA using the kernel trick for non-linear data.
• Selecting optimal parameters like kernel scale and model order in KPCA is challenging.

Purpose of the Study:

• To introduce Kernel Parallel Analysis (kPA) for automatic parameter selection in Gaussian KPCA.
• To enhance the parallel analysis method for simultaneous tuning of kernel scale and model order.
• To evaluate kPA's effectiveness in data denoising tasks.

Main Methods:

• Kernel Parallel Analysis (kPA) based on permutation testing of covariance.
• Augmentation of parallel analysis for Gaussian radial basis function kernel scale.
• Application to simulated data and the U.S. Postal handwritten digit dataset.

Main Results:

• kPA successfully automates kernel scale and model order selection for Gaussian KPCA.
• kPA demonstrates superior performance in denoising compared to other heuristics.
• Improved signal-to-noise ratio in denoised data using kPA.

Conclusions:

• kPA provides an effective and automated approach for parameter selection in KPCA.
• The proposed method enhances denoising capabilities for complex datasets.
• kPA offers a robust solution for optimizing Gaussian KPCA applications.